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)
