Question

Sarah's utility function is represented as: U = F0.5C0.5, F is quantity of food and C is quantity of clothing. If Sarah's budget constraint is represented as: 120 = 2F + C, Sarah's optimal bundle of consumption should be Group of answer choicesA.​(50F, 50C).
B.​(45F, 20C).


C.​(40F, 40C).


D.​(20F, 60C)

Answer 1

Explanation:

Utility function is given by U=F^0.5C^0.5

Find the MRS which is -MUF / MUC

MUF = dU/dF = 0.5F^-0.5C^0.5

MUC = dU/dC = 0.5F^0.5C^-0.5

Now MRS = -(0.5F^-0.5C^0.5) / (0.5F^0.5C^-0.5)

= -(C^0.5C^0.5)/(F^0.5F^0.5)

= - C/F

From the budget constraint, we have slope = -Price ratios = -coefficient of F / coefficient of C = -2/1 or -2.

At the optimal choice, utility function is tangent to budget line so MRS = slope of budget line

- C/F = -2

C = 2F

Use C = 2F in the budget equation

120 = 2F + 2F

120 = 4F

F = 120/4 = 30 units

Then C = 2F = 2*30 = 60 units

Hence her optimal bundle of consumption should be 30F and 60C

(This is the correct answer. For a generalized results, I have attached the derivation of formulas)