An agent has utility u(x1, x2) = (x-11+x-12)-1for goods x1 and x2. The prices of the goods are p1 and p2. The agent has income m. a) Show preferences are convex. You can do this graphically or by showing that MRS is decreasing in x1. b) Solve for the agent’s optimal choice of (x1, x2). c) Show the agent’s indirect utility function is given by:V=m(p1/21 + p1/22)2
An agent has utility u(x1, x2) = (x-11+x-12)-1for goods x1 and x2. The prices of the goods are p1 and p2. The agent has income m. a) Show preferences are convex. You can do this graphically or by showing that MRS is decreasing in x1. b) Solve for the agent’s optimal choice of (x1, x2). c) Show the agent’s indirect utility function is given by:V=m(p1/21 + p1/22)2
Chapter7: Consumer Choice: Maximizing Utility And Behavioral Economics
Section: Chapter Questions
Problem 1WNG
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An agent has utility u(x1, x2) = (x-11+x-12)-1for goods x1 and x2. The prices of the goods are p1 and p2. The agent has income m.
a) Show preferences are convex. You can do this graphically or by showing that MRS is decreasing in x1.
b) Solve for the agent’s optimal choice of (x1, x2).
c) Show the agent’s indirect utility function is given by:V=m(p1/21 + p1/22)2
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