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The utility function and the prices are the following: U = 40 x1 + 20 x2...

The utility function and the prices are the following:

U = 40 x1 + 20 x2

P1=4,   P2=3 and I =1,200

What is the level of maximized utility?

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Answer #1

Marginal rate of substitution for the utility function is MUX1/MUX2 = 40/20 = 2. Price ratio is P1/P2 = 4/3 = 1.33

Since the marginal rate of substitution is greater than the price ratio, utility is maximized when only X1 is consumed. This indicates that the consumer will be purchasing 1200/4 = 300 units of X1. Maximum utility is 40*300 = 12000

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