PAM200_Section 3_Solutions

# PAM200_Section 3_Solutions - PAM200 Section 3 Problem 4.2 a...

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PAM200 – Section 3 Problem 4.2 a) Ann is spending all of her income, I=22, buying 8 units of food, F=8, Find C: 7 14 2 22 2 8 2 1 = = = + = + C C C I C F b) 0 2 4 6 8 10 12 0 5 10 15 20 25 30 35 Food Clothing c) Yes, the indifference curves are convex, i.e., bowed in toward the origin. They intersect the horizontal axis. .

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0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 35 Food Clothing U=36 U=72 d) 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 35 Food U=36 U=72 Optimum at F=12, C=5 e) The tangency condition is C F C F P P MU MU = Plugging in the known information, we have that F C F C = + = + 2 2 2 1 1 Substituting this result into the budget line, 22 2 1 = + C F results in
5 20 4 22 2 ) 2 2 ( = = = + + C C C C Finally, plugging this result back into the tangency condition implies that 12 2 ) 5 ( 2 = + = F . At the optimum the consumer chooses 5 units of clothing and 12 units of food. f) 2 1 12 1 5 1 , = + = + = F C MRS C F The marginal rate of substitution is equal to the price ratio and to the slope of the indifference curve. g)

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PAM200_Section 3_Solutions - PAM200 Section 3 Problem 4.2 a...

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