Consider a consumer with the utility function U(X, Y) = X2 Y2 . This consumer has an income denoted by I which is devoted to goods X and Y. The prices of goods X and Y are denoted PX and PY.

a. Find the consumer's marginal utility of X (MUX) and marginal utility of Y (MUY).

b. Find the consumer's marginal rate of substitution (MRS).

c. Derive the consumer's demand equations for both goods as functions of the variables PX, PY, and I.

d. Assume that I = $100 and PY = $5. What is the quantity demanded for good X when PX = $2? PX = $5? PX = $10? Sketch the demand curve for good X.

e. Assume now that PX = $10 and PY = $5. What is the quantity demanded for good X when I = $100? I = $200? I = $300? Sketch the consumer's Engel curve for good X. Is X a normal good or an inferior good?

f. Show that the demand for good X is unit elastic (use the point elasticity formula).

g. Show that the income elasticity for good X is equal to 1 (use the point elasticity formula).