Econ

ECON 104A - INTERMEDIATE MICROECONOMIC THEORY

HOMEWORK #2

Due Monday, 16 APR 2018

(1) Calculate the marginal utility of x and the marginal utility of y for the following utility functions: (a) u(x,y) = 2x + 3y (b) u(x,y) = x

1 2 y

1 2

(c) u(x,y) = 12x3y 3 4

(2) Bob has the following utility function for goods x and y:

u(x,y) = x 1 4 y

3 4

Suppose that the price of good x is $2, the price of good y is $5, and Bob has an income of $100 to spend on these two goods. (a) Write down the equation for Bob’s budget line and show it in a graph. (b) Solve for the optimal bundle of goods, (x∗,y∗) that Bob will choose to maximize his utility, and indicate

this bundle in the graph. (c) Calculate Bob’s utility level from consuming the bundle (x∗,y∗).

(3) Joe has the following utility function for goods x and y:

u(x,y) = 4x + 5y

Suppose that the price of good x is $2, the price of good y is $3, and Joe has an income of $10 to spend on these two goods. (a) Write down the equation for Joe’s budget line and show it in a graph. (b) In the same graph, draw in Joe’s indifference curves, and show which bundle of goods he will choose to

consume.

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