Question

Homework Assignment 5

1. U = XY where MRS = Y/X; I = 1500, Px = Py = 15,

A. Derive optimal consumption bundle.

B. If Px increases to be $30, derive the new optimal consumption bundle

C. Using the results from A and B, derive the individual demand for good X assuming the demand is linear.

2. Assuming the market has two consumers for a very special GPU and their individual demands are given below

Consumer A: P = 450 – 4 Q; Consumer B: P = 500 – 5 Q

A. Derive the market demand for this GPU.

Also, review the handout for income and substitution effects

Answer 1

(1)

U = XY

Consumption is optimal when MRS = Px/Py

MUx = U/X = Y

MUy = U/Y = X

MRS = MUx/MUy = Y/X = Px/Py

(a) Px = Py = 15

MRS = Y/X = 15/15 = 1

X = Y

Substituting in budget line,

1500 = 15X + 15Y

1500 = 15X + 15X = 30X

X = 50

Y = X = 50

(b) When PX = 30,

MRS = Y/X = 30/15 = 2

Y = 2X

Substituting in new budget line:

1500 = 30X + 15Y

1500 = 30X + 15(2X)

1500 = 30X + 30X = 60X

X = 25

Y = 2 x 25 = 50

(C) Linear demand function: Px = a - b.QX

When Px = 15, Qx = 50

15 = a - 50b........(1)

When Px = 30, Qx = 25

30 = a - 25b........(2)

(2) - (1) yields:

15 = 25b

b = 0.6

a = 15 + 50b [From (1)] = 15 + (50 x 0.6) = 15 + 30 = 45

Linear demand equation: Px = 45 - 0.6Qx

NOTE: As per Answering Policy, 1st question is answered.