Suppose the firm short run production function is a quadratic one in the form: Q = 2L+ 0.25 L2, the firm hires any number of workers at a wage of $40/day, and sell any quantity of its output at a price of $4. Find how many workers should this firm hire to maximize profits.
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- Suppose that a firm has the following production function: q = 2L + K. The wage for a $10 per hour and the rental rate of capital is r = worker is w $10 per hour. In the short run the firm amount of capital is fixed at K = 20 units. If the firm's goal is to minimize their cost of producing 100 units, then in the short run they will hire units of labor and in the long run they will hire units of labor. (Round answers to two decimals if necessary.)Consider the following production function for a firm: Q = 500K^0.8L^0.2 where K is the amount of capital employed and L is the amount of labor employed. The price of capital, PK, is $48 and the price of labor, PL, is $12. If the firm would like to produce 10, 000 units with minimum cost, they should be using units of capital and units of labor.Consider a production function of two inputs, labor and capital given by Q=LK. Let w =5 and r = 1, where w is the price per unit of labor and r is the price per unit of capital. a) Suppose that the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q? b) If the firm is operating in the short run, with K fixed at 10 units, calculate the short-run total cost of producing 100 units of output?
- 1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No YesSuppose a short-run production function is described as Q=30L-0.05L^2 where L is the number of Labors used each hour. If each unit of output (Q) has a marginal revenue (price) of $5 and the marginal cost of labor is $40 per labor unit (L), how many units of labor (L) should be hired to maximize profit?A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with q
- A firm uses labor (L) and capital (K) to produce rocking chairs (Q) with the following production function Q=LK. The wage (w) is $10 and the rate of capital (r) is $20. The target number of rocking chairs to produce is 800. It is the short run and the amount of K is fixed at 5. What the optimal values for L* and K* in the short run? Enter the number for the the optimal amount of L in the short run? Enter the number for the the "optimal" amount of K in the short run?A firm operates in the short run with the production function Q = 10 K0.5 L 0.5, where Q is output, K is capital, and L is labor. The price of capital is $100 per unit, and the wage rate is $50 per unit of labor. How many units of capital and labor should the firm use to minimize its total cost while producing 400 units of output?Suppose a firm hires from the competitive labor and capital market to make strawberries. The per unit price of labor is $w and the per unit price of capital is $r. The firm has raised TC amount of seed money and is deciding to allocate it on hiring labor and capital in the least cost way. The production function of strawberries is written as Q = 25LKb which acts as the production target [0Suppose that the production function for a phone is ? = 20K^0.5L ^0.5 . The marginal product of labor is 10(k/l)^0.5 , and the marginal product of capital is 10(L/K) ^0.5 . Suppose that labor can be hired for $6 and capital can be hired for $9. a. When the firm is producing 49 units at lowest cost, what will the firm’s marginal rate of technical substitution be? b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 phones. Fractional units of labor and capital are allowed. c. What is the minimum cost of producing 49 phones?Suppose a firm has the following production function Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8 = (16/Q)+ 4√? (b) Draw the SRAC curve(c) By solving the first order conditions that the global minimum of production is 4(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.a) A firm operates according to the following production function: q(K,L)=100 KS LOS. The price of capital is r=$15/unit and the price of labor is w=$60 per unit. The firm currently operates with KSR-100 units of capital and wants to produce qs 4000 units of output. How much labor does the firm need to hire and what is the total cost of producing the 4000 units?SEE MORE QUESTIONS
