Answer to Question #99224 in Microeconomics for amy

Question

Suppose Peter buys Good X and Good Y only. The price of Good X is $1 per unit and the price of Good Y is $2 per unit. Peter has the weekly income of $1000. Suppose the utility function of Peter is U = 3XY and the slope of his indifference curve is –Y/X where X and Y are the quantity of Good X and Good Y in a bundle respectively.
a. What is the utility level of Bundle A with 200 units of Good X and 200 units of Good Y?
Show your workings. [5 marks]
b. Bundle B has 100 units of Good X and 300 units of Good Y. Is Bundle A preferred to Bundle
B? Explain your answer. [5 marks]
c. Is Bundle A affordable to Peter? Clearly explain your answer. [5 marks]
d. Solve for the utility maximizing bundle. Show each of your steps clearly. [10 marks]

Answer 1

a. The utility level of Bundle A with 200 units of Good X and 200 units of Good Y is:

Ua = 3*200*200 = 120,000.

b. If Bundle B has 100 units of Good X and 300 units of Good Y, then Ub = 3*100*300 = 90,000, so Bundle A is preferred to Bundle B.

c. Bundle A cost is: 200*$1 + 200*$2 = $600 < $1000, so it is affordable to Peter.

d. The utility is maximized if:

MUx/MUy = Px/Py.

If the slope of his indifference curve is MRS = -MUx/MUy = –Y/X, then MUx/MUy = Y/X, so:

Px/Py = Y/X,

Y/X = 1/2,

X = 2Y.

Px*X + Px*Y = I, so:

1*2Y + 2*Y = 1,000.

4Y = 1,000,

Y = 250 units, X = 2*250 = 500 units.