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Consider the following production function:Y = AK^αL^(1-α) where Y is units of output, K is units of capital, and L is units of labor. Both Aand are constant parameters characterizing the production technology.
(a) Derive the function for the marginal product of K.
(b) Derive the function for the marginal product of L.
(c) If 0 < α < 1, does diminishing marginal returns apply to K? To L?
(d) Does the function exhibit increasing, constant, or decreasing returns to scale?
(e) Derive the expression for the marginal rate of technical substitution for thisproduction function.(f ) If α = 0.3, the price of capital is $10 per unit and price of labor is $15 perunit, what is the cost-minimizing ratio of capital to labor.
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sales 1990 116 1991 105 1992 29 1993 59 1994 108 1995 94 1996 27 1997 119 1998 34 1999 34 2000 48 2..
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Historical records show that 70 structures with 800 square feet of floor space and 8 foot ceilings were produced in 1999.Then the materials cost for each structure was $25,000 and the cost capacity factor is 0.65. Cost index values for 1999 and 20..
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