Consider John, who likes playing both football and golf. Let the hours he spends playing football be x_f and the hours he spends playing golf be x_g". His utility function is (x_f, x_g). Every hour playing football costs him $5, and every hour playing golf costs him $10. He has $100 to spend between the two. a. John is a utility maximizer. Express the problem in terms of the objective function and the constraint. (This is not asking for the Lagrangian, that is coming next). b. Form the Lagrangian. c. Using the first order conditions, determine how many hours he will spend playing football and how many hours he will spend playing golf. d. What is the marginal utility of income? (This is the value of the Lagrange multiplier). e. How much utility will John get?

a. John is a utility maximizer. Express the problem in terms of the objective function and the constraint. (This is not asking for the Lagrangian, that is coming next)

b. Form the Lagrangian.

c. Using the first order conditions, determine how many hours he will spend playing football and how many hours he will spend playing golf.

d. What is the marginal utility of income? (This is the value of the Lagrange multiplier).

e. How much utility will John get?