Question

A) Use the Lagrange Multiplier method to solve for the quantity of X and Y when I=$14,000, Px=$7, and Py=$28, and Utility = X*Y. Show all steps.

B) Graph the budget line and the utility curve. Indicate x and y-intercepts, as well as the optimal bundle of x and y.

C) How many utils are obtained at the optimal choice? Show how you obtain your answer.

D) Show the Marginal Rate of Substitution and the slope of the budget line at the optimal choice. Are they different, or are they the same? Show where these numbers come from. Use appropriate formulas.

E) What is the utility along the budget line when X=600? How does this compare to the utility you found in part C of this question?

F) What is the Marginal Rate of Substitution for the utility curve at the point the curve intersects the budget line when X=600. Compare this Marginal Rate of Substitution to the slope of the budget line. Use these slopes to explain which way the decision-maker should move on the budget line from X=600.

G) Show the marginal utility per dollar spent for X and Y when the person is at X=600 along the budget line. Show how you get answers. Use your answers to explain how the decision-maker will reallocate her money.

Answer 1