Given the the utility function UFC FC and this budget const

Given the the utility function U(F,C) = (FC), and this budget constraint: 100,000 = 4F+40C,

a. What is the marginal rate of substitution of F for C when utility is maximized? Explain.

Solution

At the pareto optimal point,

MRS = Price ratio

That is,

MRS(F,C) = PF/PC

C/F = 4/40

C/F = 1/10

Therefore, MRS = 0.1