3 Production Function with Two Inputs Assume that a firm choose K and L inputs. At the start of a period, a firm rents K inputs and hircs L inputs to produce Y. At the end of the period, the firm sclls Y and pays intercest rates based on how much capital it rented and wage costs. Profits is denoted by a. period interest rate is r, wage is w, the price of output is p, and the production function is Cobb-Douglas. Please see the Firm's Profit Maximization Problem with Cobb Douglas Production Function (Decreasing Returns to Scale). 1. Formulate the profit maximization problem.

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3
Production Function with Two Inputs
Assume that a firm choose K and L inputs. At the start of a pcriod, a firm rents K inputs and
hircs L inputs to produce Y. At the end of the period, the firm sclls Y and pays intercst rates
based on how much capital it rented and wage costs. Profits is denoted by 7, period interest rate is
r, wage is w, the price of output is p, and the production function is Cobb-Douglas. Please see the
Firm's Profit Maximization Problem with Cobb Douglas Production Function (Decreasing Returns
to Scale).
1. Formulate the profit maximization problem.
2. What are the derivatives of profit with respcct to capital and labor choiccs? Idcntify the
marginal products of capital and marginal products of labor.
3. Log linearize the optimality conditions, and present them in matrix form.
Transcribed Image Text:3 Production Function with Two Inputs Assume that a firm choose K and L inputs. At the start of a pcriod, a firm rents K inputs and hircs L inputs to produce Y. At the end of the period, the firm sclls Y and pays intercst rates based on how much capital it rented and wage costs. Profits is denoted by 7, period interest rate is r, wage is w, the price of output is p, and the production function is Cobb-Douglas. Please see the Firm's Profit Maximization Problem with Cobb Douglas Production Function (Decreasing Returns to Scale). 1. Formulate the profit maximization problem. 2. What are the derivatives of profit with respcct to capital and labor choiccs? Idcntify the marginal products of capital and marginal products of labor. 3. Log linearize the optimality conditions, and present them in matrix form.
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