A firm pays a price w for each unit it employs of its labor î. It also incurs fixed costs equal to F. If the firm receives a price p for each unit of output produced, and it produces output given by ƒ(x) = 4x¹/4, how much of labor à should it employ to maximize profits? Verify whether your answer is indeed a maximum.
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- Suppose that a firm's only variable input is labor. The firm increases the number of employees from four to five, thereby causing the weekly output to rise by two units and total costs to increase from $3,000 per week to $3,300 per week. What is the marginal product of hiring five workers instead of four? What is the weekly wage rate earned by the fifth worker?The production function of a competitive firm is described by the equation y = 1/2, 1/2 2.x26x. The factor prices are pi $3 and P2 $4 and the firm can hire as much of either factor it wants at these prices. What is the firm's marginal cost?The production function of a competitive firm is described by the equation y = 2x11/2 6x21/2. The factor prices are p1 = $3 and p2 = $4 and the firm can hire as much of either factor it wants at these prices. What is the firm’s marginal cost?
- Suppose that the production function of the firm is: Q = 100L1/2.K1/2 K= 100, P = $1, w =$50. and r = $40. Determine the quantity of labor that the firm should hire in order to maximize the profits. What is the maximum profit of this firm?The production function for Q is given as Q = 5K1/2L1/2where K is the amount of capital employed and L is the amount of labor employed. The price of capital is $8 and the price of labor is $4. Show the input choice when output reaches 59 and find the marginal cost of the 60th unit of output. Show your steps of calculation clearly.What is the difference between the factor demand derived from cost minimization and that obtained from the profit maximization? Under what conditions they can be the same?
- Calculate the Marginal Product (MP) at each input level. If the price of printer is $100 each, calculate the Value of the Marginal of labor (VMPL). If the wage rate (per week) is $1800 , how many workers will be employed? If the firm decides to hire 14 workers, what is the maximum wage the firm would be willing to pay?QUESTION ONESuppose a firm’s production function is given by Y = 4L0.5 and its (inverse) product demand curve is P = 20 −0.5Y. The firm can hire labour at a wage rate of K12. a) Find an expression for the marginal product of labour. b) How many workers will the firm hire? c) What level of output does the firm produce? and What price will it charge?Consider the following short-run production function (where L – labour, Q - output): Q = 10L - 0.5L^2Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input as it needs at $20 per unit.Determine the marginal value of product with respect to labour.Determine the marginal cost of labour (factor cost function).Determine the optimal value of L, given that the objective is to maximize profits.
- True or false and explain Suppose a firm’s marginal product of labour is MPL = 10/L, where L is measured in labour hours, the price of the product is $600, and the cost per hour of labour is $30. The firm currently employs 150 labour hours. In order to maximize the firm’s profits in the short run, the manager should increase its labour employment by 40 labour hours.A firm’s production function is: Q = 20L -.5L2. The firm can sell all the output it wishes at $10 per unit. The wage rate for labor is PL=W=$20. a. How much labor should be hired to maximize profits?Widget factory Inc. in Wisconsin has the following production function: F(L,K)=2L L represents the number of labours hours. Workers at this factory are paid an hourly wage of $30 and they rent capital at$25/ hour.since this is a competitive market, the factory output is $50 per unit. Let's pretend the firm operates in the short run with capital fixed at 900, how many workers would widget factory Inc employ? What is their profit rate?