Suppose that a firm is producing in the short run with output given by: Q=86L-L² The firm hires labor at a wage of $37 per hour and sells the good in a competitive market at P = $14 per unit. Find the firm's optimal use of labor. Enter as a value. ROUND TO THE NEAREST WHOLE NUMBER.
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- Consider a firm that produces output using industrial robots and skilled labor. Suppose it is the case that a reduction in the price of industrial robots causes the firm's labor demand curve for skilled workers to increase (i.e., to shift to the right). This implies that: There is diminishing marginal product of robots. O There is diminishing marginal product of skilled labor. O Robots and skilled labor are complements. O Robots and skilled labor are substitutes. The unit cost of skilled labor is below the unit cost of robots.Tom Petersen is considering renovating bar stools at Dreamland. The productionfunction for new bar stools is given byq= 0.5L0.5where q is the number of stools produced during the renovation week and l represents thea number of worker hours employed during the period. The firm is a price taker for both bar stools(which sell for P) and workers (which can be hired at a wage rate of w per hour).a. What is the cost function for this firm C(w,q)?b. What is the supply function for bar stools q(P,w)?c. What is the profit function for this firm (P,w)?d. What is the firm’s demand function for labor function L(P,w)?A manager hires labour and rents capital equipment in a very competitive market. Currently the wage rate is $12 per hour and capital is rented at $8 per hour, whereas the marginal product of labour is 60 units of output per hour and the marginal product of capital is 45 units of output per hour. Show if the firm is using the cost-minimizing combination of labour and capital and give appropriate advice if necessary.
- Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the long run total cost function, C(q)? Sketch it on the diagram.What effect will a reduction in commodity price have on the input demand curve of the firmA firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.
- 1. The market price for tomatoes is $2/pound. Lynn is too small to influence the price of tomatoes. Her tomato (short-run) production function is given by q= L3 where L measures hours of labor and q measures pounds of tómatoes. (a) demand curve for labor. Lynn hires labor from a competitive labor market. Find her short run (b) elastic than her short-run demand for labor? Explain your answer. Would you expect Lynn's long-run demand for labor to be more or lessConsider 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?A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $12 per hour and capital is rented at $8 per hour. If the marginal product of labor is 60 units of output per hour and the marginal product of capital is 45 units of output per hour, is the firm using the cost-minimizing combination of labor and capital? If not, should the firm increase or decrease the amount of capital used in its production process?
- PRICE (Dollars per tracker) 30 80 70 60 ATC 20 AVC MC 10 0 0 10 20 30 40 50 60 70 80 90 100 QUANTITY (Thousands of trackers per day) In the short run, given a market price equal to $45 per tracker, the firm should produce a daily quantity of trackers. On the preceding graph, use the blue rectangle (circle symbols) to fill in the area that represents profit or loss of the firm given the market price of $45 and the quantity of production from your previous answer. Note: In the following question, enter a positive number regardless of whether the firm earns a profit or incurs a loss. The rectangular area represents a short-run of $ thousand per day for the firm.Consider the following shortrun production function: Q =100L - L2 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?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?