(a) Completed table

TR = Price × Units; MR = change in TR between successive units.

Working (examples):

• Unit 2: TR = 11 × 2 = 22; MR = 22 − 12 = 10
• Unit 7: TR = 6 × 7 = 42; MR = 42 − 42 = 0
• Unit 8: TR = 5 × 8 = 40; MR = 40 − 42 = −2

(b) Market structure

It is monopoly (or imperfect competition with a downward-sloping demand curve). The reason is that price (AR) falls as more units are sold — the firm must lower price to sell extra units — so AR slopes downward and MR lies below AR. Under perfect competition, price would stay constant and AR = MR.

(c) Curves

Plot units (1–8) on the X-axis and revenue in Rs. on the Y-axis.

• AR curve: plot the points (1,12), (2,11), (3,10), (4,9), (5,8), (6,7), (7,6), (8,5). Join them — a straight downward-sloping line.
• MR curve: plot (1,12), (2,10), (3,8), (4,6), (5,4), (6,2), (7,0), (8,−2). Join them — a straight line sloping downward more steeply than AR. It starts at the same point as AR (Rs. 12) and falls twice as fast, cutting the X-axis at unit 7.
• TR curve: plot (1,12), (2,22), (3,30), (4,36), (5,40), (6,42), (7,42), (8,40). Join them — an inverted-U (parabola) shape. TR rises while MR is positive, is maximum at unit 6–7 where MR = 0, and falls when MR becomes negative.

Key relation shown: TR rises when MR > 0, is maximum when MR = 0, and falls when MR < 0; MR lies below AR throughout.

Total profit = $TR - TC$

$= (7Q^2 - 8Q + 30) - (6Q^2 - 10Q + 20)$

$= Q^2 + 2Q + 10$

So, total profit is $Q^2 + 2Q + 10$.

Total profit = Total revenue − Total cost

$= 5{,}000 - 4{,}200 = \text{Rs. } 800$

So, total profit is Rs. 800.

(i) Completed table

Working:

• $TR = P \times Q$: $20\times1=20$, $20\times2=40$, $20\times3=60$, $20\times4=80$.
• $AR = TR/Q = 20$ for every unit.
• $MR = \Delta TR/\Delta Q$: $20-0=20$; $40-20=20$; $60-40=20$; $80-60=20$.

Since price is constant at Rs. 20, $AR = MR = P = 20$ throughout. This is the case of a perfectly competitive firm, which is a price taker.

(ii) Average and marginal revenue curves

• Plot units sold (1, 2, 3, 4) on the X-axis and revenue in Rs. on the Y-axis.
• Both AR and MR are equal to Rs. 20 at every unit, so both curves coincide as a horizontal straight line parallel to the X-axis at the height of Rs. 20.
• The line is perfectly elastic, showing that the firm can sell any quantity at the given price of Rs. 20 without affecting revenue per unit.

(Diagram: a horizontal line at Rs. 20 on the Y-axis, labelled "AR = MR", running parallel to the X-axis across all units.)

Profit = TR − TC

$\pi = (5Q^2 - 4Q + 10) - (4Q^2 - 6Q + 20) = Q^2 + 2Q - 10$

So the total profit is $\pi = Q^2 + 2Q - 10$.

Given: Quantity sold (Q) = 25 units, Price per unit (P) = Rs 30

Formula: $TR = P \times Q$

Solution: $TR = 30 \times 25 = \text{Rs } 750$

Total Revenue = Rs 750

Fixed Cost and Variable Cost

Fixed Cost (FC)

Fixed cost refers to the cost that does not change with the level of output. It remains the same even when output is zero, and it is incurred on fixed factors of production such as land, building, machinery and permanent staff. Since it cannot be avoided in the short run, it is also called supplementary cost or overhead cost.

Examples: rent of the factory building, insurance premium, salaries of permanent employees, interest on borrowed capital, depreciation of machinery, and property tax.

Variable Cost (VC)

Variable cost refers to the cost that changes directly with the level of output. It is zero when output is zero and rises as output increases. It is incurred on variable factors of production such as raw materials and casual labour. It is also called prime cost.

Examples: cost of raw materials, wages of casual labour, cost of fuel and power, packing and transport charges.

Three Differences between Fixed Cost and Variable Cost

Additional points (if required): Fixed cost is unavoidable in the short run, whereas variable cost can be avoided by stopping production; fixed cost per unit falls continuously as output rises, while variable cost per unit first falls and then rises.

Conclusion: In the short run, total cost is the sum of fixed cost and variable cost, i.e. $TC = FC + VC$. Fixed cost is independent of output while variable cost is directly related to output.

The functions are missing from the question, so the method is shown with the usual illustrative pair, demand $P = 50 - 2Q$ and cost $TC = 2Q^2 + 2Q + 10$. Substitute the actual functions in the same steps.

1. MR function

$TR = P \times Q = (50 - 2Q)Q = 50Q - 2Q^2$

$MR = \frac{d(TR)}{dQ} = 50 - 4Q$

2. MC function

$MC = \frac{d(TC)}{dQ} = 4Q + 2$

3. Profit-maximising output (MR = MC)

$50 - 4Q = 4Q + 2 \Rightarrow 8Q = 48 \Rightarrow Q = 6 \text{ units}$

4. Price

$P = 50 - 2(6) = \text{Rs } 38$

5. Second-order condition: slope of MR $= -4$ is less than slope of MC $= +4$, so profit is maximum at $Q = 6$.

6. Maximum profit

$TR = 38 \times 6 = 228,\quad TC = 2(36) + 12 + 10 = 94,\quad \pi = 228 - 94 = \text{Rs } 134$

The monopolist produces 6 units and charges Rs 38 per unit, earning a maximum profit of Rs 134.

(a) Completed table

$AR = TR/Q$ and $MR = TR_n - TR_{n-1}$ (for the first unit, $MR = TR_1 = 20$).

(b) Diagram

Take quantity on the X-axis and revenue (Rs) on the Y-axis. The TR and the AR/MR curves are usually drawn in two panels because TR is much larger.

• TR curve: plot (1,20), (2,36), (3,48), (4,56), (5,60) and join. It rises from the origin at a decreasing rate, because MR is positive but falling.
• AR curve: plot (1,20), (2,18), (3,16), (4,14), (5,12). It slopes downward and is the demand curve of the firm.
• MR curve: plot (1,20), (2,16), (3,12), (4,8), (5,4). It also slopes downward, falls faster than AR and lies below it.

Since AR falls as more is sold, the firm has price-making power (imperfect competition or monopoly), and $MR < AR$ after the first unit.

Short-run Equilibrium under Perfect Competition

Meaning

The short run is a period in which firms can change only variable factors (labour, raw material) but not fixed factors (plant, machinery), and the number of firms in the industry is fixed. A competitive firm may earn supernormal profit, normal profit or a loss in the short run.

Conditions of equilibrium

A firm is in equilibrium at the output where:

1. MR = MC (necessary condition), and
2. MC is rising, cutting MR from below (sufficient condition).

Under perfect competition the price is given to the firm by the industry, so $P = AR = MR$. The condition therefore becomes

$P = MC \quad \text{with MC rising}$

Explanation with diagram

In the diagram, the left panel shows the industry, where market demand $DD$ and supply $SS$ meet and fix the price $OP$. In the right panel the firm takes this price, so $AR = MR$ is a horizontal line at $OP$.

The MC curve cuts the MR line at point $E$, so the equilibrium output is $OQ$. At $E$ MC is rising and cuts MR from below, so both conditions hold. To the left of $OQ$, $MR > MC$ and extra output adds to profit. To the right, $MC > MR$ and extra output reduces profit. So profit is maximum at $OQ$.

Three possible situations

(i) Supernormal profit ($P > AC$): the AC curve lies below the price line at $OQ$. Profit $= (P - AC) \times OQ$, shown by the rectangle between the price line and the AC curve.

(ii) Normal profit ($P = AC$): the AC curve just touches the price line at $E$. The firm covers all costs including normal profit. This is the break-even point.

(iii) Loss ($P < AC$): the AC curve lies above the price line. If $P \geq AVC$, the firm continues production in the short run, because it covers all variable cost and part of fixed cost. If $P < AVC$, it shuts down.

Conclusion

In the short run a competitive firm is in equilibrium at $MR = MC$ with MC rising. It may earn supernormal profit, normal profit or loss, but it produces as long as price covers average variable cost. The industry is in equilibrium where $DD = SS$.

Rs 103

Marginal cost of the 8th unit = TC₈ − TC₇ = 727 − 624 = Rs 103.

a. Completed table

TFC is fixed at Rs. 20 at every level of output. TC = TFC + TVC.

Working (missing values):

• Output 0: TVC = 0 (no variable input used), so TC = 20 + 0 = 20.
• Output 1: TC = 20 + 20 = 40.
• Output 2: TVC = TC − TFC = 50 − 20 = 30.
• Output 3: TC = 20 + 45 = 65.
• Output 4: TVC = TC − TFC = 100 − 20 = 80.
• Output 5: TC = 20 + 145 = 165.

b. TVC and TC curves

Plot output on the X-axis and cost (Rs.) on the Y-axis.

• TVC curve: starts from the origin (0, 0) and rises upward to the right. It rises at a decreasing rate up to output 2 (Rs. 30), then at an increasing rate afterwards, giving it a reverse-S shape.
• TC curve: starts at Rs. 20 on the Y-axis (because TFC = Rs. 20 even at zero output) and rises upward to the right, exactly parallel to the TVC curve. The vertical distance between TC and TVC is constant at Rs. 20 at every output, since TC = TVC + TFC.

Key points to plot:

Thus the TC curve lies above the TVC curve throughout, and the vertical gap between them equals TFC (Rs. 20).

Given: $TC = 60 + 7Q^2$, $TR = 120Q - 5Q^2$

Equilibrium output ($MR = MC$)

$MR = \frac{d(TR)}{dQ} = 120 - 10Q$

$MC = \frac{d(TC)}{dQ} = 14Q$

$120 - 10Q = 14Q \Rightarrow 24Q = 120 \Rightarrow Q = 5$

Second-order condition: slope of MR $= -10$ is less than slope of MC $= 14$ (equivalently, $\pi = 120Q - 12Q^2 - 60$ has $\dfrac{d^2\pi}{dQ^2} = -24 < 0$), so profit is maximum.

Profit

$TR = 120(5) - 5(25) = 600 - 125 = 475$

$TC = 60 + 7(25) = 235$

$\pi = TR - TC = 475 - 235 = \text{Rs } 240$

Equilibrium output is 5 units and maximum profit is Rs 240.

Risk-Bearing Theory of Profit

Meaning: This theory was developed by F.B. Hawley. According to him, profit is the reward for the risk-bearing function of the entrepreneur. Every business involves risks — losses from fall in price, change in demand, bad debts, fire, theft, natural calamities, etc. The entrepreneur bears these risks, and the profit is the compensation he receives for bearing them. Hence, profit is also called the reward for uncertainty-bearing.

Explanation:

1. Risk is the source of profit: In a static economy where everything is certain, there would be no profit. Profit arises only because future conditions are uncertain. The entrepreneur who accepts this uncertainty earns profit.

2. Profit as reward for risk-bearing: The entrepreneur invests capital and organises production under conditions of uncertainty. If the venture succeeds, he gets profit; if it fails, he bears the loss. Thus profit is the price paid for the willingness to bear risk.

3. No risk, no profit: According to Hawley, the amount of profit is directly related to the degree of risk. The greater the risk involved in a business, the higher is the expected rate of profit. This is why risky industries (e.g., mining, oil exploration) earn higher profits than safe ones.

4. Functional and non-functional risks: Hawley distinguished between risks that can be insured (insurable risks) and those that cannot (non-insurable or uncertainty). Profit is the reward only for non-insurable risks, because insurable risks are covered by insurance and their cost is included in cost of production.

5. Profit varies with risk: Profit is not fixed like rent or wages. It is residual and uncertain — it may be positive, zero, or even negative. This uncertainty is precisely what makes profit a reward for risk-bearing.

Criticisms of the Risk-Bearing Theory

1. Profit is not only reward for risk: Risk-bearing alone cannot explain profit. Many people bear risks (e.g., shareholders, debenture holders, insurers) but do not earn profit. Profit also includes reward for management, innovation, and coordination.

2. Ignores other functions of entrepreneur: The theory gives too much importance to risk-bearing and neglects the entrepreneur's other functions such as organising, decision-making, and innovation.

3. Insurable risks objection: Hawley's distinction between insurable and non-insurable risks is not very clear. Many risks cannot be neatly classified, and even insurable risks affect profit indirectly.

4. Profit may arise without risk: In a monopoly or during a boom, an entrepreneur may earn huge profit without bearing much risk. Conversely, a highly risky venture may yield no profit at all. So profit and risk are not always proportional.

5. Uncertainty, not risk, is the real source: Modern economists like Knight argue that it is uncertainty (non-measurable risk), not risk in general, that gives rise to profit. Hawley failed to make this distinction sharply.

6. Static economy assumption unrealistic: The theory assumes a static economy where profit is zero, but in reality no economy is perfectly static. Hence the theory is based on an unrealistic assumption.

Conclusion: Despite criticisms, the risk-bearing theory is important because it rightly recognises that profit is closely linked with uncertainty. However, it is incomplete — profit is best explained as a combination of reward for risk-bearing, management, and innovation.

(a) Completed table

Working

• $TR = \text{Price} \times \text{Unit of goods}$
• $AR = \dfrac{TR}{\text{Unit of goods}} = \text{Price}$
• $MR = TR_n - TR_{n-1}$

So,

• For 1st unit: $TR = 25 \times 1 = 25$, $AR = 25$, $MR = 25$
• For 2nd unit: $TR = 20 \times 2 = 40$, $AR = 20$, $MR = 40 - 25 = 15$
• For 3rd unit: $TR = 15 \times 3 = 45$, $AR = 15$, $MR = 45 - 40 = 5$
• For 4th unit: $TR = 10 \times 4 = 40$, $AR = 10$, $MR = 40 - 45 = -5$

(b) Drawing AR and MR curves

Take units of goods on the X-axis and revenue in Rs. on the Y-axis.

Plot the following points for the AR curve:

$(1,25),\ (2,20),\ (3,15),\ (4,10)$

Join these points. The AR curve slopes downward from left to right. Since AR is equal to price, this is also the demand curve of the firm.

Plot the following points for the MR curve:

$(1,25),\ (2,15),\ (3,5),\ (4,-5)$

Join these points. The MR curve also slopes downward, but it lies below the AR curve after the first unit. It is steeper than the AR curve. It cuts the X-axis between the 3rd and 4th units, i.e. at 3.5 units. At the 4th unit, MR is negative while AR is still positive.

Thus, the completed table and the downward-sloping AR and MR curves show imperfect competition, where $MR < AR$ after the first unit.

Given: $TC = Q^2 + 8Q + 4$, $P = 20 - Q$

The firm faces a downward-sloping demand curve, so it is in equilibrium where $MR = MC$.

$TR = P \times Q = (20 - Q)Q = 20Q - Q^2$

$MR = \frac{d(TR)}{dQ} = 20 - 2Q$

$MC = \frac{d(TC)}{dQ} = 2Q + 8$

$20 - 2Q = 2Q + 8 \Rightarrow 4Q = 12 \Rightarrow Q = 3$

$P = 20 - 3 = \text{Rs } 17$

Second-order condition: slope of MR $= -2$ is less than slope of MC $= 2$, so profit is maximum.

Check: $TR = 17 \times 3 = 51$, $TC = 9 + 24 + 4 = 37$, profit $= \text{Rs } 14$.

Equilibrium output is 3 units and equilibrium price is Rs 17.

(a) Completed table

$TC = TFC + TVC$, $AC = TC/Q$, $MC = TC_n - TC_{n-1}$

(b) AC and MC curves

Take output on the X-axis and cost (Rs) on the Y-axis. Plot the AC and MC values against output and join the points smoothly.

• AC curve: falls from Rs 70 to a minimum of Rs 22 at 5 units, then rises (24, 27.14, 31.25). It is U-shaped.
• MC curve: falls from Rs 10 to a minimum of Rs 3 at 3 units, then rises steeply (11, 18, 34, 46, 60). It is also U-shaped.
• Relation: MC lies below AC while AC is falling, and above AC when AC is rising. MC cuts AC from below at the minimum point of AC (output 5, where AC = MC = Rs 22 approximately).

Equilibrium Output under Monopoly: MR-MC Approach

Meaning. A monopolist is the only seller, so it faces the whole downward-sloping market demand curve. Its AR (price) curve slopes downward and MR lies below AR. It maximises profit at the output where Marginal Revenue equals Marginal Cost.

Conditions of equilibrium

1. Necessary (first-order) condition: MR = MC.
2. Sufficient (second-order) condition: MC must cut MR from below, that is, slope of MC > slope of MR.

Why MR = MC gives maximum profit

• If MR > MC, the extra unit adds more to revenue than to cost, so profit rises as output increases.
• If MR < MC, the extra unit adds more to cost than to revenue, so profit falls and the firm should cut output.
• So profit rises until MR = MC and falls beyond it. The second condition ensures this point is a maximum.

Illustration (demand $AR = 11 - Q$, so MR falls by Rs 2 per unit)

MR = MC at 3 units, so equilibrium output is 3 units. The price is read from the AR (demand) curve at this output, which is Rs 8.

Diagram. Take output on the X-axis and revenue/cost on the Y-axis. Draw the downward-sloping AR and the steeper MR below it, and a U-shaped MC cutting MR from below at point $E$. Drop a perpendicular from $E$ to the X-axis to get output $OQ$. Extend it up to the AR curve to get the price $OP$.

Price and profit. Since MR < AR, at equilibrium Price > MC. If AR > AC at $OQ$, the monopolist earns supernormal profit equal to $(AR - AC) \times OQ$. Because the monopolist is a price-maker, its MC curve is not its supply curve.

Ricardian theory of rent was given by David Ricardo. According to him, rent is the payment made to the owner of land for the use of the original and indestructible powers of the soil. It arises because land differs in fertility and location, and it is a differential surplus.

Main points

• Rent arises because land is scarce and lands differ in fertility.
• Cultivation first begins on the best (grade A) land and, as population and demand for food rise, is extended to poorer lands (B, C) and intensively on the same land.
• The land that earns only enough to cover its cost of production and no surplus is the marginal land (no-rent land).
• Rent of any land = its produce − produce of the marginal land, using the same input.

Illustration (equal investment on each grade)

The price of the product is set by the cost on the marginal land, so superior lands earn a surplus above their cost, which is rent.

Conclusion: rent does not enter price. It is price-determined, not price-determining. It is higher on more fertile land.

Criticisms: rent also arises on marginal land because land has some use and scarcity; the "original and indestructible powers" of soil are unrealistic since fertility can change; it ignores the role of demand and treats land as having only one use.

(a) Total revenue $TR = P \times Q$, average revenue $AR = TR/Q$ and marginal revenue $MR = \Delta TR/\Delta Q$.

(b) To draw the curves, take quantity (units sold) on the X-axis and AR and MR (Rs.) on the Y-axis. Plot AR at the points (1, 35), (2, 30), (3, 25), (4, 20) and join them, giving a downward-sloping straight line (AR = price = demand curve). Plot MR at (1, 35), (2, 25), (3, 15), (4, 5) and join them, giving a steeper downward-sloping line that lies below AR. Label the curves AR and MR.

Here AR falls by Rs 5 per unit while MR falls by Rs 10 per unit, so the MR curve is twice as steep as AR and lies below it. This is the case when a firm must lower the price to sell more, as under monopoly.

Since price falls as output rises ($P = 200 - 8Q$), the firm faces a downward-sloping demand curve, so equilibrium is where $MR = MC$ and MC cuts MR from below.

$TR = P \cdot Q = 200Q - 8Q^2 \Rightarrow MR = \frac{dTR}{dQ} = 200 - 16Q$

$TC = 100 + 12Q^2 \Rightarrow MC = \frac{dTC}{dQ} = 24Q$

Setting $MR = MC$:

$200 - 16Q = 24Q \Rightarrow 40Q = 200 \Rightarrow Q = 5$

Price from the demand function:

$P = 200 - 8(5) = 160$

Second-order check: slope of MC (24) is greater than slope of MR (−16), so the condition holds.

Profit check: $TR = 160 \times 5 = 800$, $TC = 100 + 12(25) = 400$, so $\pi = Rs\ 400$.

Hence equilibrium output is 5 units and equilibrium price is Rs 160.

(a) $TC = TFC + TVC$, $AC = TC/Q$ and $MC = \Delta TC/\Delta Q$.

(b) Take output on the X-axis and cost (Rs.) on the Y-axis. Plot AC at the points for output 1 to 8 (60, 33, 23.33, 19, 17, 17.5, 20, 25) and join them with a smooth U-shaped curve. Plot MC (10, 6, 4, 6, 9, 20, 35, 60) and join with a smooth curve, which is also U-shaped but steeper.

Features to show: MC falls first, reaches its minimum at 3 units, and then rises sharply. AC falls up to 5 units (minimum Rs 17) and then rises. MC cuts the AC curve from below at its minimum point, between 5 and 6 units, where MC (about Rs 17) equals AC.

Rs. 50

$MR = \frac{\Delta TR}{\Delta Q} = \frac{750 - 700}{11 - 10} = \frac{50}{1} = \text{Rs. } 50$

Uncertainty Bearing Theory of Profit (also called the Risk Theory of Profit) was developed by Frank H. Knight in his book Risk, Uncertainty and Profit (1921). It explains profit as the reward earned by the entrepreneur for bearing non-insurable (true) uncertainty.

Main points of the theory:

1. Distinction between risk and uncertainty: Knight separates insurable risk (fire, theft, accident, death) from non-insurable uncertainty (changes in demand, price, technology, government policy, war). Insurable risks can be shifted to insurance companies through payment of premium, so they do not yield profit. Only non-insurable uncertainty remains with the entrepreneur and gives rise to profit.

2. Profit as reward for uncertainty bearing: The entrepreneur performs two functions — he bears uncertainty and he takes decisions under uncertain conditions. Since no one else is willing to bear this uncertainty, he must be compensated. This compensation is pure profit.

3. Profit is residual and residual income: After paying rent, wages, interest and the insurance premium, whatever surplus is left is profit. It may be positive, zero or even negative (loss), because the outcome of uncertain events cannot be foreseen.

4. Profit varies with the degree of uncertainty: The greater the uncertainty involved in a business, the higher the expected profit. That is why profits in new, dynamic and speculative industries are higher than in old, stable ones.

5. Dynamic economy is essential: Uncertainty arises only in a dynamic economy where tastes, techniques and resource supplies keep changing. In a static economy with perfect certainty, there would be no uncertainty and hence no profit.

6. Sources of uncertainty: Knight lists five main sources — (a) changes in consumer demand, (b) changes in production methods, (c) changes in factor prices, (d) changes in the supply of capital, and (e) changes in general economic and political conditions.

Four weaknesses of the theory:

1. Profit is not only the reward for uncertainty: Profit also arises from monopoly power, superior managerial ability, innovation and windfall gains. The theory ignores these sources and treats uncertainty as the sole cause of profit.

2. Uncertainty cannot be measured: Non-insurable uncertainty is subjective and unpredictable. Since its magnitude cannot be measured, it is difficult to establish a definite relationship between the degree of uncertainty and the amount of profit earned.

3. Ignores the role of other factors: The theory gives all importance to the entrepreneur and neglects the contribution of labour, capital and organisation in generating surplus. In reality, profit is a joint result of many factors.

4. Not applicable to all enterprises: In sole trading and partnership firms the owner bears uncertainty, but in joint stock companies ownership is separated from management. Here shareholders bear risk while salaried managers take decisions, so the theory fails to explain profit clearly.

5. Profit may arise even without uncertainty: A firm may earn profit due to favourable market conditions, government subsidy or patent rights, where uncertainty is negligible. Similarly, a firm may suffer loss even after bearing heavy uncertainty.

Conclusion: The theory rightly explains profit as the reward for bearing non-insurable uncertainty, but it is incomplete because it treats uncertainty as the only source of profit and ignores other determinants.

(a) Completed table

$AC = TC/Q$ and $MC = TC_n - TC_{n-1}$ (for the first unit, $MC = TC_1 = 8$).

Working: $AC_4 = 28/4 = 7$, $AC_5 = 45/5 = 9$ (matching the given values); $MC_3 = 18 - 14 = 4$; $MC_6 = 72 - 45 = 27$ (matching the given value). The table follows the TC series.

(b) AC and MC curves

Take output on the X-axis and cost (Rs) on the Y-axis.

• AC curve: plot (1,8), (2,7), (3,6), (4,7), (5,9), (6,12) and join. It falls to a minimum of Rs 6 at 3 units, then rises, giving a U shape.
• MC curve: plot (1,8), (2,6), (3,4), (4,10), (5,17), (6,27) and join. It falls to a minimum of Rs 4 at 3 units, then rises more steeply than AC.

Relation: MC is below AC and AC falls while output is up to 3 units. At 4 units MC (Rs 10) is above AC (Rs 7) and AC rises. So MC cuts AC from below at the minimum point of AC, between 3 and 4 units.

Monopoly: a single seller faces the whole market demand curve, so to sell more it must lower the price. Hence AR (= price) falls as output rises, and MR falls faster than AR and stays below it.

(a) Table of TR, AR and MR (price falls by Rs 1 for each extra unit)

$AR=\frac{TR}{Q},\qquad MR=\frac{\Delta TR}{\Delta Q}=TR_n-TR_{n-1}$

From the table:

• AR falls continuously as output rises.
• MR is less than AR at every level of output, and falls twice as fast as AR.
• TR rises while MR is positive, is maximum (Rs 30) when MR = 0, and falls when MR is negative.

(b) Curves of AR and MR (output $Q$ on the X-axis, revenue Rs on the Y-axis)

Plot the points (Q, AR): (1,10), (2,9), (3,8), (4,7), (5,6), (6,5), (7,4) and join them. This gives the AR curve (demand curve), a downward-sloping line.

Plot the points (Q, MR): (1,10), (2,8), (3,6), (4,4), (5,2), (6,0), (7,−2) and join them. This gives the MR curve, a steeper downward-sloping line lying below AR. It cuts the X-axis at $Q=6$, where TR is maximum.

Rs
10 |*
 9 | \*
 8 |  \ *
 7 |   \  *            AR (demand)
 6 |    \   *
 5 |     \    *
 0 +------\-----\----------- Q
-2 |       MR     below AR, cuts X-axis at Q = 6

Both curves slope downward, and MR lies below AR because to sell an extra unit the monopolist must also lower the price on all earlier units.

Price and Output Determination under Perfect Competition (MR–MC Approach)

1. Price Determination (4 marks)

Under perfect competition the industry (all firms together) determines price through the interaction of market demand and market supply, while each individual firm is a price taker — it must accept the price so determined.

Industry (market) equilibrium:

• Market demand curve slopes downward (law of demand).
• Market supply curve slopes upward (law of supply).
• The price is fixed where market demand = market supply (equilibrium point E), giving equilibrium price $P$ and equilibrium quantity $Q$.

Firm as price taker: Since a single firm's output is a tiny fraction of total market supply, it cannot influence price. Therefore:

• Price = Average Revenue = Marginal Revenue, i.e. $P = AR = MR$.
• The firm's demand curve (AR) is a horizontal straight line at the level of the market price.
• Because price is constant, each extra unit sells at the same price, so $MR$ is constant and equal to $P$.

$\therefore AR = MR = P \quad \text{(horizontal line)}$

---

2. Short-Run Equilibrium of the Firm — MR–MC Approach (4 marks)

Conditions of equilibrium

1. Necessary (first-order) condition: $MR = MC$
2. Sufficient (second-order) condition: $MC$ must be rising at the point of intersection (MC cuts MR from below).

Why these conditions?

• If $MR > MC$, each extra unit adds more to revenue than to cost → profit rises → firm expands output.
• If $MR < MC$, each extra unit adds more to cost than to revenue → profit falls → firm reduces output.
• So output settles only where $MR = MC$, and stability requires MC to be rising.

Diagram (MR–MC approach)

 Price/Cost
    │        MC
    │       ╱ ╲        AC
    │      ╱   ╲      ╱
  P ─┼─────E─────╲────╱──── MR = AR = P
    │    ╱ ╲      ╲  ╱
    │   ╱   ╲      ╲╱
    │  ╱     ╲
    └──┴─────┴──────────── Output
       O     Q

At point E, $MR = MC$ and MC is rising → $OQ$ is the equilibrium output and $OP$ the equilibrium price.

Three situations of short-run equilibrium

(a) Super-normal profit (abnormal profit): When $P > AC$ at equilibrium output. $\text{Profit} = (P - AC) \times Q > 0$ The firm earns more than normal profit; this attracts new firms in the long run.

(b) Normal profit (break-even): When $P = AC$ at equilibrium output. $\text{Profit} = (P - AC) \times Q = 0$ The firm earns only normal profit — the minimum needed to stay in business.

(c) Loss (sub-normal profit): When $P < AC$ at equilibrium output. $\text{Loss} = (AC - P) \times Q > 0$ The firm suffers a loss. It will still produce in the short run as long as $P \ge AVC$ (price covers average variable cost), because it can cover variable costs and part of fixed costs. If $P < AVC$, it shuts down.

Summary table

Conclusion: In the short run a competitive firm is in equilibrium where $MR = MC$ with MC rising, and it may earn super-normal profit, normal profit, or incur a loss depending on the position of its AC curve relative to the market price.