Question

A consumer's preferences are given by the utility function u=(107)^2+2(x-5)y and the restrictions x>5 and y>0 are imposed.

1. Write out the Lagrangian function to solve the consumer's choice problem. Use the Lagrangian to derive the first order conditions for the consumer's utility maximizing choice problem. Consider only interior solutions. Show your work.

2. Derive the Optimal consumption bundles x*(px,py,w) and y*(px,py,w)

3. Use the first order condition from 1 to calculate the consumer's marginal utility of income when w=200, px=4, and py=5. [Hint: you need to substitute in the optimal amounts of x or y.]

Answer 1