penn101_09s_hw2sol

penn101_09s_hw2sol - Intermediate Microeconomics(Econ 101...

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Unformatted text preview: Intermediate Microeconomics (Econ 101) Spring, 2009 Solutions to Additional Problems in Assignment 2 Solution to Question 1. Since the consumer has a constant MRS, the two goods must be perfect substitutes. Since good 2 is twice as expensive as good 1, we have p 1 p 2 = 1 2 > 1 3 = | MRS | . Therefore the consumer’s gross demand for good 1 is 0 and he only consumes good 2. This means she would sell all her endowment of good 1 and buys good 2. Solution to Question 2. (1) True. Since p 2 decreases, the relative price for good 1 ( p 1 p 2 ) increases. The substitution effect for good 1 is negative. But since the total effect for good 1 is an increase in demand, the income effect must be positive (and big enough to offset the negative substitution effect), which means the demand for good 1 increases as income increases, and hence good 1 must be a normal good. Alternatively, you can use a graph to explain this. Draw a budget line for the new price ratio through the initial optimal choice (as you would do when decomposing the substitu- tion effect and income effect for good 2). The argument for the negative sign of substitution effect leads us to conclude the new optimal choice must be a point to the left of the initial optimal choice, i.e., x 1 decreases. Since the total effect on good 1 is an increase in con- sumption, when the intermediate budget line moves out to the new budget line under the new price ratio and the initial income, x 1 must increase. This means good 1 is a normal good. (2) False. It is easy to construct examples where good 2 is normal. In fact, we cannot conclude whether good 2 is normal or inferior. Both cases are consistent with the information given.whether good 2 is normal or inferior....
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penn101_09s_hw2sol - Intermediate Microeconomics(Econ 101...

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