1. Let f(kt, lư) = [ak! + (1 - a)], P < 1, be the production function. The elasticity of substitution between the two in

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1. Let f(kt, lư) = [ak! + (1 - a)], P < 1, be the production function. The elasticity of substitution between the two inputs, capital and labor, is the percentage change in the ratio of inputs, ka, relative the percentage change in the marginal rate of substitution between the inputs, fake le. Specifically, let the elasticity of substitution be denoted ,lt) by T(kt, lt), where: (kt, lt) d/kt/lt) kt/lt dffA (kt,lt/fi(kt,lt)] fakt,lt)/fi(kt.lt) fakt.lt/fi.(kt.lt) kt/lt dfa (kt.lt) // (kelt)] dikt/lt) h. What is the firm's maximization problem? Solve this problem and give expressions for the wage rate, wt, and the rental rate for capital, flt, as a function of parameters and inputs. i. Will firms facing the same prices and having the same technology choose the same capital-labor ratio? Why, or why not? j. Is there an indeterminacy of the number of firms when firms have this technology? k. With this production function, what is the level of profits when the firm is opti- mizing?