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A4+Long+Run+Production+Function

A4+Long+Run+Production+Function - ii Truly circular iii Map...

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Frank Chapter 9 (Blue Book) q = 4K 1/2 L 1/4 What is the Long Run Production Function? What is the Long Run Average Total Product Function of Labor? What is the Long Run Marginal Product Function of Labor? What is the Long Run Average Total Product Function of Capital? What is the Long Run Marginal Product Function of Capital? Starting with the production function, q = L 1/4 K 1/2 , answer the following questions: 1. What is the Rate of Technical Substitution of this production function?

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a) Long Run Production Functions i) Assumptions (1) Single valued and continuous (2) Continuous 1 st and 2 nd derivatives (3) Inputs are continuously variable (4) Inputs and Production function do not change in character (5) Single Product ii) Functional Features (1) Can not have an additive constant (2) q(X 1 ,0) = q(0,X 2 ) = 0 (3) May be homogeneous (4) Cross derivatives are indeterminate b) Isoquant Maps (NOT Short Run) i) Contour Map for fixed output
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Unformatted text preview: ii) Truly circular iii) Map Knigthian Stages iv) Show efficient rages c) MRTS i) Fixed Output ii) Change in the amount of on input necessary to adjust for the change in another output iii) Negative to adjust for slope iv) RTS 1,2 = MP 1 /MP 2 = -dX 2 /dX 1 |q = q v) Prove from dq = 0 vi) Diminishing (1) Not purely a product of diminishing MP (a) MP is a partial assuming X 2 = X 2 (2) Mathematically true (a) P. 296 d) Common Shapes i) Linear (1) q = f(K,L) = aK + bL (2) σ 1,2 = ≡ ii) Fixed Proportions (1) q = f(K,L) = min(aK,bL) (2) σ 1,2 = 0 iii) Cobb Douglass (1) q = f(K,L) = AK a L b (2) σ 1,2 = 1, when a = b = 1 (always true?) (a) use Kas proof Answers TP = q = 4K 1/2 L 1/4 AP L = 4K 1/2 L-3/4 MP L = K 1/2 L-3/4 AP K = 4K-1/2 L 1/4 MP K = 2K-1/2 L 1/4 MRTS K,L = RTS K,L = (2K-1/2 L 1/2 )/( 2K 1/2 L-1/2 ) = L/K...
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A4+Long+Run+Production+Function - ii Truly circular iii Map...

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