a. If Jason wishes to produce the most output with the finances ($5000) available, how much labor and capital should he employ? Use a Lagrangian method for output maximization to solve this problem. b. Does this bundle of capital and labor also minimize the costs?
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- In your "toast" production function, you used your labor and a toaster as capital. Keeping capital constant, i.e., with only one toaster if you keep adding the labor, i.e., bring your friends to help you with making toasts, which of the following might happen? Group of answer choices Marginal returns to labor will be a constant. Marginal returns to labor will keep decreasing and, after a point, it will become negative. Marginal returns to labor will keep increasing. Marginal returns to labor will keep increasing and then be a constant.6. Consider the following Cobb - Douglas utility function: U = χαγβην *Note, it should be assumed that a, B.y > 0 Show that this production function can exhibit increasing returns to scale globally while maintaining diminishing returns for each individual input.6. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q = K'2 L12 where K is capital (for example nest boxes, cages the like) and L is parrot food. The price of K is $8 and the price of L is $2. and d. Does capital obey the "law of diminishing returns?" Explain. e. Suppose that Duane wants 144 parrot chicks, how much K and L should be employed to minimize costs, and what is the cost of producing 144 parrot chicks? f. Suppose that Duane is faced with the same problem as in (f) except that he has a fixed amount of K. In fact, K = 16. How much L should be employed to minimize costs, and what is the total cost?
- Jillian's slushee store faces an isocost curve given by C=10L+5K. L = number of employees, K = number of slushee machines. If Jillian's total budget is 100 and she has 5 employees, she can afford __________ machines. The slope of the isocost curve (K on the y-axis) is __________. For each additional employee, to keep her costs the same, Jillian has to give up __________ machines.If the production function describing an economy is Y= 20 KL23, then the share of income going to capital: O is about 33 percent. O depends on the state of technology. is about 67 percent. depends on the quantities of labor and capital.For the Cobb-Douglas production function P and isocost line (budget constraint, in dollars), find the amounts of labor L and capital K that maximize production, and also find the maximum production. Then evaluate and give an interpretation for |å| and use it to answer the question. (a) Maximize P = 2000L3/5K2/5 with budget constraint 15L + 32OK = 8000. L = K = P = (b) Evaluate and give an interpretation for |21. Each additional dollar of budget increases production by this amount. (c) Approximate the increase in production if the budget is increased by $80. units
- Please don't copy ans Economics You are the owner of a motorbike company that currently has two different factories, an old one and a new one. The old factory uses an old technology that requires large amounts of labor to produce motorbikes. The production technology for the old firm is given by Fo(L) = m*L^1/2 . The new factory uses a much more modern production technology given by Fn(L) = n*L^1/2 . a. What are costs as a function of output for each individual factory? b. Suppose that you want to produce 1000 motorbikes. How many motorbikes will you produce at the old factory and how many will you produce at the new factory? c. Derive an expression for the total cost of producing y motorbikes (assuming that you always divide production between the factories in the optimal way). How does this cost function compare to the individual factory cost functions? d. It turns out that you can upgrade your old factory to make it just as efficient as the new factory. To pay…A sandwich shop owner has the following information: P = MR = $4, ATC = $2, AVC = $1, MC = 4, and Q = 500. From this, she can determine: a. she has earned economic profits of $1,500. b. she has earned economic profits of $1,000. c. she has earned zero economic profits. d. her profits are not being maximized.Suppose the production function for widgets is given byq = kl - 0.8k2 - 0.2l2where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input.a. Suppose k = 10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point?b. Again assuming that k = 10, graph the MPl curve. At what level of labor input does MPl = 0?c. Suppose capital inputs were increased to k = 20. How would your answers to parts (a) and (b) change?d. Does the widget production function exhibit constant, increasing, or decreasing returns to scale?
- Assume instead that pharmacists and robots dispense prescriptions according to the following production function: Y = 10*KO.8L0.2 where Y is the number of prescriptions dispensed; L is the number pharmacist hours, and K is the number of robot hours. In addition, $10 worth of materials is used for each prescription. a. What is this type of production function called, and what are we assuming about the relationship between robots and pharmacists by using this production function? b. Derive the cost - minimizing demands for K and L as a function of output, the wage rate and the rental rate of capital. c. Use these results to derive the total cost function: costs as a function of y, r, w, and the $10 materials cost. d. Pharmacists earn $32 per hour. The rental rate for robots is $64 per hour. What are total costs as a function of Y? e. Does this technology exhibit decreasing, constant, or increasing returns to scale?f. The pharmacy plans to produce 40,000 prescriptions per week. At the…The manager of Dixie Furniture Company estimates that the daily output of her factory (in thousands of dollars) Q is given by Q = 2x1/4y3/4 where x is the amount spent on labor and y is the amount spent on capital (both measured in thousands of dollars). (a) Find the daily output of the factory if $81,000 is spent on labor and $256,000 is spent on capital each day. $ (b) Suppose that the output of the factory is to be maintained at the level found in part (a). By how much should the amount spent on capital be changed if the amount on labor is increased by $1,000? (Use the differential to calculate the answer. Round your answer to the nearest cent.) $ What is the MRTS? (Round your answer to the nearest cent.) $ per thousand dollars4:34 D *3 all 100% I 2. 3 When the inputs price ratio (slope of cost line) is greater than the MRTS, (MPK/PK > MPL/PL) the producer should use .. to minimize the cost. A More labar C Mare labor and more capital B More Capital D| None of the above 4 The optimal production method A maximizes output regardiess of cost C minimizes the normal rate of return B| maximizes inputs. Dminimizes cost 5. Refer to the information provided in the following figure, If this firm's cost of labor is $10 per unit, and the isocost line represents a total cost 2000. How much is the cost of capital per unit? 100 q-300 -200 -100 200 Units of labor Linits of capital
