Question

Given the following utility function:

U 10X + 20Y
and marginal utilities:
MUx = 10, MU, = 20
A consumer facing the following prices:
Px = $2, Py =2
chooses to consume:
10 units of good X and 9 units of good Y.
Assume that graphically good X is on the horizontal axis and good Y is on the vertical axis.
Given this consumption bundle, the marginal rate of substitution is equal to - included.). (Round your answer to two decimal places. Note that the minus sign is already
Given this value, the consumer should consume
in order to maximize his/her utility.

Answer 1

To maximize utility, the consumer should choose a consumption bundle where the MRS is equal to the ratio of the prices. In this case, the consumer should consume both goods in a ratio of 10:1.

Step-by-step explanation:

To find the utility-maximizing consumption bundle, we can use the concept of the marginal rate of substitution (MRS). The MRS is the rate at which a consumer is willing to give up one good in exchange for another while keeping utility constant. It is equal to the ratio of the marginal utilities of the two goods. In this case, the MRS is equal to -10.

To maximize utility, the consumer should choose a consumption bundle where the MRS is equal to the ratio of the prices of the goods. Given the prices of both goods are $2, the consumer should consume both goods in a ratio of 10:1, since 10/-10 = 2/2.