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hw7 - Homework Assignment 7 Econ 121b Intermediate...

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Homework Assignment # 7 Econ 121b. Intermediate Microeconomics (This homework is for practice only; it will not be graded.) 1. Consider an economy with two consumers ( A and B ), one firm, two consumption goods (1 and 2) and two input goods (capital and labor). Technology: The firm’s production functions are: y 1 D f 1 .k 1 ; ` 1 / D k ˇ 1 ` 1 ˇ 1 and y 2 D f 2 .k 2 ; ` 2 / D p k 2 ` 2 ; where ˇ 2 . 1 2 ; 1/ is a technology parameter and y 1 , k 1 and ` 1 denote the output and input levels in the production of good 1, respectively, and likewise for good 2. Preferences: Consumers’ utility functions are as in HW#6: u A .x A 1 ; x A 2 / D .x A 1 / ˛ .x A 2 / 1 ˛ and u B .x B 1 ; x B 2 / D q x B 1 x B 2 : Endowments: The consumption good is in zero net supply. Each consumer has an endowment of L units of labor and K units of capital. Thus, the levels of consumption and labor are subject to the usual feasibility constraints: x A 1 C x B 1 D y 1 x A 2 C x B 2 D y 2 k 1 C k 2 D 2K ` 1 C ` 2 D 2L: (a) Define the production possibilities frontier
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