Question

Paul consumes only books and DVDs. At his current consumption​ bundle, his marginal utility from DVDs is 21 and from books is 4 . Each DVD costs ​$11 ​, and each book costs ​$1 . Is he maximizing his​ utility? Explain. Let MU Subscript Upper B be the marginal utility of​ books, MU Subscript Upper D be the marginal utility from​ DVDs, Upper P Subscript Upper B be the price of​ books, Upper P Subscript Upper D be the price of​ DVDs, and MRS be the marginal rate of substitution. Paul is

Answer 1

Paul is NOT maximizing his utility.

Step-by-step explanation:

Given:

MU
`_(D)` = Marginal utility from DVDs = 21

MU
`_(B)` = Marginal utility from books = 4

P
`_(D)` = Price of DVDS = $11

P
`_(B)` = Price of books = $1

Under the utility maximization theory for two or more goods, utility is said to be maximized by a consumer when the ratios of the marginal utility to price per unit of each good are equal to each other. For this question, this implies that when we have:

MU
`_(D)` / P
`_(D)` = MU
`_(B)` / P
`_(B)` ………………………….. (1)

Therefore, we have:

MU
`_(D)` / P
`_(D)` = 21 / 11 = 1.91

MU
`_(B)` / P
`_(B)` = 4 / 1 = 4

Since 1.91 = MU
`_(D)` / P
`_(D)` < MU
`_(B)` / P
`_(B)` = 4, this implies that these conditions are NOT consistent with equation (1). Therefore, Paul is NOT maximizing his utility.

In order to maximize his utility, Paul should consume more DVDs and consume less books until these conditions are consistent with equation (1).