Consider a perfectly competitive firm with the following production |0.25,0.25 function: q=L' a. Solve for the long run profit maximizing labor demand and capital demand functions. b. What is the profit maximizing long run firm supply function?
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- Consider Delta, a price-taking single-output, single input firm with the following production function:f (z) = z4/5a) Define non decreasing returns to scale and non-increasing returns to scale in terms of the production function and give conditions under which f(z) satisfies these properties. b) Suppose that the price of the input z is ѿ =1. Set up the cost minimization problem and solve for the conditional factor demand correspondence and the cost function. c) Set up Delta's profit maximization problem using the cost function you derived in (b) above and solve for the supply correspondence and the profit function.Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is constant at $20/unit. The production function and marginal product function, respectively, are shown below. If the current capital stock is fixed at 2,500 units, how much labor should the firm employ in the short run? Show your work.The followings are short run production functions for two firms operating in different industries with different capital structures. Find and draw the the Value of Marginal Product for Labor for two firms? Write down the profit maximization problem and derive labor demand curves for each firm? What is the employment (for labor) level for firm 1 and firm 2 ? Find the profit level for each firm? Discuss the impact of public infrastructure investment ,and technological advancement on labor productivity and employment levels for each firm ?
- Consider a competitive firm in both input and output markets. The production function for this firm is given by q = 10 (KL)^.2. The price of K is $1 and the price of the output is $5. Derive the demand for labor when K is variable.A firm produces output according to the production function . If it sells its output in a perfectly competitive market at a price of 10, and if K is fixed at 4 units, what is this firm’s short run demand function for labor? (Remember profit maximizing labor demand).c) Give a formal definition of increasing, decreasing, and constant returns to sale, and determine if the production function above exhibits increasing, decreasing or constant returns to scale. (d) Derive the firm’s contingent labor demand function (e) Derive the firm’s unconditional labor demand function (f) Derive the profit function of the firm
- A firm's production function is: q = 16L1/2K1/3 where q is the firm's hourly total product, L is the quantity of labor employed, and K is the quantity of capital employed. Assume that the quantity of capital employed is fixed at 125 units per hour. The labor market is perfectly competitive, and the current wage, w, is $10 per hour. The firm sells its product in a perfectly competitive market and the price is $5 per unit. a. What is the firm's value of marginal product of labor? b. What is the firm's profit maximizing quantity of labor?Nn1 Edit que 3. Consider the following production function: y=f(L,K)=min{L,2K} . (c) Determine the long-run cost function c(w,r,y) , where r is the rental rate of capital, w is the wage rate, and y is the target output. (d) Suppose the market price of output is p . Solve the firm's long-run profit maximization problem (using the cost function above). Briefly describe the firm's supply decision.Consider the following equation Q = f(K, L) = K0.7 L0.3 Find (a) MRTS of labor for capital (b) Show that the production function above is homothetic (c) Returns to scale (d) Equation representing an isoquant and show that it is convex to the origin (e) Elasticity of substitution (f) Output elasticities of factors
- Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firm’s short run production function. Labor Output 0 0 1 15 2 40 3 70 4 86 5 94 6 98 In the table below, you will determine several points on the firm’s demand curve for labor. To do this, you must determine how many workers the firm should hire for different values of the wage rate in order to maximize profit. Complete the table below: Wage Rate Per Worker Quantity Demanded of Workers $30 $50 $70 $100 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firm’s short run production function. Labor Output 0 0 1 15 2 40 3 70 4 86 5 94 6 98 In the table below, you will determine several points on the firm’s demand curve for labor. To do this, you must determine how many workers the firm should hire for different values of the wage rate in order to maximize profit. Complete the table below: Wage Rate Per Worker Quantity Demanded of Workers $30 $50 $70 $100 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure. do not upload imagesSuppose the hourly wage rate is $17, the rental price of capital is $2 and the price of output is constant at $45 per unit. Firm's production technology is q = 4K0.25E0.75, the marginal product of employment is MPE =3K0.25E-0.25 and the marginal product of capital is MPK = K-0.75E0.75. What is firm's optimal demand of labor if firm plans to produce q=26 units of outputs in the long-run? (please keep 1 decimal place in your answer)