Answer to Question #274318 in Microeconomics for Juty

Question

Neville's passion is fine wine. When the prices of all other goods are fixed at current levels, Neville's demand function for high-quality claret is Q = .02M – 2P, where M is his income, P is the price of claret (in British pounds), and Q is the number of bottles of claret that he demands. Neville's income is 7500 pounds, and the price of a bottle of suitable claret is 30 pounds.

(a) How many bottles of claret will Neville buy?

(b) If the price of claret rose to 40 pounds, how much income would Neville

have to have in order to be exactly able to afford the amount of claret and the amount of other goods that he bought before the price change?

(c) At the income level you mentioned in part (b) and the higher price of claret of 40 pounds, how many bottles would Neville buy?

(d) At the original income of 7500 pounds and a price of 40, how much claret would Neville demand?

(e) Decompose the total price effect into the substitution and income effect

Answer 1

(a) q = 0.02m - 2p

q = 0.02(7500) - 2x30

q = 150 - 60 = 90 bottles

(b) When price is 30 then Neville spend 30 x 90 bottles of claret = 2700 on claret and remaining 7500- 2700 = 4800 on other goods.

When price is 40 pounds then income required to purchase 90 bottles and other goods = 90 x 40 + 4800 = 3600 + 4800 = 8400 pounds

q = 0.02(8400) - 2(40) = 168 - 80 = 88 bottles

c) q = 0.02(7500) - 2(40) = 150 - 80 = 70 bottles

(d) When price is 40 pounds then income required to purchase 90 bottles and other goods = 90 x 40 + 4800 = 3600 + 4800 = 8400 pounds

(e) Substitution effect = 88 - 90 = - 2

Income effect = 70 - 88 = - 18