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- Would you consider an interest payment on a loan to a film an explicit or implicit cost?If two painters can paint 200 square feet of wall in an hour, and three painters can paint 275 square feet, what is the marginal product of the third painter?What is the difference between a fixed input and a variable input?
- Prunella raises peaches where L is the number of units of labor she uses and T is the number of units of land she uses. Her output is f(L,T) = LT bushels of peaches. Currently, the cost of land is 8, the wage for labor is 9, and the price of peaches is 10. Prunella is currently maximizing her profits. Which occurences would cause the quantity of labor used to decrease? O An increase in the price of peaches O A increase in the price of labor O An increase in the Marginal Product of Labor O All of the aboveConsider a production process where flowers are grown (the output) using gardeners (labor) and greenhouses (capital). The quantity of flowers grown per day with various combinations of labor and capital are shown in the table. Fill in the marginal product of labor in the table below. (Enter your responses as integers.) Labor Сapital Output Marginal Product of Labor 0. 1 1 1 120 2 1 360 1 480 4 1 540 1 570 IPOALLERGENIC TITANION POSTSGopher Excavators produces shovels in a small factory and sells the shovels in a competitive market. The following table shows the company's production function: Output (Number of workers) (Shovels) Labor 1 100 195 275 4 340 380 Use the blue points (circle symbol) to plot the production function for Gopher Excavators on the following graph. 40 Producion Function 340 100 130 40 LABOR (Number of workana) Calculate the marginal product of labor (MPL) of each worker, and then plot the MPL curve on the following graph using the blue points (circle symbol). Note: Remember to plot each point halfway between two integers. For example, when the number of workers increases from 0 to 1, the MPL of the first worker should be plotted with a horizontal coordinate of 0.5, the value halfway between 0 and 1. Line segments will automatically connect the points. (genoygl indino
- 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.3. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q=K0.5 p0.5 where K is capital (for example nest boxes, cages and the like) and F is parrot food. The price of K is $8 and the price of F is $2. (a) What type of production function is this? Explain. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Provide a graph of the function using Excel. (c) Find the marginal products of capital and food. (d) Suppose that Duane wants 144 parrot chicks, how much K and F should be employed to minimise costs. What is the cost of producing 144 parrot chicks? 1 1 (e) Suppose that Duane is faced with the same problem as in (e) except that he has a fixed amount of K. In fact, K = 16. How much F should be bought to minimise costs? What is the total cost?A commercial fisherman notices the following relationship between hours spent fishing and the quantity of fish caught: Hours Quantity of Fish (in pounds) 0 hours 0 lb. 1 10 2 18 3 24 4 28 5 30 What is the marginal product of each hour spent fishing? Use these data to graph the fisherman’s production function. Explain its shape. The fisherman has a fixed cost of $10 (his pole). The opportunity cost of his time is $5 per hour. Graph the fisherman’s total-cost curve. Explain its shape.
- Each extra worker produces an additional unit of outputup to six workers. As more workers are added, noadditional output is produced. Draw the total product oflabor, average product of labor, and marginal product oflabor curves in a graph SHOW IN EXCEL PLEASE1. Juan Valdez owns a coffee farm in Colombia. His production function is: f (x1, x2) = (x1 – 1)0.25 x9-5. Assume the price of input 1 is r and the price of input 2 is w.. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm? 2. Show that the profit function is convex in (p, w). 3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x" with A > 0, a1, ¤2 > 0 and a1 + a2 0, B > 0, 0 < a < 1, and 0 + p< 1. 6. Find the profit function for the CES production function. 7. Verify Hotelling's Lemma for the CES production function with B < 1.Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R? → R+ defined by f(1, k) = Vĩ + vk, where l is the quantity of labor and k is the quantity of capital. (a) In an appropriate diagram, illustrate the map of isoquants for the firm's production function. (b) Does the firm's technology satisfy the following properties: (i) strict monotonicity (i.e., are the marginal product of labor and the marginal product of capital strictly positive), (ii) the no-free-lunch property, (iii) constant/decreasing/increasing returns to scale? (iv) 1
