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7. Suppose a perfectly competitive firm uses capital and labor to produce a single output. The...
3. Suppose a perfectly competitive firm uses capital and labor to produce a single output. The...
3. Suppose a perfectly competitive firm uses capital and labor to produce a single output. The firm's exogenous price for output is Po. The firm's exogenous cost for capital is ro. The firm's exogenous cost for laboris Wo. The firm's production function is given by Q = f(K, L) where: 8f/8K, 8f/8L >0, 82f/8K2, 82f/8L2 <0, and 82f/8K6L = 0 a) Given the profit function for the firm. b) Find the FOC's for K* and L* that allow profit maximization....
suppose a perfectly competitive firm produces 2 outputs. The firm's price for the first output is...
suppose a perfectly competitive firm produces 2 outputs. The firm's price for the first output is Pi and the price for the second output is P2. The cost function is given by: C(Q1, Q2) = 20,2 + 2022 a) Give the profit function for the firm. b) Find the FOC's for profit maximization and interpret them economically. c) Find the SOC's.
Given a perfectly competitive firm in the input and output markets where: P0= exogenous price, Q...
Given a perfectly competitive firm in the input and output markets where: P0= exogenous price, Q = f(L, K0) where dQ/dL > 0 and d2Q/dL2< 0, the cost function where: C(L, K0) = r0K0+ w0L; r0= exogenous rental rate of capital, K0= exogenous capital stock, and w0= exogenous wage. a)State the firm’s profit function in terms of L. b)Find the F.O.C. that maximizes profit at L*. c)Interpret the F.O.C. d)Find the S.O.C. that maximizes profit at L*. e)Interpret the S.O.C....
A firm uses two types of inputs, labor (L) and capital (K), to produce an output,...
A firm uses two types of inputs, labor (L) and capital (K), to produce an output, which is sold in a perfectly competitive market. The production function is given by y = f(L, K) = L 1 6 K 1 6 for all L, K ≥ 0. The price of labor is w > 0 and the price of capital is 1. Each unit of the output is sold at price p > 0. First, we consider the short-run decision...
A firm produces output Q by using capital K and labor L in fixed proportions, i.e....
A firm produces output Q by using capital K and labor L in fixed proportions, i.e. Q = F (K ,L ) = min {K, L/3}. The price of a unit of labor is w = 6, the price of a unit of capital is r = 2 and the price of output is p = 20. a) Draw the isoquant for Q = 8. b) Find the marginal product of labor. Suppose that (in part c and d) the...
9. A firm uses capital and labor to produce a single output good. The production function...
9. A firm uses capital and labor to produce a single output good. The production function is given by F(K,L)=K^0.5L, where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, respectively r=$5 and w=$6. Based on this information, characterize the optimal (output maximizing) allocation of inputs given that the firm decided to limit its total cost to $12,000. Illustrate your solution graphically:...
Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two...
Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two inputs of production; each unit of labor is paid the market wage (w), and each unit of capital is rented at the rental price of capital (r). Output (Y) is therefore a function of labor and capital, or Y = f (K, L), and is sold at the market price (P). The goal of this firm is to maximize profit given the price of...
A perfectly competitive firm uses a single input (labor) to produce a good according to a...
A perfectly competitive firm uses a single input (labor) to produce a good according to a production function Q(L) = 2/7 , where Lis the amount of labor it uses. The good sells for $180 per unit (price). The input costs $15 per unit (wage). 1. (20 pts) What is the profit-maximizing amount of input (L)? 2. (10 pts) What is the profit-maximizing amount of output (Q)? 3. (10 pts) How much profit does the firm make when it maximizes...
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital...
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital (K). The firm's production function is Q f(L, K) = min{L, K}}. The per-unit price of labor is w = 1 and the per-unit price of capital is r = 1. Recently, the government imposed a tax on Julia's firm: For each unit of labor that Julia employs, she must pay a tax of £t to the government. (a) Graph the Q unit of...
Suppose that we have perfectly competitive input markets (for both capital and labor) and output markets....
Suppose that we have perfectly competitive input markets (for both capital and labor) and output markets. Firm "Tropical Juice" produces orange juice which it sells at $6. The input price that the firm faces is an hourly wage of $5 and the rental rate of $2. Furthermore, the firm currently has a capital stock of 2. Find the labor demanded by the firm in the short run under the following production technologies. a) f(k,l) = k0.1l0.9 b) f(k,l) = max{k,...
3. Suppose a perfectly competitive firm uses capital and labor to produce a single output. The firm's exogenous price for output is Po. The firm's exogenous cost for capital is ro. The firm's exogenous cost for laboris Wo. The firm's production function is given by Q = f(K, L) where: 8f/8K, 8f/8L >0, 82f/8K2, 82f/8L2 <0, and 82f/8K6L = 0 a) Given the profit function for the firm. b) Find the FOC's for K* and L* that allow profit maximization....
suppose a perfectly competitive firm produces 2 outputs. The firm's price for the first output is Pi and the price for the second output is P2. The cost function is given by: C(Q1, Q2) = 20,2 + 2022 a) Give the profit function for the firm. b) Find the FOC's for profit maximization and interpret them economically. c) Find the SOC's.
Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two inputs of production; each unit of labor is paid the market wage (w), and each unit of capital is rented at the rental price of capital (r). Output (Y) is therefore a function of labor and capital, or Y = f (K, L), and is sold at the market price (P). The goal of this firm is to maximize profit given the price of...
A perfectly competitive firm uses a single input (labor) to produce a good according to a production function Q(L) = 2/7 , where Lis the amount of labor it uses. The good sells for $180 per unit (price). The input costs $15 per unit (wage). 1. (20 pts) What is the profit-maximizing amount of input (L)? 2. (10 pts) What is the profit-maximizing amount of output (Q)? 3. (10 pts) How much profit does the firm make when it maximizes...
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital (K). The firm's production function is Q f(L, K) = min{L, K}}. The per-unit price of labor is w = 1 and the per-unit price of capital is r = 1. Recently, the government imposed a tax on Julia's firm: For each unit of labor that Julia employs, she must pay a tax of £t to the government. (a) Graph the Q unit of...
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