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ECON-500: Microeconomic Analysis and Policy

ECON 500 Problem Set 02

Suppose that  U(x, y) = x + ln(y) (defined for positive values of x and y). Let  px, py, and I respectively denote the prices of Goods X and Y, and income (such that all three parameters are positive, as usual).

Question 1. [2 points]

Evaluate the ratio 

Question 2. [2 points]

Evaluate the ratio 

Question 3. [2 points]

Evaluate esx,px.

Question 4. [2 points]

Suppose that the utility function is  U(x, y) = x αy 1−α, where the domain of the utility function comprises bundles with strictly positive amounts of goods X and Y, and 0 < α < 1.

Let px, py and I respectively denote the prices of Goods X and Y, and income. This problem considers how consumer welfare changes when px increases from 1 to 2 (1/α) (and py and I do not change).

For this increase in px from 1 to 2 (1/α), evaluate 

Question 5. [2 points]

Suppose that the utility function is  U(x, y) = α ln(x) + (1 − α)y where the domain of the utility function comprises bundles with strictly positive amounts of goods X and Y, and .0 < α < 1

Let px, py, and I respectively denote the prices of Goods X and Y, and income.

Determine