Madison has an income of $50, which she spends on Pizza (P) and soft drinks (S). Her marginal rate of substitution is MRSPS = S/P. The price of pizza (PP) is $5 and the price of soft drinks (PS) is $2.50. Finally, the formula for her indifference curves is given by S = 2U/P (a) Find Madison's uncompensated demand curve for pizza. (b) Find Madison's compensated demand curve for pizza
What will be an ideal response?
(a) The tangency condition requires that (S/P) = (PP/PS), which implies that S = (PP/PS) P. Substitution into the budget line gives M = PPP + PS (PP/PS)P. Solving for P yields P = M/2PP. This is Madison's uncompensated demand curve for pizza.
(b) Madison's uncompensated demand curve for pizza is P = M/2PP. Similarly, S = M/2PS. Substituting for M, PP and PS yields the consumption bundle (5, 10). Madison's compensated consumption bundle must lie on the same indifference curve that passes through the point (5, 10). Substituting these values into the indifference curve formula yields 10 = 2U/5, which means U = 25. The formula for the indifference curve is thus S = 50/P.
Substituting PS = 2.50 into the tangency condition (S/P) = (PP/PS) yields S = PPP/2.50. A bundle can satisfy both the tangent condition and the budget line formula if PPP/2.50 = 50/P. Solving for P yields P = 125/PP. This is Madison's compensated demand curve for pizza.
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