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

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Question

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

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

business economics

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Answer 1

Answer #1

(1)

(A)

Consumption is optimal and utility is maximized when MRS = Px/Py

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

100 = 2X + Y (Dividing by 15)

100 = 2X + 2X = 4X

X = 25

Y = 2 x 25 = 50

(C)

Demand function for good X is: Px = a - bQx

When Px = 15, Qx = 50

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

When Px = 30, Qx = 25

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

(2) - (1) yields: 15 = 25b

b = 15/25 = 0.6

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

Linear demand function is:

Px = 45 - 0.6Qx

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

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Answer 2

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

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