4) Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2). Consumers' endowments are e1 = (4, 2) and e? = (6, 6) And their preferences are represented by utility functions: u Cr.v) = x³y and a (x,y) = x³y} (d) Set up the utility maximization problem for each consumer and solve for their Marshallian demand functions. (e) Compute the market demand for each good. (f) State the Walrus law for this economy and explain its economic interpretation.

ENGR.ECONOMIC ANALYSIS
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Author:NEWNAN
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Chapter1: Making Economics Decisions
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4)
Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2).
Consumers' endowments are
e1 = (4, 2) and e? = (6, 6)
And their preferences are represented by utility functions:
u(x, y) = x³y and u(x,y) = x³y$
(d) Set up the utility maximization problem for each consumer and solve for their
Marshallian demand functions.
(e) Compute the market demand for each good.
() State the Walrus law for this economy and explain its economic interpretation.
(g) Assume the excess demand for good x is zero, i.e., EDx = 0, and calculate the
ratio of prices, i.e., p Ipy . Then, use this ratio of prices to show that the
excess demand for good
Yis also zero, i.e., EDy= 0. Briefly explain how this relates to the Walrus' law.
(h) Given the price ratio found above, calculate the equilibrium allocations and show
that feasibility, individual rationality, and Pareto efficiency holds.
Transcribed Image Text:4) Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2). Consumers' endowments are e1 = (4, 2) and e? = (6, 6) And their preferences are represented by utility functions: u(x, y) = x³y and u(x,y) = x³y$ (d) Set up the utility maximization problem for each consumer and solve for their Marshallian demand functions. (e) Compute the market demand for each good. () State the Walrus law for this economy and explain its economic interpretation. (g) Assume the excess demand for good x is zero, i.e., EDx = 0, and calculate the ratio of prices, i.e., p Ipy . Then, use this ratio of prices to show that the excess demand for good Yis also zero, i.e., EDy= 0. Briefly explain how this relates to the Walrus' law. (h) Given the price ratio found above, calculate the equilibrium allocations and show that feasibility, individual rationality, and Pareto efficiency holds.
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