# Consider the utility maximization problem subject to a budget constraint with the following utility function

November 24, 2016

Problem 7. Consider the utility maximization problem subject to a budget constraint with the

following utility function: U(x, y) = 8×0.5y1.5 and the associated MRS is y/3x. Assume that Px is

the price of x, Py is the price of Y and I is the consumer’s income.

(a) Are the Marshallian demand functions scale invariant (i.e. homogeneous of degree zero)?

(b) Are the goods Giffen?

(c) Show why or why not the goods are inferior or normal.

Problem 8. Suppose a consumer’s tastes are described by the utility function above in #7.

Suppose currently Px=\$2.50 and Py=\$3.33 and the consumer has a fixed exogenous income I=40.

(a) Find the values of X*, Y*, and the maximum utility that the consumer attains at this

optimal bundle.

(b) Now suppose that Px decreases to Px=\$2.00. Calculate the substitution effect.

(c) Calculate the income effect.

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