7. [Profit Maximizing Input Demand-II] Consider a competitive firm with the following profit function ? =...
7. [Profit Maximizing Input Demand-II] Consider a competitive firm with the following profit function
? = PQ?wL?rK,
where P = 3, w = 1 and r = 1 and
Q(K,L) = 9K^1/3L^1/3 .
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7. [Profit Maximizing Input Demand-II] Consider a competitive
firm with the following profit function
? =...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
Consider an industry with 7 identical competitive firms. The production function of a representat...
Consider an industry with 7 identical competitive firms. The production function of a representative firm is q = min{√x1, √x2}, where x1 and x2 are the inputs that the firm uses to produce output q. Suppose that the input prices are w1 = 4 and w2 = 3. The demand function is q^D(p) = 48 − p. Assume that firms cannot enter or exit the market. Find the equilibrium price and quantity. Compute the profit of each firm.
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...
2. Consider the following cost minimization problem. A firm minimizes total cost given by, TC =...
2. Consider the following cost minimization problem. A firm minimizes total cost given by, TC = wL+rK subject to an output constraint as given by the production function, y=f(K,L)=8K05 +420S, where TC refers to total cost, L is labor input, K is capital input, r is the price of capital, w is the wage rate, and y is output. a. Derive the factor demand functions and the optimal cost function. The first order conditions and all the steps involved in...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,r,q) and labor L*(w,r,q), and the long run minimized cost C* (w,r,q). (Hint: reduce the cost function for the next part. (b) Setup and solve the profit maximization problem over quantity using the cost function you solved for in the previous part. Solve for the profit maximizing quantity q *(p,w,r), cost...
1.1. What is the set of profit-maximizing inputs if the profit function of a firm is...
1.1. What is the set of profit-maximizing inputs if the profit function of a firm is given by: π(X, Y) = P ln[X + aY] – wX – wY where P - price of output f(X,Y) = ln[X + 0.5Y] - production function X - input 1, X>=0 Y - input 2, Y>=0 w - same price of input for inputs 1 and 2 a - parameter between 0 and 1 1.2 What is the set of profit-maximizing inputs if...
A price-taking and profit-maximizing firm produces one output at the rate y> 0 using one input...
A price-taking and profit-maximizing firm produces one output at the rate y> 0 using one input r>0 by way of the production function () , where f(x)竺2x2 . The firm's output sells at the price p >0 while the input is purchased at the price wo (a) (b) (c) Determine the lalue of the input that solves the FONC, and denote it by x (p,w). Is Set up the profit maximization problem. Derive the FONC and SOSC. x(p,w) unique? Explain....
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization...
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3. [30%] Consider a competitive industry. Each firm has the following production func- tion: f (K,...
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Consider a perfectly competitive market comprised of identical firms each facing the following cost function: C(q)...
Consider a perfectly competitive market comprised of identical firms each facing the following cost function: C(q) = 4 +q? where q is the firm-specific level of production of the representative firm. The market demand function is Q(p) = 400 - 4p where Q(p) is the aggregate demand in the market (expressed as function of price) and p is the price a) Derive the firm-specific supply function of the representative firm as a function of price b) Assume there are N...
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...
2. Consider the following cost minimization problem. A firm minimizes total cost given by, TC = wL+rK subject to an output constraint as given by the production function, y=f(K,L)=8K05 +420S, where TC refers to total cost, L is labor input, K is capital input, r is the price of capital, w is the wage rate, and y is output. a. Derive the factor demand functions and the optimal cost function. The first order conditions and all the steps involved in...
A price-taking and profit-maximizing firm produces one output at the rate y> 0 using one input r>0 by way of the production function () , where f(x)竺2x2 . The firm's output sells at the price p >0 while the input is purchased at the price wo (a) (b) (c) Determine the lalue of the input that solves the FONC, and denote it by x (p,w). Is Set up the profit maximization problem. Derive the FONC and SOSC. x(p,w) unique? Explain....
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
3. [30%] Consider a competitive industry. Each firm has the following production func- tion: f (K, L) = K}L. WON (a) Set up the cost-minimization problem of the firm, given output y, output price p and input prices are WK = WL = 1. (b) Derive the firm's cost function. (c) Derive the equilibrium price p, given no entry cost to this industry.
Consider a perfectly competitive market comprised of identical firms each facing the following cost function: C(q) = 4 +q? where q is the firm-specific level of production of the representative firm. The market demand function is Q(p) = 400 - 4p where Q(p) is the aggregate demand in the market (expressed as function of price) and p is the price a) Derive the firm-specific supply function of the representative firm as a function of price b) Assume there are N...
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