Cobb Douglas Production Function

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CHAPTER 7 HOMEWORK Suppose the following Cobb-Douglas production function was estimated using monthly data over a 3-year period: LnQ = 0.18 + 0.28 LnL + 0.63 LnK + 0.12 LnF R2 = 0.82 (3.0) (1.87) (5.25) (1.71) Where: Q = output in millions of passenger miles L = labor input in worker hours K = Capital input in bus transit hours F = fuel input in gallons. The numbers in parenthesis are t-values. A. Rewrite the equation in the form of the power function (i.e. without the logarithms) LnQ= 0.18 + 0.28 LnL + 0.63 LnK + 0.12 LnF LnQ= 0.18 + 0.28(10,000) + 0.63(7000) + 0.12(8000) LnQ= 0.18 + 2.58 + 5.58+ 1.08 =9.42 Anti-Log= 12,332.58 B. Estimate the output Q when L=10,000 hours; K = 7,000 hours; and F = 8,000 gallons MP (L)= a*Q/L = 0.28*12,332.58/10,000= 0.345 MP (K)= b*Q/K= 0.63*12,332.58/7000= 1.109 MP (F)= c*Q/F= 0.12 12,332.58/8000= 0.184 C. Find the marginal products of Labor, Capital and Fuel when L=10,000 hours; K = 7,000 hours; and F = 8,000 gallons Output elasticity of L= 0.28 Output elasticity of K= 0.63 Output elasticity of F= 0.12. L+K+F= 1.03. A 10% increase in L= 0.31, K = 0.69, F= 0.13. L increased by 10% then output increases by = 0.03 K increased by 10% then output increases by = 0.07 F increased by 10% then output increases by = 0.01 D. Find the output elasticities of L, K and F. By how much does output increase when each input increases by 10%, one at a time? L+K+F= 1.03 Output increase by 10% at a time: L= .31 K= .68 F= .13 10% increase in: L, Output increase by .03 K, Output increase by .07 F, Output increase by .01 E. Determine the Returns to Scale in production. By how much does output increase when all inputs increases by 10%, at the same time? L+K+F= 1.03 Increase of 10% in L, K and F causes increase in quantity produced Output= .11

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