Jan's preference for yams (Y) and artichokes (A) can be described by a Cobb Douglas type utility function of the form U(Y, A) = 10Y0.5A0.5. Jan's weekly budget for the two good is $40, and the price is yams is $2 per pound, artichokes cost $4 per pound.

a. (1) Determine Jan's equation for the budget line.

b. (2) Calculate the marginal utility of yams and the marginal utility of artichokes.

c. (1) Determine the marginal rate of substitution between yams and artichokes (MU(Y)/MU(A)).

d. (3) Determine Jan's optimal consumption bundle, given the utility function and budget line above.

e. (2) Now suppose that the price of yams changes to $4 per pound. How would this change Jan's consumer optimum? Does Jan change her consumption of artichokes as the price of yams rises?

f. (1) Explain in words how Jan's budget line changes as the price of yams increases.