If you like apples and oranges with the utility function, U=20C-C^2+18B-3B^2. 1)

Question

If you like apples and oranges with the utility function, U=20C-C^2+18B-3B^2.

1) If you do not regard money, how many apples and oranges should you consume? What is U? (I got: dU/dC=20-2C and dU/dB=18-6B for the partial derivatives, should I set these equations to 0 to find the optimum quantities for apples and oranges? Is this on the right track?)

2) If the doctor says that consumption should be restricted such that B+C=5, then how much should be consumed of each? What is U now? (I'm thinking that I should use the LaGrangian function with B+C=5 as the constraint?)

Explanation / Answer

1) yes, you are going right.

because, here consumer is not concern about money so, prices of goods does not matter. so for optimal bundles we put partial derivatives equal to 0

i.e dU/dC=20-2C = 0

C= 10

dU/dB=18-6B=0

B=3

2) now there is restriction that consumption is restricted to 5.

so, now we have to maximize utility function with constrained B+C=5

your method is correct

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