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- Roland Umbrellas has a production function given by Q = L0.5K0.5. The wage (W) is $80 per day and the rental per unit of capital (R) is $5 per day. In the long run, how many units of capital will Roland want to buy for each unit of labor?Consider the following shortrun production function: (Q=100L- L*L), where Q is the output level and L is labour input If the price of output in the market is K.sh 50 and labour costs K.sh 1200 per hour, how many hours would the firm use to maximize profits. What is the profit maximizing level of output?Suppose a firm uses two inputs: capital, K, and labour, L. The profit function is π(K, L, p, w, r) = pf(K, L) − wL − rK where p is the output price and w and r are the wage rate and rental rate respectively. (a) Evaluate the rate of change in the maximum profit function from a change in p. (b) Evaluate the rate of change in the maximum profit function from a change in w.(c) Evaluate the rate of change in the maximum profit function from a change in r.
- A firm produces output that can be sold at a price of $10. The production function is given by Q = F(K, L) = K2L!2 If capital is fixed at 1 unit in the short run, how much labor should the firm employ to max- imize profits if the wage rate is $2?A. Consider a firm who sells output at p=10 and has a short run production function Q(L)=20L-L2. Its wage rate is w=40. 1. Suppose the fırm sells in a perfectly competitive market and is a price taker in the input market, how much labor will it hire to maximize profits? 2. How much wage will it pay? 3. Show the graph of the profit-maximizing level of L and w solved in 1&2.A. Consider a firm who sells output at p=10 and has a short run production function Q(L)=20L-L2. Its wage rate is w=40. Suppose the firm sells in a perfectly competitive market and is a price taker in the input market, how much labor will it hire to maximize profits?
- Question 8 2 points Suppose a firm's production function is: q = √KL. Assume capital is fixed at 4 units, and the rental rate on capital is 10 and the wage rate is 8. Which of these represents the firm's total cost equation (expressed as a function of q)? O TC = 2q² + 32 O TC = 2q² + 40 O TC = 2q0.5 + 40 O TC = 4q² + 40 O none of the above Save AnswerXYZ Co. operates in a competitive market. Its production function is q = Lα Kβ . The firm takes the wage, rental rate and price as given. a) Derive the firm's conditional labor and capital demand functions. b) How does the firm react to an increase in the wage rate? c) Derive the firm's cost function.Given the production function f(x,x2) x,ax,, calculate the profit maximizing demand and supply functions, and the profit function. ii. %3D
- 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 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.)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
