Question

Q02 A consumer is choosing between good 'X' and a composite good Y.' The price of 1 unit of good X is $2. The below diagram shows the consequences of a change in the price of good X.' The initial pre-change optimal bindle is the new post-change optimal consumption bundle is Ez. Use the information provided in the diagram to answer the following questions. a. Did the price of 1 unit of good 'X' increase or decrease? b. Use the TOP diagram to decompose the change in the quantity demanded of good X (prompted by the change in P.) into the substitution and income effects. Analogously, decompose the corresponding! change in the quantity demanded of good 'Y' into the substitution and income effects. Clearly label these substitution and income effects. c. Use the BOTTOM diagram to draw the demand curve for good X'Clearly label the two points on this demand curve that correspond to points E, and E. Make sure to also label the axes as well as the coordinates of these two points of the demand curve. - see next page for the diagram

Answer 1

(a) Price of X is given as $2 and consumer can afford 60 units of good X if all of the money is spent on good X only. Hence, total money income of the consumer is $2*60 = $120. Now after price change, the consumer is able to afford only 20 units of good X if all the money is spent on good X. Hence, the new price can be calculated as the ratio of total income and total units = $120/20 = $6. Therefore, price has increased from $2 to $6.

(b) Initially, the consumers optimal bundle is determined corresponding to E1, i.e., 26 units of X and O1 units of other things. Due to increase in price of good X from $2 to $6, the new optimal bundle is 5 units of X and O2 units of other thing. So, the total price effect on good X is 26-5 = 21. These 21 units can be decomposed into substitution and income effect. Due to increase in price of good X, X is relatively expensive than other goods and hence some amount of good X will be substituted by other goods by the consumer. If we compensate for the decrease in real income (due to increase in price of X) so that the budget constraint shifts as shown by the blue line (parallel to the new budget line with price of X as $6. The income is compensated by an amount so that the consumer can choose a bundle in the original indifference curve (say at point E3) in the below figure. The movement from point E1 to E3 is known as substitution effect (labelled in the diagram). And once the compensated income is taken back then consumer moves from E3 to E2 due to income effect.

For other goods, the substitution effect would be O1O3 and the income effect would be O3O2.

(c) If you consider the price and quantity combinations of good X with original price and the increased price, you can sketch the demand curve as shown in BOTTOM diagram. At price of $2 per unit of X, quantity demanded is 26, which gives us a point (26,2) on the quantity-price space. Further, at price $6, quantity demand falls from 26 to 5 and hence we get another combination of quantity and price as (5,6). By joining the two points, we get the demand curve (D) for good X in the price-quantity space of good X as shown in the BOTTOM diagram.

Substitution Effect 23 Income Effect S20 26 2 ----------- 05 26