Answer to Question #273334 in Microeconomics for cookie

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

Solution:

a.). Demand: Q = 0.02M – 2P

Q = 0.02(7,500) – 2(30) = 150 – 60 = 90

Neville will buy 90 bottles of claret.

 

b.). 90 = 0.02M – 2(40)

90 = 0.02M – 80

90 + 80 = 0.02M

170 = 0.02M

M = 8,500

Neville will have an income of 8,500 if the price increase to 40

 

c.). Q = 0.02(8,500) – 2(40) = 170 – 80 = 90

Neville will buy 90 bottles of claret

 

d.). Q = 0.02(7,500) – 2(40) = 150 – 80 = 70

Neville will demand 70 bottles of claret.

 

e.). When both the income and the price increase, both the income and substitution will move in the opposite direction and the effect will be zero. When only the price increase, only the substitution effect will take place as consumers will substitute the more expensive goods with cheaper goods. As a result, the demand for the goods will fall.