MECON PS3 sol

# MECON PS3 sol - Microeconomics 100A Problem Set 3 Solutions...

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8 Slope =-2 4 Slope =-1 2 6 X e. If she buys only Z, she can have 8Z. To get the first X she must give up 2Z. To get the second X she must also give up 2Z (note that the slope of the budget line is -2=Px/Pz=\$10/\$5). Now that she has two X, the price falls to \$5 and so, to get the third X, she only has to give up one Z (note that the slope of the budget line is -1=Px/Pz=\$5/\$5). 2. Toni’s utility is 3 2 3 ) , ( z x z x U = a. Does Toni consider X and Z goods? (“Goods” are items we like more of, ie. more is better. “Bads” are items that we like to have less of, ie. less is better. For example, pizza is a good. Garbage is a bad.) Prove your answer. b. What is Toni’s marginal rate of substitution between goods x and z (her MRS)? c. Are Toni’s indifference curves convex? Prove you answer. a. X and Z are goods (assuming x and z>0) because MU is positive for x and z. 3 6 ) , ( xz x z x U = >0 and 2 2 9 ) , ( z x z z x U = >0 b. The MRS is x z z x xz z z x U x z x U MRS 3 2 9 6 ) , ( ) , ( 2 2 3 - = - = - = , Yes, the indifference curves are convex since the absolute value of MRS falls as z decreases and x increases. 3.
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MECON PS3 sol - Microeconomics 100A Problem Set 3 Solutions...

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