Question

A consumer's utility function is U = ln(xy^2) (a) Find the values of x and y which maximise utility subject to the budgetary constraint 12x + 4y = 108. Use the method of substitution to solve this problem. (b) Show that the ratio of marginal utility to price is the same for x and y. (a) x = 3 and y = 18 (Simplify your answers.) (b) The values of the marginal utilities at the optimum are ?U/?x = [ ] and ?U/?y = [ ] (Give your answers to three decimal places as needed.)

          A consumer's utility function is U = ln(xy^2)
(a) Find the values of x and y which maximise utility subject to the budgetary constraint 12x + 4y = 108. Use the method of substitution to solve this problem.
(b) Show that the ratio of marginal utility to price is the same for x and y.
(a) x = 3 and y = 18 (Simplify your answers.)
(b) The values of the marginal utilities at the optimum are
?U/?x = [ ] and ?U/?y = [ ]
(Give your answers to three decimal places as needed.)

A consumer's utility function is U = ln(xy^2)
(a) Find the values of x and y which maximise utility subject to the budgetary constraint 12x + 4y = 108. Use the method of substitution to solve this problem.
(b) Show that the ratio of marginal utility to price is the same for x and y.
(a) x = 3 and y = 18 (Simplify your answers.)
(b) The values of the marginal utilities at the optimum are
?U/?x = [ ] and ?U/?y = [ ]
(Give your answers to three decimal places as needed.)

Added by Guillermo C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/20/2023

Step 1

We can rewrite the budget constraint as follows: 12x + 4y = 108 Divide both sides by 4: 3x + y = 27 Now, we can solve for y in terms of x: y = 27 - 3x Show more…

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A consumer's utility function is U = ln(xy^2). (a) Find the values of x and y which maximize utility subject to the budgetary constraint 12x + 4y = 108. Use the method of substitution to solve this problem. (b) Show that the ratio of marginal utility to price is the same for x and y. (a) x = 3 and y = 18 (Simplify your answers.) (b) The values of the marginal utilities at the optimum are [missing information] and [missing information]. (Give your answers to three decimal places as needed.)