A beach-goer has utility defined by

u(xF,xT) = xFxT

where xF is the number of pairs of flip-flops she uses in a summer and xT is the number of beach towels she uses in the same period.

1) Compute the marginal utilities UF(xF,xT) and UT(xF,xT).

2) Sketch an indifference curve for this utility function with towels on the x-axis and flip-flops on the y-axis. Are these goods complements? Substitutes?

3) Suppose that this beach-goer has y = $500 to spend on flip-flops and towels over the summer. Further, suppose she faces prices pF = $20 and pT = $40. Write expression for her budget constraint, and draw it with towels on the x-axis and flip-flops on the y-axis. Be sure to label the intercepts in your drawing for full credit!

4) Derive the optimal number of flip-flops and towels consumed. Represent the choice on a graph.