Price Leadership: Dominant Firm and Low-Cost Firm

(a) How the dominant firm and the low-cost firm achieve price leadership

Price leadership is a form of tacit (non-official) collusion in oligopoly in which one firm — the leader — sets the price for the industry and the remaining firms — the followers — accept that price and sell as much as they wish at it. The leader does not fix the followers' output; it only announces the price. Price leadership is of three types: dominant-firm leadership, low-cost-firm leadership and barometric leadership. The first two are explained below.

1. Dominant firm price leadership

Here one firm controls a very large share of the market (say 60–70 per cent) and a large number of small "fringe" firms share the rest. The dominant firm has a cost advantage (economies of scale, superior technology, better management) and acts as a price maker; the fringe firms are price takers. The price is determined as follows.

Step 1 — Fringe supply curve. Add the marginal cost curves (above minimum AVC) of all the small firms horizontally to get the fringe supply curve $S_f$. It slopes upward: the higher the price, the more the fringe firms supply.

Step 2 — Residual demand curve. The dominant firm faces not the whole market demand but only the demand left over after the fringe has sold its output. If $D_m$ is market demand and $S_f$ is fringe supply, then at every price

$Q_d = Q_m - Q_f \quad\Rightarrow\quad D_d = D_m - S_f$

This residual demand curve $D_d$ is flatter (more elastic) than the market demand curve, because at a high price the fringe supplies a lot and leaves little for the dominant firm. At the price where $S_f$ equals $D_m$, the residual demand becomes zero — this is the "competitive" ceiling price.

Step 3 — Profit maximisation by the leader. The dominant firm derives its marginal revenue curve $MR_d$ from $D_d$ and equates it with its own marginal cost:

$MR_d = MC_d$

This gives the leader's output $Q_d$ and the leadership price $P_L$.

Step 4 — Followers accept the price. At the announced price $P_L$ the fringe firms equate price to their marginal cost, $P_L = MC_f$, and supply $Q_f$. Total market output is $Q_d + Q_f = Q_m$.

The result is a price that lies below the monopoly price but above the competitive price. The dominant firm achieves leadership because (i) its large market share lets it act as a price setter, (ii) its lower costs give it a comfortable profit margin even at $P_L$, and (iii) the fringe firms are too small to influence price and find it profitable to simply follow — they can sell all they produce at $P_L$ without advertising or price competition.

2. Low-cost firm price leadership

Here the leader is not necessarily the largest firm but the most efficient one — its average and marginal costs are lower than those of the other firms in the industry. It achieves leadership in the following way.

• The low-cost firm selects the price that maximises its own profit, i.e. where $MR_L = MC_L$. Because its $MC_L$ is low, this price is lower than the price the high-cost rivals would have chosen.
• The rivals, having higher costs, find that at this price they still cover their costs and earn a normal or modest profit. Since they cannot produce profitably at a lower price, they accept the leader's price and sell their output as price takers.
• The leader thus earns a larger profit per unit and a larger total profit than any follower, because its cost per unit is smaller at the same selling price. This cost advantage is the source of its leadership power.
• The followers do not undercut the leader because a price war would drive price below their own costs while the leader could still survive — the threat is credible, so they follow.

Barometric leadership (for completeness) occurs when a firm with better forecasting ability acts as the industry's "barometer": it is the first to announce a price change that others copy because it correctly reads market conditions, not because it is dominant or low-cost.

Conditions necessary for successful price leadership: small number of firms, homogeneous product, inelastic demand, high entry barriers, a clear cost or size leader, stable market shares, absence of price undercutting, and no strict legal prohibition on such conduct.

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(b) Price level needed to drive out rivals, and critical arguments

Price level that removes rival firms

To eliminate rivals, the leader must set a price below the rivals' minimum average variable cost (their shutdown point) so that they incur losses and are forced to leave. In terms of the models:

• Dominant firm leadership: the leader cuts price to $P = \min AVC_f$ of the fringe firms (or even to its own $\min AVC_d$ if it wants to drive out all rivals). This is predatory pricing — pricing below cost to eliminate competition.
• Low-cost firm leadership: the efficient leader can set price just below the minimum long-run average cost of the high-cost firms ($P < \min LAC_f$). Since its own cost is lower, it still earns profit while rivals make losses. This is limit pricing when used to stop entry, and predatory pricing when used to drive out existing firms.

Is it easy to remove rivals? Critical arguments

Arguments that it is NOT easy:

1. Legal barriers. Predatory pricing is illegal under competition law — in Nepal, the Competition Promotion and Market Protection Act, 2063 (amended 2073) prohibits abuse of dominance and predatory pricing; similarly the Sherman Act and EU competition rules. A leader using such a price faces fines, penalties and damage claims. This makes the strategy legally risky and often impractical.

2. Cost of the price war (the "long purse" problem). The leader must sell its own large output at a loss-making price. The bigger the leader's market share, the greater its total loss. A dominant firm with 70 per cent share loses far more than a fringe firm with 5 per cent share, so the leader may run out of reserves before the small firms do. Deep pockets are essential and not always available.

3. Rivals may not exit. Fringe firms may have lower fixed costs, loyal customers, a niche segment, or family labour; they may survive on normal profit, merge with each other, or be subsidised. They may also cut costs and become efficient rather than leave.

4. Re-entry after the price is raised. Once rivals are driven out and the leader raises price to recoup losses, the high price and profits attract new entrants (and imports). Unless entry barriers are very high, the leader must repeat the costly exercise — an endless, unprofitable cycle. This is the core of the Chicago School critique: predatory pricing is irrational because recoupment is uncertain and it is cheaper to buy out a rival than to ruin it.

5. Credibility of the threat. Followers may treat a price cut as a bluff. If the leader cannot convince rivals that it will sustain losses long enough, they will not exit. In repeated games, cooperation (accepting leadership) yields higher long-run profit than a price war for both sides, so rivals rationally stay and follow.

6. Loss of market share and goodwill. A price war damages the leader's reputation, invites retaliation, may trigger a general price collapse in the industry, and can attract the attention of the competition authority. It may also reduce the leader's own market share if buyers switch to cheaper substitutes or imports.

7. Information problems. The leader may not know the exact costs or financial strength of rivals, so it cannot calculate the exact price needed to drive them out. Underestimating rivals' staying power leads to a prolonged, costly war.

8. In the low-cost firm case, accommodation is more profitable. The low-cost leader usually gains more by allowing the high-cost fringe to exist and follow its price (earning a "quiet life" profit) than by cutting price to $\min LAC_f$, which reduces its own profit on every unit sold. Hence price leadership, not price war, is the rational strategy.

Arguments that it CAN work (conditions):

• The leader has a substantial and durable cost advantage (superior technology, scale economies, cheap raw material).
• Entry barriers are high (patents, licences, capital requirements, brand loyalty), so re-entry is difficult.
• Rivals are financially weak, highly leveraged, or have high fixed costs.
• The product is homogeneous, demand is inelastic, and there are no close substitutes or imports.
• The legal environment is weak or the conduct cannot be proved as predatory.

Conclusion: Although a dominant or low-cost firm can theoretically set a price below rivals' minimum average variable cost and drive them out, it is not an easy task. It requires deep financial reserves, high entry barriers, weak rivals, credible threats and a permissive legal environment. In practice, legal restrictions, the cost of the price war, the risk of re-entry and the greater profitability of tacit price leadership make elimination of rivals difficult and often irrational. Hence firms generally prefer to lead and be followed rather than to destroy rivals.

(a) Types and conditions of economic efficiency

Economic efficiency means using scarce resources in the best possible way to maximise social welfare. Its main types and conditions are:

1. Allocative efficiency
   Resources are allocated to produce the goods and services most valued by society.
   Condition: (P = MC) for each good, or (MSB = MSC). In perfect competition, (P = MC); with externalities, social marginal benefit must equal social marginal cost.

2. Productive efficiency
   Goods are produced at the minimum possible cost.
   Condition: Firms use the least-cost combination of inputs and operate on the production possibility frontier. In the long run, (P = \text{minimum } AC).

3. Dynamic efficiency
   Efficiency over time through innovation, research and development, and technological progress.
   Condition: Adequate incentives, secure property rights, competition, and investment in innovation.

4. Pareto efficiency
   No one can be made better off without making someone else worse off.
   Conditions: Exchange efficiency ((MRS_A = MRS_B)), production efficiency ((MRTS_X = MRTS_Y)), and product-mix efficiency ((MRS = MRT)).

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(b) Equilibrium price, quantity and total surplus before tax

Given:

[ Q_d = 500 - 20P ]

[ Q_s = -100 + 10P ]

At equilibrium:

[ Q_d = Q_s ]

[ 500 - 20P = -100 + 10P ]

[ 600 = 30P ]

[ P = 20 \text{ Rs/kg} ]

Quantity:

[ Q = 500 - 20(20) = 100 ]

So,

[ Q = 100 \text{ thousand kg} ]

Inverse demand:

[ P = 25 - \frac{Q}{20} ]

Inverse supply:

[ P = 10 + \frac{Q}{10} ]

Consumer surplus:

[ CS = \frac{1}{2}(25 - 20)(100) ]

[ CS = 250 \text{ thousand Rs} = Rs,250{,}000 ]

Producer surplus:

[ PS = \frac{1}{2}(20 - 10)(100) ]

[ PS = 500 \text{ thousand Rs} = Rs,500{,}000 ]

Total surplus before tax:

[ TS = CS + PS = 250 + 500 = 750 \text{ thousand Rs} ]

[ TS = Rs,750{,}000 ]

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(c) Price, quantity and total surplus after tax

Tax imposed on sellers:

[ t = Rs,5 \text{ per kg} ]

Let:

[ P_b = \text{price buyers pay} ]

[ P_s = \text{price sellers receive} ]

Then:

[ P_b = P_s + 5 ]

Supply after tax:

[ Q_s = -100 + 10P_s ]

[ Q_s = -100 + 10(P_b - 5) ]

[ Q_s = -150 + 10P_b ]

Equate demand and supply after tax:

[ 500 - 20P_b = -150 + 10P_b ]

[ 650 = 30P_b ]

[ P_b = \frac{65}{3} = 21.67 \text{ Rs/kg} ]

Quantity:

[ Q = 500 - 20\left(\frac{65}{3}\right) ]

[ Q = \frac{200}{3} = 66.67 \text{ thousand kg} ]

Seller’s price:

[ P_s = P_b - 5 ]

[ P_s = \frac{65}{3} - 5 = \frac{50}{3} = 16.67 \text{ Rs/kg} ]

Consumer surplus after tax:

[ CS = \frac{1}{2}\left(25 - \frac{65}{3}\right)\left(\frac{200}{3}\right) ]

[ CS = \frac{1000}{9} = 111.11 \text{ thousand Rs} ]

[ CS = Rs,111{,}111.11 ]

Producer surplus after tax:

[ PS = \frac{1}{2}\left(\frac{50}{3} - 10\right)\left(\frac{200}{3}\right) ]

[ PS = \frac{2000}{9} = 222.22 \text{ thousand Rs} ]

[ PS = Rs,222{,}222.22 ]

Tax revenue:

[ \text{Tax revenue} = t \times Q ]

[ = 5 \times \frac{200}{3} = \frac{1000}{3} = 333.33 \text{ thousand Rs} ]

[ \text{Tax revenue} = Rs,333{,}333.33 ]

Total surplus after tax including tax revenue:

[ TS = CS + PS + \text{Tax revenue} ]

[ TS = \frac{1000}{9} + \frac{2000}{9} + \frac{1000}{3} ]

[ TS = \frac{2000}{3} = 666.67 \text{ thousand Rs} ]

[ TS = Rs,666{,}666.67 ]

If total surplus means only consumer and producer surplus, then:

[ CS + PS = \frac{1000}{9} + \frac{2000}{9} = \frac{1000}{3} ]

[ = 333.33 \text{ thousand Rs} = Rs,333{,}333.33 ]

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(d) Change in consumer and producer surpluses, tax revenue and deadweight loss

Change in consumer surplus:

[ \Delta CS = CS_{\text{after}} - CS_{\text{before}} ]

[ = \frac{1000}{9} - 250 ]

[ = -\frac{1250}{9} = -138.89 \text{ thousand Rs} ]

[ \Delta CS = -Rs,138{,}888.89 ]

Change in producer surplus:

[ \Delta PS = PS_{\text{after}} - PS_{\text{before}} ]

[ = \frac{2000}{9} - 500 ]

[ = -\frac{2500}{9} = -277.78 \text{ thousand Rs} ]

[ \Delta PS = -Rs,277{,}777.78 ]

Tax revenue generated by government:

[ = Rs,333{,}333.33 ]

Deadweight loss:

[ DWL = TS_{\text{before}} - (CS_{\text{after}} + PS_{\text{after}} + \text{Tax revenue}) ]

[ DWL = 750 - \left(\frac{1000}{9} + \frac{2000}{9} + \frac{1000}{3}\right) ]

[ DWL = 750 - \frac{2000}{3} ]

[ DWL = \frac{2250}{3} - \frac{2000}{3} = \frac{250}{3} ]

[ DWL = 83.33 \text{ thousand Rs} = Rs,83{,}333.33 ]

Alternatively,

[ DWL = \frac{1}{2} \times t \times \Delta Q ]

[ = \frac{1}{2} \times 5 \times \left(100 - \frac{200}{3}\right) ]

[ = \frac{1}{2} \times 5 \times \frac{100}{3} ]

[ = \frac{250}{3} = 83.33 \text{ thousand Rs} ]

[ DWL = Rs,83{,}333.33 ]

Factors that maximize utility of the managers (5 marks)

Managers, like consumers, seek to maximize their own utility — satisfaction, income, prestige, security and power — while running an organization. The main factors that determine and maximize a manager's utility are:

1. Monetary rewards (salary, bonus, perks). Higher pay, performance bonuses, profit-sharing, fringe benefits and stock options directly raise a manager's utility. Since income is a major source of satisfaction, managers prefer positions and decisions that increase their total compensation.

2. Non-monetary rewards and prestige. Status, recognition, titles, awards, respect from subordinates and peers, and a good reputation in the market add to utility. A manager values being seen as successful and influential.

3. Job security and stability. Security of employment, a steady career path, pension and retirement benefits reduce uncertainty. Since managers are generally risk-averse, greater security increases utility.

4. Power, authority and discretion. The ability to make decisions, control resources, allocate budgets and influence organizational outcomes gives managers a sense of control and self-actualization, which is a strong utility driver.

5. Working conditions and leisure. Pleasant office environment, reasonable working hours, autonomy, and a balance between work and personal life increase satisfaction. Managers value both income and leisure, so they trade off effort against free time.

6. Professional growth and achievement. Opportunities for promotion, training, challenging assignments and recognition of performance satisfy esteem and self-actualization needs (Maslow), thereby maximizing utility.

7. Social and organizational relationships. Good relations with colleagues, subordinates and superiors, team support and a cooperative culture contribute to job satisfaction and hence utility.

Conclusion: A manager's utility is maximized when the combination of monetary rewards, security, power, prestige, working conditions and growth opportunities yields the greatest overall satisfaction. Managers make decisions — such as expanding staff, budgets or perquisites — up to the point where the marginal utility of each additional factor equals its marginal cost.

Application of Opportunity Cost in Determining Economic Profit (5 marks)

1. Concept of opportunity cost. Opportunity cost is the value of the next best alternative forgone when a resource is put to one use. It includes both explicit costs (actual money payments) and implicit costs (the value of self-owned resources used in the business).

2. Economic profit vs. accounting profit. Accounting profit considers only explicit costs, whereas economic profit is calculated as:

$\text{Economic Profit} = \text{Total Revenue} - (\text{Explicit Costs} + \text{Implicit Costs})$

Since implicit costs are measured by opportunity cost, opportunity cost is the bridge between accounting profit and economic profit.

3. Why firms must apply it. A firm survives in the long run only if it earns at least a normal profit — that is, revenue sufficient to cover the opportunity cost of all resources. If economic profit is negative, the owner could earn more elsewhere, and the firm should exit the industry. Thus opportunity cost guides decisions on entry, exit, resource allocation and expansion.

4. Suitable examples.

• Owner's own labour: A person resigning a job paying Rs 80,000 per month to run a shop earns an accounting profit of Rs 1,00,000 per month. After deducting Rs 80,000 as the opportunity cost of his labour, economic profit is only Rs 20,000.
• Own building and capital: A firm using its own premises worth Rs 50 lakh (which could earn Rs 3 lakh rent) and its own funds of Rs 20 lakh (which could earn Rs 2 lakh interest) must treat Rs 5 lakh as implicit cost. Ignoring it overstates profit.
• Choice between products: A farmer with one ropani of land choosing maize over wheat forgoes the wheat income; that forgone income is the opportunity cost and must be charged while judging which crop is truly more profitable.
• Machinery use: A machine that can be rented out for Rs 1 lakh a year but is used in production must have that Rs 1 lakh counted as cost.

Conclusion. Opportunity cost makes profit measurement realistic by including forgone alternatives. It tells firms whether they are earning a true surplus over their next best option, and hence is central to efficient resource use and long-run business decisions.

Factors Causing Government Failure

Government failure occurs when government intervention in the economy fails to improve efficiency and instead creates inefficiency or worsens resource allocation. The major factors are:

1. Imperfect Information Government planners cannot accurately know consumer preferences, costs, or the true value of public goods. Unlike markets where prices reveal information, the government often relies on estimates. This leads to wrong decisions — for example, overproducing a public good that people do not value or underproducing one they do. Justification: without reliable price signals, resource allocation is based on guesswork, causing inefficiency.

2. Bureaucracy and Administrative Inefficiency Government projects pass through many layers of officials, causing delays, red tape, and high administrative costs. The cost of delivering a service often exceeds its benefit. Justification: slow and rigid procedures mean resources are consumed in the process itself rather than in producing the intended output.

3. Lack of Incentives and Cost Consciousness Government officials do not face profit-and-loss signals. Since they spend taxpayers' money, there is little pressure to cut costs or improve quality. Justification: absence of competition and market discipline makes public enterprises inefficient and prone to waste.

4. Rent-Seeking and Corruption Interest groups and officials use the political process to obtain favours, licences, and subsidies (rents) rather than to create wealth. Corruption diverts public funds. Justification: resources spent on lobbying and bribes are socially wasteful and distort allocation away from productive use.

5. Regulatory Capture Regulatory agencies set up to control industries are often influenced or "captured" by the very firms they are supposed to regulate. Justification: instead of protecting consumers, regulation ends up protecting producer interests, defeating its purpose.

6. Political Self-Interest and Short-Termism Politicians may choose policies that win votes rather than those that are economically efficient. Justification: decisions driven by election cycles ignore long-run welfare, leading to populist but inefficient spending.

7. Unintended Consequences Well-intentioned policies may produce harmful side effects — for example, price controls causing shortages or black markets. Justification: when incentives are not properly considered, intervention creates new problems instead of solving the old ones.

Conclusion: These factors — imperfect information, bureaucratic inefficiency, weak incentives, rent-seeking, regulatory capture, political self-interest, and unintended effects — together explain why government intervention often fails to achieve allocative efficiency.

Given: $Q_X = 1000 - 2P_X + 4Y + 3A - 2P_Y$ $P_X=4,\quad Y=1500,\quad A=4000,\quad P_Y=5$

First compute quantity demanded: $Q_X = 1000 - 2(4) + 4(1500) + 3(4000) - 2(5)$ $Q_X = 1000 - 8 + 6000 + 12000 - 10 = 18982$

Elasticity formulas and computations

1. Price elasticity of demand, (e_{P_X})

$$e_{P_X}=\frac{\partial Q_X}{\partial P_X}\cdot \frac{P_X}{Q_X} = -2 \times \frac{4}{18982} = -0.000421$$

2. Income elasticity of demand, (e_Y)

$$e_Y=\frac{\partial Q_X}{\partial Y}\cdot \frac{Y}{Q_X} = 4 \times \frac{1500}{18982} = 0.3161$$

3. Advertising elasticity of demand, (e_A)

$$e_A=\frac{\partial Q_X}{\partial A}\cdot \frac{A}{Q_X} = 3 \times \frac{4000}{18982} = 0.6322$$

4. Cross-price elasticity of demand, (e_{XY})

$$e_{XY}=\frac{\partial Q_X}{\partial P_Y}\cdot \frac{P_Y}{Q_X} = -2 \times \frac{5}{18982} = -0.000527$$

Summary table

Interpretation

• (e_{P_X}=-0.000421): Demand for good X is highly price inelastic. A 1% increase in the price of X reduces quantity demanded by only about 0.000421%. Since (|e_{P_X}|<1), the firm can raise price and increase total revenue.

• (e_Y=0.3161): Income elasticity is positive but less than 1. Good X is a normal good, and more specifically a necessity-type good. A 1% increase in per capita disposable income increases demand for X by about 0.316%.

• (e_A=0.6322): Advertising elasticity is positive and less than 1. Advertising increases demand for X, but the response is inelastic. A 1% increase in advertising expenditure raises demand by about 0.632%.

• (e_{XY}=-0.000527): Cross-price elasticity is negative, so goods X and Y are complements. A 1% increase in the price of Y decreases demand for X by about 0.000527%. The magnitude is very small, so the complementary relationship is weak.

Given:
[ C=aQ^b,\quad \log a=4,\quad b=-0.4 ] Taking (\log) as base 10, [ a=10^4=10000 ] So, [ C(Q)=10000Q^{-0.4} ]

Computation of learning rates

The learning rate is the ratio of cost at doubled cumulative output to cost at original output: [ \text{Learning rate}= \frac{C(2Q)}{C(Q)}=2^b ] Here, [ b=-0.4 ] Therefore, [ \text{Learning rate}=2^{-0.4}=\frac{1}{2^{0.4}}=0.757858\approx 75.79% ]

So, when cumulative output doubles, cost becomes approximately (75.79%) of the previous cost. The cost reduction is: [ 100%-75.79%=24.21% ]

The learning rate is the same for both intervals because in each case cumulative output doubles.

For verification: [ C(100)=10000(100)^{-0.4}=1584.89 ] [ C(200)=10000(200)^{-0.4}=1201.12 ] [ C(400)=10000(400)^{-0.4}=910.28 ] [ \frac{C(200)}{C(100)}=\frac{1201.12}{1584.89}=0.7579 ] [ \frac{C(400)}{C(200)}=\frac{910.28}{1201.12}=0.7579 ]

Implications of learning curve in managerial decisions

1. Cost forecasting: Managers can estimate future unit costs as cumulative output increases.
2. Pricing decisions: Lower costs due to learning allow competitive pricing and penetration pricing strategies.
3. Production planning: Output levels can be planned to achieve targeted cost reductions.
4. Budgeting and standard setting: Cost standards can be set by considering expected learning effects.
5. Make-or-buy decisions: Internal learning-adjusted costs can be compared with supplier prices.
6. Capacity and resource planning: Future labor, material, and overhead requirements can be better anticipated.
7. Performance evaluation: Actual cost reductions can be compared with the learning curve benchmark.
8. Strategic decisions: Learning curve helps in gaining market share, improving competitive advantage, negotiating contracts, and investing in training and process improvement.

Answer (5 marks)

Managerial economics is the application of economic theory and decision-science tools to business problems. Firms use it not only for internal decisions (pricing, output, cost control) but also to read, interpret and respond to the economic environment in which they operate. The economic environment consists of the forces outside the firm — demand conditions, costs of inputs, competition, government policy, technology, and the macroeconomy — that shape its opportunities and threats. Firms assess these issues in the following ways:

1. Demand analysis and forecasting. Firms use demand theory (elasticity of demand, demand estimation, regression and forecasting techniques) to measure how sensitive their sales are to price, income of consumers, prices of substitutes and complements, and advertising. This helps them judge whether the economic environment is expanding or shrinking their market, and how a recession or a rise in consumer income will affect sales.

2. Cost and production analysis. Using production functions, cost concepts (fixed vs variable, explicit vs implicit, opportunity cost) and break-even analysis, firms assess how changes in wage rates, raw material prices, interest rates and technology affect their cost structure. This tells them whether they can remain competitive when input prices rise.

3. Market structure and competitive environment. By identifying whether the industry is perfectly competitive, monopolistic, oligopolistic or a pure monopoly, firms assess the degree of competition, the pricing power they enjoy, the threat from new entrants and rivals, and the appropriate competitive strategy (price war, product differentiation, non-price competition).

4. Pricing and profit policy. Cost-plus, marginal cost, discriminating and penetration pricing rules derived from managerial economics let firms set prices that protect profit margins even when the environment changes — for example, during inflation or a price war.

5. Government policy and regulation. Firms analyse the impact of fiscal policy (taxes, subsidies), monetary policy (interest rates, credit availability), trade policy (tariffs, quotas), and regulations (minimum wage, pollution control, competition law) on their costs, prices and investment plans, and adjust their decisions accordingly.

6. Macroeconomic and business-cycle assessment. Using national income, inflation, unemployment and balance-of-payments data, firms forecast booms and recessions and plan capacity, inventory, hiring and capital investment to match the cycle.

7. Risk, uncertainty and investment appraisal. Tools such as risk analysis, decision trees, capital budgeting (NPV, IRR) and cost-benefit analysis help firms evaluate uncertain environmental conditions before committing funds.

8. Input sourcing and pricing of factors. Marginal productivity theory and factor-market analysis guide decisions on how much labour and capital to employ and what wages or rents to pay when factor markets change.

Conclusion. Thus, managerial economics supplies the analytical framework — demand and cost estimation, market-structure analysis, forecasting, and policy evaluation — through which a firm scans its economic environment, predicts the effects of external changes on its costs, sales and profits, and frames pricing, production, investment and competitive strategies to survive and grow.

Given

Production function:
$Q = 100\sqrt{KL}$

• Rate of interest, (r = \text{Rs }40)
• Wage rate, (w = \text{Rs }50)
• Price of output, (P = \text{Rs }4)

Marginal products:

$MP_L = \frac{\partial Q}{\partial L} = 50\sqrt{\frac{K}{L}}$

$MP_K = \frac{\partial Q}{\partial K} = 50\sqrt{\frac{L}{K}}$

Marginal rate of technical substitution:

$MRTS_{LK} = \frac{MP_L}{MP_K} = \frac{K}{L}$

For least-cost combination:

$\frac{MP_L}{MP_K} = \frac{w}{r}$

$\frac{K}{L} = \frac{50}{40} = 1.25$

$\therefore K = 1.25L$

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a) Optimal labour, capital, profit and maximum output when total cost outlay = Rs 4,000

Total cost:

$C = wL + rK = 50L + 40K = 4000$

Substitute (K = 1.25L):

$50L + 40(1.25L) = 4000$

$50L + 50L = 4000$

$100L = 4000$

$L = 40$

$K = 1.25 \times 40 = 50$

Maximum output:

$Q = 100\sqrt{50 \times 40} = 100\sqrt{2000}$

$Q = 100 \times 44.721 = 4472.14 \text{ units}$

Total revenue:

$TR = P \times Q = 4 \times 4472.14 = \text{Rs }17888.54$

Total cost:

$TC = \text{Rs }4000$

Profit:

$\pi = TR - TC = 17888.54 - 4000 = \text{Rs }13888.54$

Answer:
Labour (= 40) units, capital (= 50) units, maximum output (= 4472.14) units, profit (= \text{Rs }13888.54).

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b) Optimal labour, capital, profit and minimum cost when output (Q = 4472) units

Using the least-cost condition:

$K = 1.25L$

Given:

$Q = 100\sqrt{KL} = 4472$

Substitute (K = 1.25L):

$4472 = 100\sqrt{1.25L^2}$

$4472 = 100L\sqrt{1.25}$

$4472 = 111.803L$

$L = \frac{4472}{111.803} = 39.9988 \approx 40$

$K = 1.25 \times 39.9988 = 49.9985 \approx 50$

Minimum cost:

$C = 50L + 40K$

$C = 50(39.9988) + 40(49.9985)$

$C = 1999.94 + 1999.94 = \text{Rs }3999.88$

Total revenue:

$TR = 4 \times 4472 = \text{Rs }17888$

Profit:

$\pi = 17888 - 3999.88 = \text{Rs }13888.12$

Answer:
Labour (\approx 40) units, capital (\approx 50) units, minimum cost (\approx \text{Rs }3999.88), profit (\approx \text{Rs }13888.12).

Note: If (Q = 4472) is treated as the rounded value of (100\sqrt{2000} = 4472.14), then the answer is exactly the same as in part (a): (L=40), (K=50), (C=\text{Rs }4000), profit (=\text{Rs }13888.54).

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c) Business implications of the law of diminishing marginal rate of technical substitution

The law of diminishing MRTS states that as a firm substitutes more and more of one input for another while keeping output constant, the amount of the replaced input that can be given up for one additional unit of the substituting input goes on falling. For the given production function,

$MRTS_{LK} = \frac{K}{L}$

As labour increases along an isoquant, capital decreases, so (MRTS_{LK}) falls. This means labour and capital are not perfect substitutes.

Business implications:

1. Limited factor substitution: A biscuit factory cannot replace all machines with workers. After a point, adding more workers without machines adds little output.
2. Optimal input mix: The firm should choose labour and capital so that
   $\frac{MP_L}{MP_K} = \frac{w}{r}$
   Here, (w/r = 50/40 = 1.25), so the optimal capital-labour ratio is (K/L = 1.25). Thus the firm uses a relatively capital-intensive technique.
3. Response to factor price changes: If wages rise relative to interest, the firm substitutes capital for labour, i.e. it moves toward automation. If interest rises relative to wages, it substitutes labour for capital.
4. Cost control: Overstaffing or over-automation both raise cost. A balanced combination of labour and capital is necessary for minimum cost.
5. Production planning: Diminishing MRTS makes isoquants convex to the origin, ensuring a unique least-cost input combination. This helps the firm decide its scale of employment and investment in machinery.

Demand Forecasting: Meaning and Importance

Demand forecasting is the process of estimating the future demand for a firm's product or service over a specified time period. It is the foundation of production, marketing, inventory, and financial planning decisions.

Why Firms Forecast Demand

1. Production planning — Forecasts determine how much to produce, when to produce, and what capacity (plant, machinery, manpower) is required. Without them, a firm either overproduces (waste, inventory cost) or underproduces (lost sales).

2. Inventory and material management — Accurate forecasts fix the level of raw materials, work-in-progress, and finished goods, reducing carrying cost and stock-out risk.

3. Sales and marketing planning — Sales targets, territory allocation, advertising budgets, and sales-force size all rest on expected demand.

4. Financial planning — Sales forecasts drive the cash budget, profit projection, capital expenditure plan, and working capital requirement. Lenders and investors also judge the firm on the basis of its demand estimates.

5. Manpower planning — Recruitment, training, and shift scheduling depend on the volume of work expected.

6. New product and market decisions — Whether to launch a new brand, enter a new territory, or diversify depends on estimated demand.

7. Pricing and promotion decisions — The price level, discount structure, and promotional effort are set according to the elasticity and size of demand.

8. Reducing business risk — Forecasting converts uncertainty into a measurable range, allowing the firm to prepare contingency plans and avoid sudden shocks.

9. Scheduling and capacity utilisation — Smooth, continuous operation at optimum capacity is possible only when demand is anticipated in advance.

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Appropriate Forecasting Method in Each Situation

(i) Issue of a New Brand — Survey Method (Consumer Survey / Test Marketing)

When a firm launches a new brand, no historical sales data exist, so time-series and trend methods are useless. The firm must go directly to the consumer.

• Consumer survey method — prospective buyers are interviewed about their buying intention, brand preference, and price expectation. This gives a first-hand estimate of the potential market.
• Test marketing — the product is launched in a small representative market and actual sales are observed, then projected to the whole market. This is the most reliable method for a new brand because it records real buying behaviour, not stated intention.
• Sales-force opinion / expert opinion (Delphi) may supplement the above.

Justification: Since past data are absent and consumer taste is unknown, only methods that gather primary information from consumers or a trial market can give a dependable figure. Hence the survey/test-marketing method is most appropriate.

(ii) Adoption of Advanced Technology — Expert Opinion Method (Delphi Technique)

When a firm adopts advanced technology, the demand pattern changes because of new features, new price points, and new uses of the product. The change is structural, not a continuation of the past.

• Delphi method — a panel of experts (engineers, technologists, market analysts) is consulted in successive rounds until a consensus forecast emerges.
• Sales-force composite method — salespeople who know the field and the new technology's appeal can estimate demand region-wise.
• Market simulation / input–output analysis may be used where the technology affects many industries.

Justification: Time-series methods assume the future repeats the past; under a technology shift this assumption fails. Only judgement-based methods that capture expert knowledge of the new technology can forecast reliably. Hence the expert opinion (Delphi) method is most appropriate.

(iii) Long-Term Business Plan — Trend Projection / Econometric (Regression) Method

A long-term business plan (5–15 years) needs a stable, macro-level estimate of demand, not a short-run figure.

• Trend projection (least squares / time-series trend) — fits a trend line to past sales and extends it into the future. Simple, cheap, and suitable for steady, established products.
• Econometric / regression method — relates demand to determinants such as national income, population, price index, and investment. This is superior for long-range planning because it explains why demand changes.
• Delphi method may be used for very long horizons where data are weak.

Justification: Over a long period, cyclical and random fluctuations average out, leaving the underlying trend and the effect of major economic variables. Trend and econometric methods capture exactly these, so they are most appropriate for long-term business planning.

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Conclusion

Thus the choice of forecasting method is not universal — it depends on the availability of data, the time horizon, and the nature of the change the firm is undertaking.

Answer (5 marks)

Advertising and pricing as strategic games

Firms in an oligopoly are mutually interdependent: each firm's profit depends not only on its own price or advertising decision but also on the decisions of rival firms. Such situations are modelled as games, and the Prisoner's Dilemma explains why firms often end up advertising heavily or cutting prices even though all firms would be better off if they restrained themselves.

The advertising game

Consider two firms, A and B, deciding whether to advertise. The payoff matrix (profits in Rs million) is:

• If B advertises, A earns 40 by advertising against 20 by not advertising → A advertises.
• If B does not advertise, A earns 70 by advertising against 60 by not advertising → A still advertises.

Advertising is therefore a dominant strategy for A, and by symmetry for B. The Nash equilibrium is (Advertise, Advertise) with profits of Rs 40 million each. Yet both would have earned Rs 60 million each at (No advertising, No advertising). The equilibrium is Pareto-inefficient — this is the Prisoner's Dilemma. Advertising is largely self-cancelling: it shifts demand between firms without expanding the market much, so advertising expenditure rises while joint profit falls.

The pricing game

The same logic explains price wars. With prices of Rs 100 (high) and Rs 80 (low):

Each firm gains by undercutting the rival whatever the rival does, so the dominant-strategy equilibrium is (Low price, Low price) earning Rs 35 million each, although both would earn Rs 50 million at the high price. This is why cartels and price-fixing agreements are unstable: each member has an incentive to cheat by slightly undercutting, and the agreement collapses back to the competitive outcome.

How firms actually follow these strategies

1. Dominant strategy advertising — firms advertise because not advertising risks losing market share, so advertising becomes a defensive necessity rather than a profit-maximising choice.
2. Price matching and most-favoured-customer clauses — by promising to match any lower price, a firm removes the rival's gain from undercutting, converting the game toward the cooperative (high-price) outcome.
3. Product differentiation and non-price competition — firms compete through branding, quality, warranties and service instead of price, softening the price war.
4. Tacit collusion and price leadership — firms follow a dominant firm's price or use focal-point pricing (e.g., Rs 99) to sustain high prices without explicit agreement.
5. Repeated game and reputation — since the game is played repeatedly, the threat of retaliation (a price war next period) sustains cooperation, as in tit-for-tat strategies.
6. Cartels and legal restraints — formal agreements raise joint profit but are illegal in most countries and inherently unstable due to the cheating incentive.

Conclusion

The Prisoner's Dilemma shows that individually rational advertising and price-cutting decisions lead to a collectively inferior outcome. Firms therefore try to escape the dilemma through differentiation, price matching, tacit collusion and reputation effects, though the incentive to cheat keeps the equilibrium fragile.

Concept of antitrust policy (2)

Antitrust (competition) policy is the set of laws and regulatory measures through which the government prevents monopoly, restrains collusion and unfair trade practices, and keeps markets competitive. It rests on three ideas:

1. Concentrated market power lets firms raise prices, restrict output and exploit consumers.
2. Competition improves allocative efficiency, quality and innovation.
3. The state must act as referee, protecting competition rather than individual competitors.

Approaches to the working of antitrust policy (6)

(a) Structural approach. Targets market structure (number of firms, concentration ratio, market share). Based on the Structure-Conduct-Performance paradigm: a highly concentrated market is presumed to lead to poor conduct, so mergers that create excessive concentration are blocked and dominant firms may be broken up, whatever their conduct. Criticism: large size may reflect efficiency, not abuse.

(b) Conduct (behavioural) approach. Targets behaviour, not size. Size is lawful; abuse of size is not. Two legal tests are used here:

• Per se rule: some acts are illegal automatically, e.g. price fixing, cartels, bid rigging, market sharing.
• Rule of reason: other practices (exclusive dealing, tying, resale price maintenance, predatory pricing) are judged by their actual effect on competition and consumers.

(c) Performance approach. Judges firms by outcomes: prices, profits, output, efficiency and consumer welfare. Intervention is justified only when these show harm (persistent excess profit, restricted output, deadweight loss).

(d) Preventive / regulatory approach. Acts before harm occurs through merger notification and approval, licensing, and price or tariff regulation of natural monopolies (electricity, telecom, petroleum).

(e) Promotional (advocacy) approach. The competition authority educates businesses and consumers, issues guidelines, studies markets and advises government against policies that restrict competition.

(f) Enforcement approach. Investigation, hearing, decision and appeal, with remedies such as fines, cease-and-desist orders, divestiture and compensation.

Major antitrust provisions adopted in Nepal (7)

Nepal's framework rests mainly on the Competition Promotion and Market Protection Act, 2063 (2007), supported by the Consumer Protection Act, 2075 (2018) and sector regulators (Nepal Telecommunications Authority, Electricity Regulatory Commission, SEBON, Nepal Rastra Bank, Insurance Authority).

1. Ban on anti-competitive agreements. Agreements among firms to fix prices, limit output or supply, share markets or customers, or rig bids are prohibited.
2. Ban on abuse of dominant position. A firm in a dominant position may not impose unfair or discriminatory prices or conditions, limit production to the prejudice of consumers, or drive out rivals.
3. Control of monopoly and restrictive trade practices. Creating or maintaining a monopoly through exclusive dealing, refusal to supply, tie-in sales or predatory pricing is prohibited.
4. Merger and acquisition control. Combinations that would substantially lessen competition may be examined and restricted.
5. Unfair trade practices and consumer protection. Hoarding, black-marketing, artificial shortage, adulteration, false labelling, misleading advertisement, overcharging above the marked price and short weights are punishable.
6. Institutions. A statutory Board (the Competition Promotion and Market Protection Board) formulates policy and decides cases, with the Department of Commerce, Supplies and Consumer Protection and its offices doing investigation and market monitoring; consumer protection councils and district-level bodies handle consumer complaints.
7. Penalties and remedies. Fines, orders to stop the practice, compensation to affected parties, and confiscation or other action in serious cases, with a right of appeal to the court.
8. Market regulation tools. Power to fix prices of essential goods in specified situations, stock and licensing controls, quality standards (Nepal Bureau of Standards and Metrology) and the right of consumers to information.
9. Sector regulation and exemptions. Natural-monopoly sectors are regulated by their own regulators, and some activities (e.g. public utilities, certain small or cooperative enterprises) are treated specially.

Assessment. The legal framework exists, but enforcement is weakened by limited staff and resources, political and syndicate influence (e.g. transport and cement), a small market and low public awareness. Greater autonomy for the regulator, stronger penalties and more advocacy are needed.

Managerial Economics is the application of economic theory and analytical tools to business decision-making. It studies how a manager uses microeconomic concepts — demand, cost, production, pricing, profit — along with quantitative methods to solve practical problems of a firm and achieve its objectives such as profit maximisation, sales maximisation, and long-run growth. In short, it is economics applied to management decisions.

Characteristics:

1. Microeconomic in nature — It deals mainly with the study of individual units: a single firm, a single consumer, a single product, a single market. Macroeconomic factors are considered only as they affect the firm.

2. Normative (prescriptive) in approach — Unlike positive economics, which explains "what is," managerial economics is normative; it tells the manager "what ought to be done" to attain the firm's goals.

3. Uses both theory and tools — It blends economic concepts (elasticity, cost curves, market structures) with quantitative techniques (linear programming, regression, break-even analysis, capital budgeting) to reach decisions.

4. Pragmatic and decision-oriented — It is not concerned with abstract theorising but with solving real business problems — how much to produce, what price to charge, how to allocate scarce resources.

5. Uses macroeconomics too — Although micro-based, it considers the macroeconomic environment — national income, inflation, taxation, government policy — since these influence business conditions.

6. Multi-disciplinary — It draws on economics, statistics, mathematics, accounting, and management theory, making it an applied, inter-disciplinary subject.

7. Normative goal-oriented — Its central aim is to help the firm achieve its objectives, chiefly profit maximisation, by choosing the best among alternative courses of action.

8. Art and science combined — It is a science because it uses systematic theory and tools, and an art because its successful application depends on the manager's judgement and experience.

Moral hazard is a situation in insurance (and in any principal–agent relationship) where one party, after entering into a contract or transaction, changes their behaviour to the disadvantage of the other party because the cost of the risk is now borne by the other party. The party who is protected against loss takes less care than they would have taken in the absence of the protection. It arises because of asymmetric information — the insurer (or principal) cannot perfectly observe or monitor the actions of the insured (or agent) after the contract is signed.

Key features:

• It occurs after the contract is made (unlike adverse selection, which occurs before).
• The insured's actions become less careful because they no longer bear the full cost of a loss.
• It leads to inefficiency — more claims and higher losses than would occur with full care, which raises premiums for everyone.

Examples:

1. Vehicle insurance: A person who buys comprehensive car insurance may drive more recklessly or park carelessly, knowing that the insurer will pay for any damage. Without insurance, they would drive more cautiously to avoid bearing the repair cost themselves.
2. Health insurance: An insured person may smoke, drink, or skip exercise and regular check-ups, knowing that medical bills will be covered by the insurer. This increases the insurer's claim cost.
3. Fire insurance on a building: The owner may neglect fire safety measures (faulty wiring, no extinguishers) because the loss from fire will be compensated by the insurance company.
4. Principal–agent (business) context: A manager (agent) may shirk work or take excessive risks because the shareholders (principal) bear the consequences, while the manager enjoys the benefits of any success.

Measures to control moral hazard:

• Deductibles / excess clauses: The insured bears a part of the loss, so they remain careful.
• Co-insurance: The insurer pays only a fixed percentage of the loss, sharing risk with the insured.
• No-claim bonus: Premium discounts for claim-free years encourage careful behaviour.
• Monitoring and inspections: Periodic checks of the insured property or health.
• Exclusions and policy conditions: Certain risky acts are excluded from coverage.

Thus, moral hazard is a post-contract information problem in which the insured's reduced care imposes extra costs on the insurer, and it is controlled mainly through deductibles, co-insurance, and incentive schemes.

Why firms examine their performance using economic profit

Economic profit is total revenue minus all costs — both explicit (accounting) costs and implicit (opportunity) costs. It differs from accounting profit, which deducts only explicit costs. Firms examine their performance using economic profit for the following reasons:

1. It measures true profitability. Accounting profit can look healthy while the firm is actually destroying wealth. Economic profit shows whether the firm earns more than the return its resources could get in their next-best use. A firm with accounting profit of Rs 5,00,000 but an implicit cost (owner's forgone salary and forgone interest on own capital) of Rs 7,00,000 has an economic loss of Rs 2,00,000 — it would be better off closing and deploying its resources elsewhere.

2. It guides resource allocation and exit/entry decisions.

• Economic profit > 0 (supernormal profit): the firm is using resources better than the market alternative, so it should expand, and new firms are attracted into the industry.
• Economic profit = 0 (normal profit): the firm is covering all opportunity costs and is indifferent between staying and leaving; this is the long-run equilibrium in perfect competition.
• Economic profit < 0: the firm should contract or exit, and resources should move to higher-valued uses.

3. It measures managerial performance correctly. Managers are judged on value creation. Economic profit (or its refined form, EVA = operating profit after tax − cost of capital employed) tells whether management has generated a return above the cost of the capital it uses. A division earning 12% on capital when the firm's cost of capital is 15% is destroying value even though it reports a profit.

4. It supports investment, pricing and strategy decisions. Only projects with positive net present value — i.e. positive economic profit — add value. Pricing below full economic cost (including the cost of capital) may win sales but erode firm value.

Examples:

• Owner-run retail shop: The owner invests Rs 20,00,000 of savings and works full time. Accounting profit Rs 4,00,000; forgone interest at 10% = Rs 2,00,000 and forgone salary elsewhere = Rs 3,00,000. Economic profit = 4,00,000 − 5,00,000 = −Rs 1,00,000. The shop is not worth continuing as run.
• Perfectly competitive farmer: In the long run price equals minimum average total cost, so economic profit is zero. Farmers still stay because normal profit covers their land, labour and capital in their next-best use.
• Monopolist / innovative firm: A firm with a patent earns positive economic profit; this signals other firms to enter (or imitate after patent expiry), driving profit down toward normal in the long run.
• Corporate division: A division with capital employed Rs 1 crore, operating profit Rs 18,00,000 and cost of capital 15% (Rs 15,00,000) has EVA of Rs 3,00,000 — genuine value creation.

Conclusion: Economic profit is the better performance yardstick because it captures opportunity cost, signals whether to enter, expand or exit, and aligns managerial decisions with the creation of long-run firm value.

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price:

$E_p = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$

Firms use this concept in the following ways:

(i) Price discrimination

Price discrimination means charging different prices to different buyers for the same product. A firm can profitably discriminate only if the buyers' sub-markets have different price elasticities of demand and can be kept separate (no resale between markets).

• The firm charges a higher price in the market with inelastic demand (few substitutes, strong need) and a lower price in the market with elastic demand (many substitutes, price-sensitive buyers).
• The logic follows the marginal revenue–price relationship:

$MR = P\left(1 - \frac{1}{|E_p|}\right)$

Profit is maximised where $MR = MC$ in each sub-market. Since $MC$ is the same, the market with lower elasticity gets a higher price and the market with higher elasticity gets a lower price. This increases total revenue and profit compared to a single uniform price.

• Example: A cinema charges full price to adults (inelastic demand) and a concessional rate to students (elastic demand); airlines charge different fares to business and leisure travellers; doctors charge rich and poor patients differently.

(2) Pricing of joint products

Joint products are two or more products produced together from the same raw material and process (for example, petrol, diesel and kerosene from crude oil; meat and hide from cattle). The cost of the joint process cannot be traced separately to each product, so price is set on the basis of each product's own demand elasticity.

• The product with inelastic demand (for example, petrol) is priced high, because buyers will buy it even at a higher price.
• The product with elastic demand (for example, kerosene or a by-product facing substitutes) is priced low, so that the quantity produced can be sold off and total revenue from the joint output is maximised.
• Since output is technically tied (one cannot be produced without the other), the firm uses elasticity to decide the price mix so that the combined revenue covers the joint cost and yields profit. If a by-product has highly elastic demand, it may even be priced at marginal cost or sold at a nominal price to clear stock.

Conclusion: Elasticity guides the firm in segmenting markets for price discrimination and in setting different prices for joint products so that total revenue and profit are maximised.

Given:
(Q = 98L - 3L^2), (MR = \text{Rs }20), (w = \text{Rs }40), (TFC = \text{Rs }12000)

Marginal product of labour: [ MP_L = \frac{dQ}{dL}=98-6L ]

Marginal revenue product of labour: [ MRP_L = MR \times MP_L = 20(98-6L)=1960-120L ]

Profit is maximized where: [ MRP_L = w ]

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a. Optimal employment, output and profit

Set (MRP_L = w): [ 1960-120L=40 ] [ 120L=1920 ] [ L=16 ]

Output: [ Q=98(16)-3(16)^2 ] [ Q=1568-768=800 ]

Total revenue: [ TR=MR \times Q=20 \times 800=\text{Rs }16000 ]

Total variable cost: [ TVC=wL=40 \times 16=\text{Rs }640 ]

Total cost: [ TC=TVC+TFC=640+12000=\text{Rs }12640 ]

Profit: [ \pi=TR-TC=16000-12640=\text{Rs }3360 ]

Answer:
Optimal labour (L=16), output (Q=800) units, profit (=\text{Rs }3360).

Note: The production function itself reaches its maximum at (L=\frac{98}{6}=16.33), where (Q=800.33). But the profit-maximizing employment is (L=16), giving output (800).

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b. When wage rate increases to Rs 160

Set (MRP_L = w): [ 1960-120L=160 ] [ 120L=1800 ] [ L=15 ]

Output: [ Q=98(15)-3(15)^2 ] [ Q=1470-675=795 ]

Total revenue: [ TR=20 \times 795=\text{Rs }15900 ]

Total variable cost: [ TVC=160 \times 15=\text{Rs }2400 ]

Total cost: [ TC=2400+12000=\text{Rs }14400 ]

Profit: [ \pi=15900-14400=\text{Rs }1500 ]

Effect:

• Employment falls from (16) to (15) units of labour.
• Output falls from (800) to (795) units, i.e. by (5) units.
• Profit falls from (\text{Rs }3360) to (\text{Rs }1500), i.e. by (\text{Rs }1860).

Demand: $P = 420 - 10(Q_1+Q_2)$. With equal market shares, $Q_1 = Q_2 = Q$, so each firm faces

$P = 420 - 20Q$

Low-cost firm (price leader). $TC_1 = 20Q_1$, so $MC_1 = 20$.

$TR = 420Q - 20Q^2 \Rightarrow MR = 420 - 40Q$

Setting $MR = MC$:

$420 - 40Q = 20 \Rightarrow Q_1 = 10$

$P = 420 - 20(10) = \text{Rs } 220$

$\pi_1 = 220(10) - 20(10) = 2200 - 200 = \text{Rs } 2{,}000$

Is this acceptable to the high-cost firm? $TC_2 = 60Q_2$, so $MC_2 = 60$.

• If it follows the leader's price of Rs 220, it sells $Q_2 = 10$ and earns $\pi_2 = 220(10) - 60(10) = \text{Rs } 1{,}600$.
• If it set its own profit-maximising price: $420 - 40Q = 60 \Rightarrow Q_2 = 9$, $P = 420 - 180 = \text{Rs } 240$, and $\pi_2 = 240(9) - 60(9) = 2160 - 540 = \text{Rs } 1{,}620$.

Since Rs 1,620 > Rs 1,600, the high-cost firm would prefer the higher price of Rs 240. The leader's price of Rs 220 is therefore not acceptable to the high-cost firm, so price leadership at this price is unstable; it would press for a higher price or break away.