Consider a landowner that uses water as a primary input into the production of food. Similar...
Consider a landowner that uses water as a primary input into the production of food. Similar to the problemabove, suppose the land has a general production function of f(w) =aw−(b/2)(w^2) ,where w is the amount of water applied to the land. Suppose food output receives a price of Pf in a perfectly competitive market.
a) Suppose that water is allocated in a competitive market. Denote the price of water as Pw. Derive the landowner’s demand for water.
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Consider a landowner that uses water as a primary input into the
production of food. Similar...
4. Consider a monopolist that only hires one input, labor, to produce output. The monopolist's demand...
4. Consider a monopolist that only hires one input, labor, to produce output. The monopolist's demand curve is p 100 q, its production function is q-L5, and the price of labor is w. (The labor market is competitive however.) Derive the firm's labor demand function, which is a function of w. If w 24, how many units of labor will it employ? 0.5
A firm has a production function Y 2 K05L05. Use w to denote the wage rate...
A firm has a production function Y 2 K05L05. Use w to denote the wage rate and r to denote the capital rental price Let us first consider the short run situation, where the firm has K = 25 and In order to produce 10 units of output, how many units of labour does the firm need to hire? What is the average cost of the firm? Let us first consider the short run situation, where the firm has K-25....
4. Suppose a firm uses only one input (L) to produce output y, with the production...
4. Suppose a firm uses only one input (L) to produce output y, with the production function y L Suppose the firm sells its output in a competitive market at price p, and buys labor in a competitive market at price w. a. Write an expression for the profits of the firm as a function of w, p, and L. b. What is the marginal cost of hiring an additional unit of labor? Graph the marginal cost of labor curve...
A firm has a production function Y = 2 Ko5L05 use w to denote the wage...
A firm has a production function Y = 2 Ko5L05 use w to denote the wage rate and r to denote the capital rental price. Let us first consider the short run situation, where the firm has K = 25 and r = 2. In order to produce 10 units of output, how many units of labour does the firm need to hire? What is the average cost of the firm? a. b. Let us first consider the short run...
1. Consider a firm in the short run, when capital is fixed and the only variable...
1. Consider a firm in the short run, when capital is fixed and the only variable input is labor. For simplicity, we will simply ignore capital. In this situation, suppose that the firm’s production function is given by Q = f(L) = αL – (1/2)L2 , where Q represents the quantity of output produced, L represents the amount of labor employed, and the parameter α is a positive constant. a. Derive this firm’s marginal product of labor function? Under what...
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....
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.
2. A competitive firm must decide on how much labor L to employ in production of...
2. A competitive firm must decide on how much labor L to employ in production of output Y. Suppose that Y = 0 In(L) with probability T, and Y =0,In(L) with probability 1-2, where 0<x<1 and > > 0. Thus, the marginal product of labor is a random variable. Each unit of labor costs w and each unit of output is sold at the market price P. Both wage and output price are known to the firm. The firm has...
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the outpu...
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the output good is p > 0. The prices of the inputs Labour and Capital are w> 0 and r>0 respectively. The firm chooses L and K in order to maximize profits, (L.K). (a) How does the short-run production function differ from the long-run production function? (b) Write out the profit function for the firm, (L,K). (c) Derive the first order...
(20 marks) Consider a perfectly competitive local market for retail gasoline fuel in Ontario for which...
(20 marks) Consider a perfectly competitive local market for retail gasoline fuel in Ontario for which the demand side comprises 30,000 vehicles. Each gasoline firm in the market has an annual long-run total cost function of TC(q) = F +0.629 + 125,000,000 if q> 0 if q = 0 (TC(q) = 0 where F is fixed cost and q is firm-level output in litres of gasoline retailed per year. Each firm owns a single facility i.e. gas station), hires a...
4. Consider a monopolist that only hires one input, labor, to produce output. The monopolist's demand curve is p 100 q, its production function is q-L5, and the price of labor is w. (The labor market is competitive however.) Derive the firm's labor demand function, which is a function of w. If w 24, how many units of labor will it employ? 0.5
A firm has a production function Y 2 K05L05. Use w to denote the wage rate and r to denote the capital rental price Let us first consider the short run situation, where the firm has K = 25 and In order to produce 10 units of output, how many units of labour does the firm need to hire? What is the average cost of the firm? Let us first consider the short run situation, where the firm has K-25....
4. Suppose a firm uses only one input (L) to produce output y, with the production function y L Suppose the firm sells its output in a competitive market at price p, and buys labor in a competitive market at price w. a. Write an expression for the profits of the firm as a function of w, p, and L. b. What is the marginal cost of hiring an additional unit of labor? Graph the marginal cost of labor curve...
A firm has a production function Y = 2 Ko5L05 use w to denote the wage rate and r to denote the capital rental price. Let us first consider the short run situation, where the firm has K = 25 and r = 2. In order to produce 10 units of output, how many units of labour does the firm need to hire? What is the average cost of the firm? a. b. Let us first consider the short run...
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....
2. A competitive firm must decide on how much labor L to employ in production of output Y. Suppose that Y = 0 In(L) with probability T, and Y =0,In(L) with probability 1-2, where 0<x<1 and > > 0. Thus, the marginal product of labor is a random variable. Each unit of labor costs w and each unit of output is sold at the market price P. Both wage and output price are known to the firm. The firm has...
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the output good is p > 0. The prices of the inputs Labour and Capital are w> 0 and r>0 respectively. The firm chooses L and K in order to maximize profits, (L.K). (a) How does the short-run production function differ from the long-run production function? (b) Write out the profit function for the firm, (L,K). (c) Derive the first order...
(20 marks) Consider a perfectly competitive local market for retail gasoline fuel in Ontario for which the demand side comprises 30,000 vehicles. Each gasoline firm in the market has an annual long-run total cost function of TC(q) = F +0.629 + 125,000,000 if q> 0 if q = 0 (TC(q) = 0 where F is fixed cost and q is firm-level output in litres of gasoline retailed per year. Each firm owns a single facility i.e. gas station), hires a...
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