# 1.The demand for gym is given by P=15-Q/2. (i) Suppose that initially the admission to the gym is set at $1. What is the consumer surplus in this case? (ii) Now suppose that the price of admission had been raised to 5. What is the change in the consumer surplus compared to part (i)? 2.Compute the expenditure function of a person who has utility function of two goods x and y: u(x,y)=x1/2+y1/2 (this can be simply rewritten as square root of x plus square root of y). What income does this person need to achieve utility level 2 at px=1 and py=3?

1.The demand for gym is given by P=15-Q/2.

(i) Suppose that initially the admission to the gym is set at $1. What is the consumer surplus in this case?

(ii) Now suppose that the price of admission had been raised to 5. What is the change in the consumer surplus compared to part (i)?

2.Compute the expenditure function of a person who has utility function of two goods x and y: u(x,y)=x1/2+y1/2 (this can be simply rewritten as square root of x plus square root of y). What income does this person need to achieve utility level 2 at px=1 and py=3?

Answer:

P = 15-Q/2

at Q = 0, P = 15

and also at P=1

1= 15 – Q/2

Q/2 = 14

Q = 28

and also at P=5

5= 15 – Q/2

Q/2 = 10

Q = 20

Consumer Surplus($1) = 0.5*(15-1)*28 = 196

Consumer Surplus = 0.5*(15-5)*20 = 100

change in CS = 196-100 = 96