3) Suppose that people derive utility from two goods - Barbecue (B, measured in
ID: 1167620 • Letter: 3
Question
3) Suppose that people derive utility from two goods - Barbecue (B, measured in lbs/week) and all other goods (Y, the composite good). a. Show a typical consumer?s allocation of his or her income between B and Y (a generic budget constraint and utility maximizing indifference curve). b. Suppose that the local government decides that the amount of barbecue being consumed by the typical consumer in part o (say, B?) is woefully substandard and downright un-American and requires that all people buy B?(some quantity greater than B?) lbs per week of barbecue instead. Show, using the same graph, that this law would reduce this person?s satisfaction. c. One way to return this person to the initial level of enjoyment would be to give him or her extra income. On your graph, show how much extra income this would require. (Note: return the consumer to their original indifference curve. Do not answer in terms of monetary values. Just show graphically). d. Another way to return this person to his or her initial level of utility would be to provide a barbecue subsidy that reduces the price of each pound of barbecue. On your graph, show this solution as well.Explanation / Answer
a) Budget line = p1B + p2Y=M
Its slope is p1/p2. Marginal rate of substituion is the slope of indifference curve and it is the rate at which consumer is willing to substitute one for the other.
For utility maximisation, slopes of budget constraint should be equal to MRS. It implies indifference curve should be tangent to budget line.
AB is the budget line and IC is the budget line
b) In part a we showed consumer is utility is maximised, but now he is forced to consume more of B. His income is inchanged. New bundle was previously affordable but rejected in favour the bundle chosen in part a. In order to consume more of B, he has to reduce consumption of Y. It means his utility is less now. So he is worse off.
B** lies below the indifference curve which says that B** gives less satisfaction than B*.
c) In order to get the consumer on the original indifference curve, we need to increase income proportionally so that he could atleast consume original bundle.
Increase in income will shift the budget line outwards and new bundle can be chosen now with more of both the goods.
d) Giving the consumer subsidy for B implies price is reduced, which is itself like increase in income. With reduced price income is saved and this saved income can be spent on any other good depending on his tastes.
With the inroduction of subsidy good B becomes less expensive. Hence the slope of budget line decreses and as a result budget line becomes steeper and pivots. New bundle is chosen with more of both the goods at the point where new budget line is tangent to the original indifference curve.
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