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Unformatted text preview: Problem Set #4 1 Production Functions - Basics 1. For the following production functions, find expressions for the Marginal Rate of Technical Substitution and sketch a typical Isoquant. (a) x = L α K 1- α (b) x = α ln L + (1- α )ln K (c) x = ( L- δ ) α K 1- α , where δ is a positive parameter. (d) x = Min [ αL, (1- α ) K ] 2. In consumer theory, we saw that production functions ( a ) and ( b ) were identical representations of preferences. Is this true for production functions? Do these functions have the same properties with regards to returns to scale? Consider the Generalized Constant Elasticity of Substitution Function x = A bracketleftBig σL α + (1- σ ) K α + αγL δ K α- δ bracketrightBig 1 α where α , σ , and γ are positive parameters. 3. Show that this function exhibits Constant Returns to Scale. 4. What is the Marginal Rate of Technical Substitution for this function?...
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This note was uploaded on 11/12/2009 for the course ECONOMICS 701 taught by Professor Baker during the Spring '09 term at CUNY Hunter.
- Spring '09