Tina consumes only fuel and carpet. Her utility function is U(F, C) = 2C 0.5F 0.5...

Tina consumes only fuel and carpet. Her utility function is U(F, C) = 2C 0.5F 0.5 , in which C is the number of carpet and F is the number of fuel. She has $200 in her pocket right now and plans to spend all of her money on carpet and fuel. The price of one unit of carpet is $4 and the price of one unit of fuel is $1. (a) Define the constrained utility maximization problem. (b) Write out the budget constraint equation. Graph it. Label the axes and intercepts. (c) What is the optimality condition? How is this point represented in the graph? (d) What is her marginal utility with respect to fuel (MUF )? (e) What is her marginal utility with respect to carpet (MUC )? (f) What is her marginal rate of substitution (MRS)? (g) What is her marginal rate of transformation? (h) Solve for the optimal (utility- maximizing) bundle. Use any method. (i) Bonus: How much utility does this bundle provide?

Solutions

Expert Solution

A. Maximize utility subject to budget constraint

Thus maximise utility= 2C^.5F^.5

B. Budget constraint 4C+F=200

C. At optimality MRS=MUF/MUC=PF/PC.

It means slope of budget line is equal to slope of indifference curve. i.e. a point where budget line is tangent to indifference curve

D. MUF=dU/dF=2(0.5)C^0.5 F^-0.5

E. MUC= C^-0.5F^0.5

f. MRS=MUF/MUC=C/F

G. MRT=PF/PC=1/4

H. At optimality C/F=1/4. F=4C

Put in budget line. 8C=200. Thus C=25 and F=100

I. Utility=2*25^0.5100^0.5=2×5×10=100

Rahul Sunny answered 1 year ago

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