Important Questions: Theory of Consumer Behaviour

Q1: What is a budget line? Why is it downward sloping?
Ans: Budget line is a line showing different combinations of two goods that a consumer can purchase with a given income at prevailing market prices of the goods.
Symbolically, the budget line is given by P_x·Q_x + P_y·Q_y = M, where P_x, P_y are the prices of goods X and Y, Q_x, Q_y are the quantities, and M is income.
It is negatively (downward) sloped because, with a fixed income, to obtain more of one good the consumer must give up some units of the other good. This trade-off implies that as quantity of X increases, quantity of Y must fall so that total expenditure remains equal to income. The slope of the budget line equals -P_x/P_y, which shows the rate at which the market requires substitution of Y for X.

Q2: Define budget line.
Ans: Budget line is a line showing different combinations of two goods that a consumer can afford with a given income and the market prices of the goods.
Mathematically, P_x·Q_x + P_y·Q_y = M.

Q3: Define a budget line. When can it shift to the right?
Ans: Budget line is a line showing different combinations of two goods that a consumer can afford with a given income and market prices of the goods,
e.g. P_x·Q_x + P_y·Q_y = M.
It can shift to the right (outward) in the following situations:
(i) When the level of income increases - With a higher income the consumer can afford more of both goods, so the entire budget line moves outwards parallel to the original line.
(ii) When the prices of both goods fall proportionately - If both P_x and P_y fall while income remains the same, the consumer can buy more of both goods and the budget line shifts outwards. (If only one price changes, the budget line rotates rather than shifting parallel.)

Q4: Define budget set.
Ans: Budget set refers to the set of all possible combinations of two goods that a consumer can afford given income and market prices.
It is represented by combinations for which P_x·Q_x + P_y·Q_y ≤ M. The boundary where expenditure equals income (P_x·Q_x + P_y·Q_y = M) is the budget line; points inside the set (strictly less than M) are affordable and leave some unspent income.

Q5: Explain the three properties of indifference curve.
Ans: Indifference curve is a curve showing different combinations of two goods, each combination offering the same level of satisfaction to the consumer.
Properties of indifference curves are:

• Indifference curves are negatively sloped - This shows that to keep the same level of satisfaction, an increase in the quantity of one good must be accompanied by a decrease in the quantity of the other good. Thus more of one commodity implies less of the other so that total satisfaction remains constant.
• Indifference curves are convex to the point of origin - Indifference curves are usually bowed inwards because of a diminishing Marginal Rate of Substitution (MRS). As the consumer obtains more of good X and less of good Y, the amount of Y he is willing to give up for an additional unit of X decreases.
• Indifference curves do not touch the X-axis or Y-axis - It is assumed that the consumer purchases positive amounts of both goods. Therefore an indifference curve representing a typical balanced preference will not meet an axis; meeting an axis would imply zero consumption of one good, which is not assumed here.

Q6: What is budget set? Explain what can lead to change in budget set.
Ans: Budget set refers to the set of all possible combinations of two goods that a consumer can afford given income and market prices.
It is represented by P_x·Q_x + P_y·Q_y ≤ M.

• When the level of income changes - An increase in income expands the budget set (more combinations become affordable); a decrease in income contracts it.
• When the price of one good changes - A fall in the price of one good makes combinations with larger quantities of that good affordable, causing the budget set to expand in the direction of that good (the budget line rotates). A rise in price contracts the set.
• When the prices of both goods change - If both prices fall (with income unchanged), the budget set expands (outward shift). If both prices rise, the budget set contracts (inward shift). If prices change in unequal proportions, the budget line will rotate rather than shift parallel.

Note: A budget line is constructed from the consumer's income and the prices of the two goods. Therefore, any change in income or in the prices of the goods changes the budget line and hence the budget set.

Example (simple numerical illustration): If a consumer moves from bundle A = (X = 1, Y = 8) to bundle B = (X = 2, Y = 6), he gives up 2 units of Y to gain 1 unit of X. The MRS between these two bundles (average rate) is 2. At points closer together on a smooth indifference curve, MRS measures how many units of Y the consumer is willing to sacrifice for one extra unit of X.

Equilibrium is struck where the MRS equals the price ratio (slope of budget line). At the point of equilibrium, the indifference curve and the budget line are tangent to each other, implying equal slopes.

If a consumer wants to have more of X, marginal utility (MU) of X tends to fall. Therefore, he will be willing to sacrifice fewer units of Y for additional units of X. As he continues to obtain more of X, MU of X keeps declining and the MRS falls, which is why the indifference curve is convex.

(ii) Budget line refers to the bundle of two goods that costs exactly equal to the consumer's income. Consider the following numerical example used earlier: price of Good-1 is ₹2 per unit, price of Good-2 is ₹1 per unit and the consumer has ₹60 to spend. The budget equation is:

P₁·Q₁ + P₂·Q₂ = M =  2·Q₁ + 1·Q₂ = 60.

When the consumer spends all income on Good-1 (Q₂ = 0), maximum Q₁ = 60/2 = 30 units. When he spends all income on Good-2 (Q₁ = 0), maximum Q₂ = 60/1 = 60 units. These two intercepts (30,0) and (0,60) determine the budget line.

Q8: Explain the conditions of consumer's equilibrium under indifference curve approach.
or
A consumer consumes only two goods. Explain the conditions of consumer's equilibrium with the help of indifference curve analysis. (Foreign 2014; All India 2010)
Ans: According to the indifference curve approach, a consumer reaches equilibrium at the point where the budget line is tangent to the highest attainable indifference curve. At this tangency the slopes are equal. The two conditions for consumer's equilibrium are:

(i) Equality of slopes (Tangency condition) - The slope of the indifference curve (MRS) must equal the slope of the budget line (price ratio). In formula form: MRS = P_x/P_y. This means the rate at which the consumer is willing to substitute Y for X equals the market rate of exchange between the goods.

(ii) Convexity / Diminishing MRS (Second condition) - At the point of equilibrium, the indifference curve must be convex to the origin, implying a diminishing MRS. This ensures the tangency point corresponds to a maximum utility subject to the budget constraint rather than a minimum.

P is the equilibrium point where the budget line touches the highest affordable indifference curve IC₂. IC₃ is not affordable because the consumer's income does not permit it. Point A cannot be equilibrium because at A MRS > P_x/P_y; the consumer values X relatively more, so he will substitute towards more X and less Y until MRS falls to equal the price ratio. At point B, MRS < P_x/P_y; the consumer values Y relatively more on the margin, so he will move towards more Y and less X until MRS rises to meet the price ratio. The process ends at point P where MRS = P_x/P_y.