5. Mr. Smith has a weekly income of M = $24. Initially the prices of X and Y are

Question

5. Mr. Smith has a weekly income of M = $24. Initially the prices of X and Y are both $2/unit and Mr. Smith buys 6 units each of X and Y each week, a bundle on indifference curve I0. Then, ceteris paribus, the price of X increases to $4/unit, with the result that Mr. Smith now buys 3 units of X and 6 units of Y per week, which is a bundle on indifference curve I1. It is also the case that, if Mr. Smith’s income were $34 a week after the price increase (it isn’t, but if it were…) he would buy 4 units of X and 9 units of Y, which is a bundle on indifference curve I0 ($34 is the minimum income required for Mr. Smith to attain his initial indifference curve after the price increase).

How much of the change in Mr. Smith’s consumption of X, as a result of the increase in the price of X, is due to the substitution effect? How much of the change in Mr. Smith’s consumption of X is due to the income effect?

Explanation / Answer

In this case, 24/2= 12x or 12 y He buys 6 each From the decrease we know that 3x or 6 dollars in from the substitution effect since he substituted these goods for other goods when the price increases. Additionally, we know 34/4=8.5 8.5-6=2.5 2.5*2 dollars each =5 is from the income effect Hope this helps

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