Question

7) The picture below shows several indifference curves of a consumer and several budget lines: X2 1 2 3 4 5 6 7 8 9 10 11 12 Note that the lines passing through A, C, and E are parallel. Also the lines passing through B, D, and F are parallel. Move over at each bundle labeled with a letter, the budget line and indifference curve passing through that bundle are tangent. The consumption levels at each of the labeled bundles are as follows: A = (6,7), B = (9,3), C = (1.5,9), D = (6.5,1.5), E = (2,5) and F=(4,2). The consumer has an income of 12TL that he will spend on the two goods. a. (3pts.) If the price of good 1 is 2TL/unit and the price of good 2 is 1TL/unit, what is the optimal bundle that the consumer will consume? b. (10pts.) If the price of good 2 increases from 1TL/unit to 2TL/unit, how much does his con- sumption of good 2 change? How much of this change is due to income effect and how much of it is due to substitution effect? Explain.

Answer 1

2 Px2 = 2 : Budget constraint : (2x xg) + (1x X2 ) = 12 52x1 + x2= 12) Only bundle C (1.5, 9) Satisfy this egn. " optimal bundle = c(1.5, 9) Pxy = 2 Pt2 = 2 Budget constraint! 2x, + 2 X 2 = 12 : x + x2=6 :. Optim Bundle = F (4,2)

Due to increase in price of goods, his consumption changes from 9 to 2] le decrease og (9-2)= _unitas

Two things have gone on here. There is a substitution effect whereby the consumer is deciding to substitute some of good X2 for some good X1 because X2 is now more expensive relative to good X1. There is also an income effect whereby the fact that X2 has got more expensive while X1 is unchanged in price, means that the consumer is now relatively poorer than he was before.

We can break down the substitution and income effects like this:

C D : Substitution effect CO(1.5,9) D -> Fi on come Effect CSF: Total Effect .(6.5,1.5) ty tition effect I oncome effect Suess tithan Income

Here we have drawn a new budget line (the black dashed line) with the same slope as the final budget line, indicating the same relative prices between X1 and X2 as the final relative prices after the price change. This has been moved to the point that is tangential to the indifference curve that the original bundle, C, was on. Now this budget line effectively represents an increased budget, because it is a parallel shift outwards from final budget line .

It shows us the budget that the consumer would have needed, to stay at the original level of utility, the same indifference curve as he was on at bundle C. However C would not be the optimal choice bundle here, it would be bundle D(6.5,1.5). Bundle D gives the same level of utility as bundle C, but it would satisfy the new relative prices after the price change. This shows us the substitution effect. If the consumer was compensated by being given enough raise in income to allow him to stay at the same level of utility as he was on at bundle C, he would have responded to the change in relative prices by shifting his spending to buy less of X2 and more of X1, hence the move from C to D.

The rest of the effect is the income effect. The shift from D to F.