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3. Suppose that Karen’s utility function is given by U = 2A + 5B. a. Calculate...

3. Suppose that Karen’s utility function is given by U = 2A + 5B. a. Calculate Karen’s marginal utility of good A and her marginal utility of good B. b. Suppose that the prices of the goods PA and PB are such that Karen is (optimally) consuming positive quantities of both goods. What is the price of good A in terms of the price of good B? c. How will her consumption change if PA doubles, while PB does not change?

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Answer #1

a. MUA = ∂U/∂A = 2
MUB = ∂U/∂B = 5

b. This is a substitutes goods utility function where both the goods are consumeed only if MRS equals price ratio.
So, MRS = MUA/MUB = PA/PB
So, 2/5 = PA/PB
So, PA = 2PB/5
So, PA = 0.4PB

c. If PA doubles while PB is constant, then price ratio will increase which means MRS becomes less than the price ratio. So, only good B will be consumed.
Thus, she will not consume any amount of good A and buy good B with all of her income.

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