Question

Suppose your utility is given by U(A,B)=10A+B

a) Find the marginal utility of each good

b) What is the marginal rate of substitution?

c)If I(income)=20, pa=5, pb=2 what is the optimal consumption of
products A and B?

Answer #1

a. MU of A = U/A.

MU of A = 10.

Similarly, MU of B = U/B.

MU of B = 1.

b. MRS A,B = MU-A/MU-B.

MRS = 10/1 or 10.

c. Clearly, in the given utility function, both the goods A & B are perfect substitutes of each other, because the utility function is additive. This means, either good A or good B would be consumed, and depends on their respective prices. Since Pb < Pa, so all the money income would be spent on good B.

Consumption og B = m/Pb = 20/2 or 10 units.

Consumption of A = 0.

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