Question

Given a budget constraint and an indifference cure, draw a demand curve for product Y, assuming X and Y are normal product.

Answer 1

What is an indifference curve?

An indifference curve is a graph showing combination of two goods that give the consumer equal satisfaction and utility. Each point on an indifference curve indicates that a consumer is indifferent between the two and all points give him the same utility. It is represented as:

What is a budget constraint?

A budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within his or her given income. It is represented as:

What are normal goods?

A normal good is any good for which demand increases when income increases, i.e. with a positive income elasticity of demand. Eg: Whole wheat, etc.

Demand Curve of Product Y:

Let us suppose that a consumer has got income of $ 300 (Budget of the consumer) to spend on goods. In the graph below, money is measured on the Y-axis, while the quantity of the good Y whose demand curve is to be derived is measured on the X-axis. An indifference map of a consumer is drawn along with the various budget lines showing different prices of the good Y. Budget line PL1 shows that price of the good Y is $ 15 per unit.

As price of good Y falls from $ 15 to $ 10, the budget line shifts to PL2. Budget line PL2 shows that price of good Y is $ 10. With a further fall in price to $ 7.5 the budget line takes the position PL3. Thus PL3 shows that price of good Y is $ 7.5. When price of good Y falls to $ 6, PL4 is the relevant budget line.

With the budget line PL1 the consumer is in equilibrium at point Q1 on the price consumption curve PCC at which the budget line PL1 is tangent to indifference curve IC1. In his equilibrium position at Q1 the consumer is buying OA units of the good X. In other words, it means that the consumer demands OA units of good X at price $ 15.

When price falls to $ 10 and thereby the budget line shifts to PL2, the consumer comes to be in equilibrium at point Q2 the price-consumption curve PCC where the budget line PL2 is tangent to indifference curve IC2. At Q2, the consumer is buying OB units of good X.

With the above information, we can draw up the demand schedule:

Price of Good X ($)	Budget Line	Quantity Demanded
15	PL1	OA
10	PL2	OB
7.5	PL3	OC
6	PL4	OD

In the graph below, where on the X-axis the quantity demanded is shown as in indifference curves diagram in the top pannel, but on the Y- axis in the diagram in the bottom panel price per unit of the good Y is shown instead of total money. In order to obtain the demand curve, various points K, L, S and T representing the demand schedule of the above table are plotted. By joining the points K, L, Sand T we get the required demand curve DD.

In most cases the demand curve of individuals will slope downward to the right, because as the price of a good falls both the substitution effect and income effect pull together in increasing the quantity demanded of the good. Even when the income effect is negative, the demanded curve will slope downward to the right if the substitution effect is strong enough to overwhelm the negative income effect. Only when the negative income effect is powerful enough to outweigh the substitution effect can the demand curve slope upward to the right instead of sloping downward to the left.