Question 1 Suppose that a firm produces output with capital and labor. Suppose that the production function is given by: S(k,l) = k÷1+ As usual, w denotes the wage rate, r denotes the rental price of capital, p denotes the price of output, and ydenotes the firm's target output level. Suppose that w = 1, r = 1, p = 1. We assume that factor markets are perfectly competitive (the factor supply functions are perfectly clastic). We also assume that the firm faces a perfectly competitive output market. 1. Set up and solve the firm's one step profit maximization problem. Obtain the firm's labor and capital demand, the firm's output, and its profits. 2. Set up and solve the firm's cost minimization problem. Find the firm's conditional labor and capital demands, minimum cost, and marginal cost if the firm must produce the output in part (1) at minimum cost. 3. Plot the solution to the cost minimization problem making sure that you label all important components of your plot. Plot the isoquant in red and the isocost line in blue. 4. Set up and solve the firm's two step profit maximization problem. Plot your solution in price output space. Draw the price line in black and marginal cost in red. Make sure vou label everything clearly.
Question 1 Suppose that a firm produces output with capital and labor. Suppose that the production function is given by: S(k,l) = k÷1+ As usual, w denotes the wage rate, r denotes the rental price of capital, p denotes the price of output, and ydenotes the firm's target output level. Suppose that w = 1, r = 1, p = 1. We assume that factor markets are perfectly competitive (the factor supply functions are perfectly clastic). We also assume that the firm faces a perfectly competitive output market. 1. Set up and solve the firm's one step profit maximization problem. Obtain the firm's labor and capital demand, the firm's output, and its profits. 2. Set up and solve the firm's cost minimization problem. Find the firm's conditional labor and capital demands, minimum cost, and marginal cost if the firm must produce the output in part (1) at minimum cost. 3. Plot the solution to the cost minimization problem making sure that you label all important components of your plot. Plot the isoquant in red and the isocost line in blue. 4. Set up and solve the firm's two step profit maximization problem. Plot your solution in price output space. Draw the price line in black and marginal cost in red. Make sure vou label everything clearly.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Question 1
Suppose that a firm produces output with capital and labor. Suppose that the production function is given
by:
f(k, l) = k+1ł
As usual, w denotes the wage rate, r denotes the rental price of capital, p denotes the price of output, and
ydenotes the firm's target output level. Suppose that w = 1, r = 1, p = 1. We assume that factor markets
are perfectly competitive (the factor supply functions are perfectly clastic). We also assume that the firm
faces a perfectly competitive output market.
1. Set up and solve the firm's one step profit maximization problem. Obtain the firm's labor and capital
demand, the firm's output, and its profits.
2. Set up and solve the firm's cost minimization problem. Find the firm's conditional labor and capital
demands, minimum cost, and marginal cost if the firm must produce the output in part (1) at minimum
cost.
3. Plot the solution to the cost minimization problem making sure that you label all important components
of your plot. Plot the isoquant in red and the isocost line in blue.
1. Set up and solve the firm's two step profit maximization problem. Plot your solution in price output
space. Draw the price line in black and marginal cost in red. Make sure you label everything clearly.
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