The firm Greench produces Nutella. The production function is given by the following: Nutella = min{ 44 L, 27 K} The price of labor is $36, the price of capital is $10, the price of Nutella is $25, and Greench's costs are $3607. What is the optimal amount of labor that the firm should hire?
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- What is the difference between a fixed input and a variable input?Would you consider an interest payment on a loan to a film an explicit or implicit cost?The following graph shows the marginal and average product curves for labor, the firm's only variable input. The monthly wage for labor is $2,800. Fixed cost is $160,000. When the firm uses 120 units of labor, what is its marginal cost at this output?
- Suppose that firm's short-run 4 a production function is q=10/T – 1. 5.1 Find the level(s) of maximise the firm's average product of L that labour (APL). 5.2 Calculate the value of the second- order derivative (SOD) at the value of L found in 5.1 that maximises APL 5.3 Calculate the marginal product of labour (MPL) at the level(s) of L that maximises APLBrian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. 1. 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 L(q) and K(q)?Show that a firm's marginal product of labor MP(E) intersects the maximum point of its average product of labor AP(E) graphically and algebraically.
- What is the marginal product of labor? the average output of a unit of labor the total output obtained by using one more unit of labor the average output obtained by using one more unit of labor the extra output obtained by using one more unit of laborThe 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.Describe the difference between a diminishing marginal product of labor and a negative marginalproduct of labor. Why would a profit-maximizing firm always choose to operate where the marginalproduct of labor is decreasing (but not negative)?
- Exercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capital8. Average and marginal product of labor Caroline's pizza restaurant uses a combination of workers and ovens to produce pizzas. The total number of pizzas produced per hour is given by the function q = 4K0.5 10.5, where K is the number of ovens and I is the number of workers. Although the two inputs are relatively substitutable, the number of ovens is fixed in the short run, and therefore Caroline is primarily interested in the marginal and average product of labor given her current number of ovens (4). Complete the following table using the production function given. Ovens Workers Pizzas Per Hour Average Productivity (K) (L) (9) 4 1 4 4 4 2 3 4 11.31 13.86 Given Caroline's production function, she faces marginal productivity of workers (q/L) 5.66 4.62 MPL returns to scale. However, you can see that when one input is held constant, the as more and more workers are added. Still holding the number of ovens (K) fixed at 4, it would take workers to produce 32 pizzas per hour.