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.