5.

Your utility function over the goods X and Z takes the following form: U(X, Z) = XO'5 + Z[}'5 You want to maximize your utility subject to your budget constraint. Assume that the price of X is $5 per unit and the price of Z is $10 per unit, and that the total income you have to spend on X and Z is $150. The consumption bundle that will maximize your utility subject to your budget constraint is X = 20 and Z = 5 (enter only numbers in the blanks, and please round to the nearest integer if necessary). Hint: First solve for the marginal rate of substitution (M RS). Setting that equal to the negative price ratio will give you an optimal ratio of X and Z to consume, which you can use in combination with the budget constraint to determine the exact optimal quantities of X and Z to consume. As in question 5, your utility function over the goods X and 2 takes the following form: U(X, Z) = XO'5 + Z[}'5 You want to maximize your utility subject to your budget constraint. Assume again that the price of X is $5 per unit and the price of Z is $10 per unit, but that owing to a new government welfare program, the total income you have to spend on X and Z is $180 instead of $150. The consumption bundle that will now maximize your utility subject to your budget constraint is X = 24 and Z = 5 (enter only numbers in the blanks, and round to the nearest integer if necessary). As in the previous two questions, your utility function over the goods X and Z takes the following form: U (X, Z) = X05 + 20-5 Suppose now that the government wants to discourage consumption of Z. lt places a tax on Z such that the price consumers now face is $15 per unit instead of $10 per unit. Assume that the price of X remains at $5 per unit and that your income is $180. The consumption bundle that will now maximize your utility subject to your budget constraint is X = 27 and Z ll 00 (enter only numbers in the blanks, and round to the nearest integer if necessary)