Answer to Question #99371 in Microeconomics for Sofia

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. Solve for the utility maximizing bundle. Show each of your steps clearly. [10 marks]
b. Depict the utility maximizing bundle in a well-labeled diagram. [10 marks]
c. Find the marginal rate of substitution at the utility maximizing bundle. [5 marks]
d. If the sellers of Good X launch a promotional activity that consumers, after buying 500 units
of Good X at $1 per unit, can buy more Good X at a price less than $1 per unit. Use your
diagram in part (b) to show the effect of such a promotional activity on the budget line and the
utility maximizing bundle. [10 marks]

Answer 1

a. 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.

b) The utility maximizing bundle is depa

icted as intersection of indifference curve and budget line.

c) MRS(XY) = -Y/X = -250/500 = -0.5.

d) If the sellers of Good X launch a promotional activity that consumers, after buying 500 units of Good X at $1 per unit, can buy more Good X at a price less than $1 per unit, then the budget line will change, and its maximal point at X-axis will increase. The resulting equilibrium bundle will consist of more units of X and less units of Y.