Suppose your utility function is given byU(x,y)=xy^2

. The price of x isP_x

, the price of y isP^2_x

, and your income isM=9Px2P^2_x

.

a) Write out the budget constraint and solve for the MRS.

b) Derive the individual demand for good x. (Hint: you need to use the optimality condition).

c) Is x an ordinary good? Why or why not?

d) Suppose there are 15 consumers in the market for x. They all have individual demand functions equal to the one you derived in part b. The market supply for good x is given byQ^s=2P_x

. What is the market equilibrium price and quantity for good x?