Microeconomics: demand, supply and market equilibrium; elasticity of demand and supply; consumer behaviour

The demand and supply functions are missing from the question as printed, so the equilibrium price cannot be determined. To find it, set
[ Q_d(P)=Q_s(P) ] and solve for (P). For example, if (Q_d=100-2P) and (Q_s=20+2P), then
[ 100-2P=20+2P \Rightarrow 80=4P \Rightarrow P=20. ] But without the actual functions, there is no unique equilibrium price.

Law of Demand

The law of demand states that, other things remaining constant (ceteris paribus), there is an inverse relationship between the price of a commodity and its quantity demanded. In other words, when the price of a good rises, its quantity demanded falls, and when the price falls, the quantity demanded rises.

Statement

According to Prof. Alfred Marshall, "The amount demanded increases with a fall in price and diminishes with a rise in price, other things being equal."

Schedule and Curve

When these price–quantity combinations are plotted on a graph, with price on the vertical axis and quantity demanded on the horizontal axis, the resulting curve slopes downward from left to right. This downward-sloping curve is called the demand curve, and its negative slope is the graphical expression of the law of demand.

Assumptions

1. Income of the consumer remains constant.
2. Prices of related goods (substitutes and complements) remain constant.
3. Tastes and preferences of the consumer remain unchanged.
4. No expectation of future price changes.
5. The good is a normal good, not a prestige or Giffen good.

Reasons for the Law

1. Law of diminishing marginal utility: As a consumer buys more units of a good, the additional satisfaction from each extra unit falls, so he is willing to pay a lower price for more units.
2. Income effect: When the price of a good falls, the consumer's real income rises and he can buy more of it.
3. Substitution effect: When the price of a good falls, it becomes cheaper relative to other goods, so consumers substitute it for other goods.
4. New buyers: A fall in price brings new consumers into the market who could not afford the good earlier.
5. Multiple uses: A good with several uses is put to less important uses only when its price falls.

Exceptions

1. Giffen goods: For inferior goods of great importance, quantity demanded may fall when price falls.
2. Prestige goods: Demand for diamonds and costly jewellery may rise with price because of their snob value.
3. Expectation of further price change: If buyers expect prices to rise further, they may buy more even at a high price.
4. Ignorance: Consumers may buy more of a high-priced good believing it to be of better quality.

Thus, the law of demand expresses the normal inverse price–quantity relationship, subject to the assumptions stated above.

a. Elasticity of supply when price increases from Rs. 5 to Rs. 15

Given:

• Initial price, $P_1 = Rs.\ 5$
• Initial quantity supplied, $Q_1 = 1$ Kg.
• Final price, $P_2 = Rs.\ 15$
• Final quantity supplied, $Q_2 = 3$ Kg.

Formula:

Calculation:

So, the elasticity of supply is 1, i.e. supply is unitary elastic.

b. Elasticity of supply when price decreases from Rs. 15 to Rs. 10

Given:

• Initial price, $P_1 = Rs.\ 15$
• Initial quantity supplied, $Q_1 = 3$ Kg.
• Final price, $P_2 = Rs.\ 10$
• Final quantity supplied, $Q_2 = 2$ Kg.

Formula:

Calculation:

So, the elasticity of supply is 1, i.e. supply is again unitary elastic.

Conclusion:
In both cases, the elasticity of supply is $E_s = 1$. This is because the supply curve passes through the origin, so supply is unitary elastic throughout.

a. Completed table

Marginal utility (MU) is the addition to total utility from consuming one more unit: $MU_n = TU_n - TU_{n-1}$

b. Total and marginal utility curves

Plot units (1–8) on the X-axis. On the Y-axis, plot TU and MU.

• TU curve: rises from 5 at unit 1, keeps rising (9, 12, 14, 15) but with a falling slope, becomes flat between units 5 and 6 (TU = 15, the saturation point), then slopes downward to 14 and 12.
• MU curve: starts at 5, falls steadily (4, 3, 2, 1), touches the X-axis at unit 6 (MU = 0), and turns negative thereafter (−1, −2).

c. Relationship between TU and MU

1. TU is the sum of MU: TU at any unit equals the sum of marginal utilities up to that unit. For example, at 3 units, TU = 5 + 4 + 3 = 12.
2. MU is the slope of the TU curve: MU at a point equals the change in TU per extra unit, i.e. $MU = \Delta TU / \Delta Q$.
3. When MU is positive, TU rises: From units 1 to 5, MU is positive (5 to 1), so TU increases (5 to 15).
4. When MU is zero, TU is maximum: At unit 6, MU = 0 and TU is at its maximum (15). This is the point of satiety.
5. When MU is negative, TU falls: From units 7 to 8, MU is negative (−1, −2), so TU declines (14, 12).
6. MU falls faster than TU: Because of the law of diminishing marginal utility, MU declines from the very first additional unit, while TU rises at a decreasing rate until it peaks.

(a) Completed table

Average product (AP) $= \dfrac{TP}{L}$ and Marginal product (MP) $= TP_n - TP_{n-1}$

(b) Three stages of production

[Diagram: on the X-axis take units of labour (1–8); on the Y-axis take TP, AP and MP in Kg. Plot TP as a curve rising at an increasing rate up to labour 3 (point of inflexion at L = 3), rising at a diminishing rate from 3 to 6, and falling after 6. Plot AP and MP as curves; MP lies above AP up to L = 4, cuts AP at its maximum at L = 4, and falls below AP thereafter; MP becomes zero at L = 6 and negative after that.]

Stage I – Increasing returns (from origin to L = 4, where AP is maximum): TP increases at an increasing rate up to L = 3 and then at a diminishing rate; MP rises first and then falls but remains greater than AP; AP rises throughout. This happens because the fixed factor (land) is abundant relative to labour, so each extra worker adds more to output than the previous one. It ends where AP is maximum and MP = AP.

Stage II – Diminishing returns (from L = 4 to L = 6, where MP = 0): TP increases at a diminishing rate and reaches its maximum at L = 6; both AP and MP fall, but MP remains positive and less than AP. The fixed factor now becomes scarce relative to labour, so the addition to output from each extra worker keeps falling. It ends where MP = 0 and TP is maximum.

Stage III – Negative returns (after L = 6): TP starts falling, AP continues to fall and MP becomes negative. Too many workers crowd the fixed land, obstruct one another's work and reduce total output. Hence MP is negative.

A rational producer operates in Stage II, because in Stage I there is still scope to raise output by adding labour, and in Stage III extra labour actually reduces total output.

A shift in the demand curve means that the whole demand curve moves to the right or left because of a change in factors other than the price of the good. At every price, the quantity demanded becomes more or less than before. This is called an increase or decrease in demand, unlike a movement along the curve, which is caused only by a change in the good's own price.

Explanation

• Rightward shift (increase in demand): From $D_0$ to $D_1$, more is demanded at each price. Causes: rise in consumers' income (for normal goods), a change in tastes in favour of the good, a rise in the price of a substitute, a fall in the price of a complement, an increase in population, or an expectation of higher future prices.
• Leftward shift (decrease in demand): From $D_0$ to $D_2$, less is demanded at each price. Causes are the opposite: a fall in income, unfavourable tastes, a fall in the price of a substitute, a rise in the price of a complement, or an expectation of lower future prices.

Diagram description: With price on the $Y$-axis and quantity on the $X$-axis, draw the original curve $D_0$ sloping downward. A parallel curve $D_1$ to its right shows an increase in demand, and a parallel curve $D_2$ to its left shows a decrease in demand.

Four determinants of supply are:

1. Price of the good: a higher price encourages producers to supply more.
2. Cost of production (price of inputs): a rise in the cost of raw materials, labour or capital reduces supply.
3. State of technology: better technology lowers cost and raises supply.
4. Government policy (taxes and subsidies): taxes reduce supply while subsidies increase it.

(Other determinants are the prices of related goods, the number of sellers and the goals of producers.)

Price elasticity of demand measures the degree of responsiveness of the quantity demanded of a good to a change in its price. It is the ratio of the percentage change in quantity demanded to the percentage change in price: $E_d = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}$

The law of diminishing marginal utility states that, other things remaining the same, as a consumer consumes more units of a commodity, the marginal utility obtained from each additional unit goes on decreasing.

At equilibrium, $Q_d = Q_s$: $200 - 15P = 50 + 10P$ $150 = 25P \Rightarrow P = 6$ The equilibrium price is Rs 6 (equilibrium quantity $= 50 + 10 \times 6 = 110$ units).

Marginal utility is the change in total utility from consuming one more unit: $MU_n = TU_n - TU_{n-1}$

Relationship between TU and MU

1. While MU is positive (units 1 to 4), TU rises, but at a decreasing rate because MU is falling.
2. When MU is zero (5th unit), TU is at its maximum (27). This is the point of satiety.
3. When MU becomes negative (6th unit), TU starts to fall.
4. TU is the sum of all MUs: $TU = \sum MU$. For example, $12 + 8 + 5 + 2 = 27$.

This is the law of diminishing marginal utility: MU falls as consumption increases, so the MU curve slopes downward, while the TU curve rises, peaks where $MU = 0$, and then falls.

Computation

$AP = \dfrac{TP}{L}$ and $MP = TP_n - TP_{n-1}$

Graph (description)

Draw labour on the X-axis and TP on one panel, AP and MP on another panel below it. TP rises at an increasing rate up to 3 workers, then at a decreasing rate, reaches its maximum (90) at 5 to 6 workers, and then falls. MP rises to a peak (25) at 3 workers, then falls, cuts the X-axis at 6 workers and becomes negative. AP rises to its peak (20) at 3 to 4 workers, and then falls. MP cuts AP at its maximum point. The three stages are marked by vertical lines: at the maximum of AP (4 workers) and at $MP = 0$ (6 workers).

The three stages (Law of Variable Proportions)

Stage I: Increasing returns (0 to 4 workers)

• This stage runs from the origin to the point where AP is maximum.
• The fixed factor (land) is under-used, so adding labour allows better division of labour and specialisation. MP and AP rise (MP rises to 25 at 3 workers).
• MP is above AP while AP is rising. TP rises rapidly.
• A rational producer will not stop here, since the fixed factor is not fully used.

Stage II: Diminishing returns (4 to 6 workers)

• It runs from the maximum AP to the point where $MP = 0$.
• MP and AP both fall, but MP stays positive and below AP. TP continues to increase at a decreasing rate, reaching its maximum of 90 when MP is zero.
• This is the stage where the producer operates. Land and labour are used in their best proportion, and the optimum output is chosen here.

Stage III: Negative returns (beyond 6 workers)

• MP is negative ($-6$, $-12$), so TP falls (84, 72) and AP keeps falling.
• Overcrowding of labour on the fixed land makes workers obstruct one another.
• No rational producer will operate here, as reducing labour would raise output.

Conclusion: The law of variable proportions states that when a variable input is added to a fixed input, TP first rises more than proportionately, then less than proportionately, and finally falls. A rational producer operates only in Stage II.

At equilibrium, $Q_d = Q_s$: $100 - 5P = 20 + 3P$ $80 = 8P \Rightarrow P = 10$ The equilibrium price is Rs 10 (equilibrium quantity $= 20 + 3 \times 10 = 50$ units).

Average product (AP) is the output produced per unit of the variable input. It is total product divided by the number of units of the variable input: $AP = \frac{TP}{L}$

The law of substitution (law of equi-marginal utility) says that a consumer gets maximum satisfaction when he spends his income so that the marginal utility per rupee is equal across all goods:

$\frac{MU_x}{P_x}=\frac{MU_y}{P_y}$

It does not hold perfectly in practice. Its main limitations or exceptions are:

1. Ignorance: Consumers may not know the utility of goods, or the prices and substitutes available, so they cannot compare marginal utilities.
2. Irrationality and habit: Habits, customs, fashion and impulse buying lead consumers to ignore marginal utility calculations.
3. Indivisible goods: Goods such as a car, a house or a television cannot be bought in small units, so exact equality of marginal utility per rupee cannot be reached.
4. Utility cannot be measured exactly: The law assumes utility can be measured in numbers, which is difficult in real life.
5. Changing conditions: Changes in prices, income, tastes or fashion disturb the equilibrium before it is reached.
6. Necessities and goods without substitutes: Goods like medicine have no real substitutes, so the consumer cannot shift spending from one to another.
7. Limited income and large price differences: A very small income or very unequal prices may force a consumer to buy goods in a fixed pattern.

Despite these limitations, the law is a useful guide to rational spending by consumers, producers and the government.

Price elasticity of demand is the degree of responsiveness of the quantity demanded of a good to a change in its price:

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

Total outlay (total expenditure) method

This method was given by Marshall. It compares the total money spent by consumers on a good, $TE = P \times Q$, before and after a price change. Elasticity is judged by the direction in which total outlay moves.

Rules

1. If price falls and total outlay rises (or price rises and outlay falls), demand is elastic, $E_d>1$.
2. If total outlay remains the same when price changes, demand has unitary elasticity, $E_d=1$.
3. If price falls and total outlay falls (or price rises and outlay rises), demand is inelastic, $E_d<1$.

Diagram

Take total outlay (TE) on the $X$-axis and price on the $Y$-axis. The TE curve has three parts:

• Elastic part ($E_d>1$): a fall in price raises outlay, so the curve slopes down and to the right (equivalently, up and to the left).
• Unitary part ($E_d=1$): outlay is the same at different prices, so the curve is vertical.
• Inelastic part ($E_d<1$): a fall in price reduces outlay, so the curve slopes down and to the left (equivalently, up and to the right).

This method is simple, but it only tells whether demand is elastic, unitary or inelastic, and does not give the exact numerical value of elasticity.

Marginal utility is the additional utility obtained from consuming one more unit of a good. $MU=\dfrac{\Delta TU}{\Delta Q}$.

Substitute $P=5$ in $Q_s=10+2P$:

$Q_s=10+2(5)=10+10=20$

The quantity supplied is 20 units.

Law of supply: Other things remaining constant, the quantity of a good supplied rises when its price rises and falls when its price falls. There is a direct (positive) relationship between price and quantity supplied.

Supply schedule

Diagram

Take quantity supplied on the $X$-axis and price on the $Y$-axis. Plotting the five points and joining them gives the supply curve $SS$, which slopes upward from left to right. At a price of Rs 10 the supplier offers 100 kg, and at Rs 50 offers 500 kg. The upward slope shows the law of supply.

Assumptions (ceteris paribus): Cost of production, technology, prices of related goods, number of sellers, taxes and subsidies, and producers' expectations remain unchanged.

Reasons for the law

1. A higher price brings higher profit, so producers have an incentive to supply more.
2. At higher prices, new firms enter the market.
3. Because of rising marginal cost, producers will supply more only at a higher price.

Meaning

The law of variable proportions explains the short-run relation between inputs and output when at least one factor is fixed and another factor is varied. It states that when more units of a variable input (such as labour) are added to a fixed input (such as land), total product at first increases at an increasing rate, then at a decreasing rate, reaches a maximum and finally falls. It is also called the law of returns to a factor, and its middle phase is the law of diminishing returns.

Assumptions

1. The state of technology is constant.
2. At least one factor is fixed, so it is a short-run law.
3. Units of the variable factor are homogeneous.
4. Factors can be combined in different proportions.

Concept with an example

Here $AP=\dfrac{TP}{L}$ and $MP=\dfrac{\Delta TP}{\Delta L}$.

Three stages

1. Stage I (increasing returns): From the first unit up to the point where AP is maximum (here $L=4$). TP rises at an increasing rate, then at a decreasing rate. MP rises to a peak and then falls, and the fixed factor is under-used.
2. Stage II (diminishing returns): From maximum AP until MP becomes zero (here $L=4$ to $6$). TP increases at a decreasing rate until it reaches its maximum, and AP and MP both fall. This is the rational stage where producers operate.
3. Stage III (negative returns): After MP becomes negative ($L>6$). TP falls, because too much labour crowds the fixed factor. No rational producer works here.

Diagram: Take labour on the $X$-axis and output on the $Y$-axis. The TP curve rises, reaches a peak where MP is zero and then falls. The AP and MP curves are inverted-U shaped, with MP cutting AP at the maximum of AP and MP going below the axis in Stage III.

Causes: In Stage I, better division of labour and fuller use of the fixed factor. In Stage II, the fixed factor becomes scarce relative to labour. In Stage III, over-crowding and poor co-ordination.

$Q_d=50-5P=50-5(4)=50-20=30$

The quantity demanded is 30 units.

In economics a market is not a particular place but the whole arrangement through which buyers and sellers come into contact to buy and sell a commodity at a price. The components (conditions) needed for a market are:

1. Buyers and sellers: There must be at least one buyer and one seller. They are the two sides of exchange.
2. A commodity or service: There must be a good or service to be exchanged, such as rice, cloth or banking services.
3. Price: The commodity must have a price, which is determined by the interaction of demand and supply.
4. Contact between buyers and sellers: They must be in touch with each other, directly or through telephone, internet, brokers or advertisements. Place is therefore not essential.
5. Demand and supply (competition): There must be demand for the commodity and a supply of it. A single price tends to rule for the same good because of competition.
6. Exchange process: The transaction must be completed, usually with money as the medium of exchange.

When these components exist together, a market is formed.

An inverse (negative) relationship: when price rises, quantity demanded falls, and when price falls, quantity demanded rises, other things remaining constant.

Total utility is at its maximum when marginal utility is zero, because additional units no longer add anything to total utility.

Price elasticity of demand is the degree of responsiveness of quantity demanded to a change in the price of the good, other things being equal.

$E_d = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} = \frac{\Delta Q}{\Delta P}\times\frac{P}{Q}$

Types

1. Perfectly elastic demand ($E_d = \infty$): A very small change in price causes an infinite change in quantity demanded. The demand curve is horizontal.
2. Perfectly inelastic demand ($E_d = 0$): Quantity demanded does not change at all when price changes. The curve is vertical.
3. Unitary elastic demand ($E_d = 1$): The percentage change in quantity equals the percentage change in price. The curve is a rectangular hyperbola.
4. Relatively elastic demand ($E_d > 1$): Quantity changes by a greater percentage than price. The curve is flatter.
5. Relatively inelastic demand ($E_d < 1$): Quantity changes by a smaller percentage than price. The curve is steeper.

At equilibrium, quantity demanded equals quantity supplied: $Q_d = Q_s$.

$100 - 2P = 20 + 2P$

$80 = 4P \implies P = 20$

Substituting into the demand function:

$Q = 100 - 2(20) = 60$

Check with the supply function: $Q_s = 20 + 2(20) = 60$. It matches.

Equilibrium price $P = 20$ and equilibrium quantity $Q = 60$.

Statement: The law of diminishing returns states that when more and more units of a variable factor (such as labour) are combined with fixed factors (such as land), keeping technology constant, the marginal product of the variable factor will eventually decline.

Assumptions: at least one factor is fixed; technology is constant; the variable factor units are homogeneous; and factors can be combined in varying proportions.

Schedule (land fixed at 1 hectare):

Explanation: Up to the 2nd unit, MP rises (increasing returns). From the 3rd unit MP falls (diminishing returns). At the 6th unit, TP is maximum and MP is zero. After this, MP is negative and TP falls (negative returns).

Diagram: On the $X$-axis show units of labour and on the $Y$-axis product. The TP curve rises, first at an increasing rate, then at a decreasing rate, reaches a maximum and then falls. The MP curve rises to a peak, then falls, cuts the $X$-axis where TP is maximum and goes below it. The AP curve rises, reaches its peak where MP = AP, and then falls.

Causes: The fixed factor becomes overcrowded, the proportion between factors worsens, and imperfect substitutability of factors. The law applies strongly in agriculture, but also in mining, fisheries and industry.