1. Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W).

the MRS = -N/W.

The budget constraint is: 1,600 = 2*N + 20*W

Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis.

SOLVE:

a. Graph the budget constraint. label all points. What is the slope of the budget constraint?

b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph.

c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the substitution effect and income effect.