1 [75 points; Chapter 5] You are to solve the consumer choice problem for three different...

1.

a.

The consumer's problem is:

The consumer's problem is:

The consumer's problem is:

b.

For U1:

As the quantity of X rises, the MRS increases. This implies that the indifference curves are not C shaped and the consumer's problem will have a corner solution.

For U2:

As the quantity of X rises, the MRS diminishes.

This implies that the indifference curves are C shaped and the consumer's problem will have an interior solution.

For U3:

As the quantity of X rises, the MRS diminishes.This implies that the indifference curves are C shaped and the consumer's problem will have an interior solution.

c. Solving problem 1:

Since the indifference curves are not C shaped and MRS increases as X increases, the problem will have a corner solution. The consumer will either consume X or Y. Upon consuming only X, the consumer can purchase 75 units and his utility is 5625. Upon consuming only Y, the consumer can consume 50 units and his utility is 50. Since the consumer attains a higher satisfaction from consuming only X, the consumer's optimal bundle is (75,0).

Solving problem 2:

Since MRS diminishes as X increases, the problem has an interior solution which can be computed by equating MRS and price ratio as follows:

Substituting this value in the consumer's budget line:

Solving problem 3:

Since MRS diminishes as X increases, the problem has an interior solution which can be computed by equating MRS and price ratio as follows:

Substituting this value in the consumer's budget line: