Harold's utility function is U(x, y)= (x + 3)(y + 2).The price of x is $1.The price of y is $2.At all incomes for which Harold consumes positive amounts of both goods, he will consume
A)more than twice as many units of x as of y.
B)more than twice as many units of y as of x.
C)1 more unit of x than of y.
D)1 more unit of y than of x.
E)2/3 as many units of y as of x.

Question

Quizplus · Accepted Answer

To determine Harold's consumption pattern, we need to analyze the marginal utility per dollar spent on each good. Given the utility function U(x, y) = (x + 3)(y + 2), the marginal utility of x (MUx) is the partial derivative of U with respect to x, which is (y + 2), and the marginal utility of y (MUy) is the partial derivative of U with respect to y, which is (x + 3). The price of x is $1, and the price of y is $2. Therefore, the marginal utility per dollar spent on x is MUx/Px = (y + 2)/1, and for y, it is MUy/Py = (x + 3)/2.For Harold to maximize his utility given his budget, he will equalize the marginal utility per dollar spent on each good. However, without specific income information, we can't solve for exact quantities. Yet, the utility function's structure suggests that as Harold consumes more of either good, the marginal utility per dollar spent on each good changes in a way that encourages the consumption of more x relative to y, given the prices and the way utility increases with consumption.The statement that Harold will consume "more than twice as many units of x as of y" is consistent with the idea that the lower price of x combined with the utility function's form encourages the consumption of x more heavily than y. This is because, for every unit of y that Harold considers buying, he could instead buy two units of x for the same price, and given the utility function, this would often provide more utility, especially considering the additional utility gained from consuming x is directly added to the utility function, while y's utility is also dependent on x's consumption. This encourages a consumption pattern where x is favored over y, likely leading to a scenario where Harold consumes more than twice as many units of x as of y, especially as income increases and allows for more of both goods to be consumed.

Harold's Utility Function Is U(x, Y)= (X + 3)(y