Recipes2 - ADDITIONAL RECIPES AND FORMULAS FOR EXAM 2 Short-cuts for Cobb-Douglas production functions q = AL α K β Average product of labor AP L

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Unformatted text preview: ADDITIONAL RECIPES AND FORMULAS FOR EXAM 2 Short-cuts for Cobb-Douglas production functions q = AL α K β Average product of labor: AP L = AK β L 1- α since AP L = q L = AL α K β L = AK β L 1- α ! Average product of capital: AP K = AL α K 1- β since AP K = q K = AL α K β K = AL α K 1- β ! Marginal product of labor: MP L = α q L since MP L = ∂q ∂L = αAL α- 1 K β = α AL α K β L = α q L ! Marginal product of capital: MP K = β q K since MP K = ∂q ∂K = βA L α K β- 1 = β AL α K β K = β q K ! Slope along isoquants: d K d L =- α β K L since d K d L =- MP L MP K =- ∂q ∂L ∂q ∂K =- α q L β q K =- α β q L q K =- α β q L × K q =- α β K L ! Returns to scale: if q 1 = AL α K β and q 2 = A (2 L ) α (2 K ) β , then q 2 = 2 α + β q 1 since q 2 = A (2 L ) α (2 K ) β = A 2 α L α 2 β K β = 2 α 2 β ( AL α K β ) = 2 α + β q 1 ! so returns to scale are decreasing if α + β < 1, constant if α + β = 1, and increasing if α + β > 1 1 Useful formulas for manipulating equations with exponents:...
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This note was uploaded on 04/02/2008 for the course FIN 4900 taught by Professor Spam during the Spring '08 term at Wyoming.

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Recipes2 - ADDITIONAL RECIPES AND FORMULAS FOR EXAM 2 Short-cuts for Cobb-Douglas production functions q = AL α K β Average product of labor AP L

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