Using the demand curve for good x derived above calculate

Question

Question: Consider the following Utility Functions below:

a. U = X² + Y²

b. U = X²Y²

c. U = XY²

d. U=XY + X + Y

1. Assume the initial prices are Px = $2, Py =$4 and M = $100. Find the utility maximizing consumption bundle for each utility function.

2. Now derive the demand curve for Good X for each of the utility functions (Hint: solve the equations but do not substitute in for Px)

3. Using the demand curve for Good X derived above, calculate the price elasticity of demand for Good X at Px=$2. Note: calculate the point elasticity of demand.