Suppose an economy has 100 units of capital, 100 units of labor, and the efficiency of each worker is equal to 2. The effective number of workers for this economy is _____ and the capital per effective worker is _____. 50; 2 200; 1/2 50; 1/2 200; 2
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Suppose an economy has 100 units of capital, 100 units of labor, and the efficiency of each worker is equal to 2. The effective number of workers for this economy is _____ and the capital per effective worker is _____.
- 50; 2
- 200; 1/2
- 50; 1/2
- 200; 2
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- Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.Suppose that production function of certain devices is determined by: q = k * L - 0.8 k2 - 0.2 L2 Where q represents annual quantity of devices produced, k represents annual quantity of capital factor, and L represents annual quantity of labor factor. (a) Suppose k = 10; draw a graph with average and total labor productivity. What is level of labor (L) factor at which average productivity reaches a maximum? How many devices are produced at that point? (b) Assuming again that k = 10, plot Marginal Product (MP) curve. At what level do we have that labor (L) factor is MP = 0? (c) Suppose capital (k) factor were to increase to k = 20. How would your previous answers change?
- Suppose that capital and labour are perfect complements in a one-to-one ratio in a firm's production function. The firm is currently at an efficient production level, employing an equal number of machines and workers. Suppose the cost of labour were to double and the cost of capital were to fall by half. If the firm wanted to produce the previous level of output, the firm would hire (1) the same amounts of labour and capital. (2) twice as much labour as capital. (3) more labour and less capital. (4) less labour and more capital. Suppose in a particular production process that capital and labour are perfect substitutes so that three units of labour are equivalent to one unit of capital. If the price of capital is $4 per unit and the price of labour is $1 per unit, the firm should. (1) employ labour only. (2) employ capital only. (3) use three times as much capital as labour. (4) use three times as much labour as capital.Suppose the production function for widgets is given by KL – 0.5K2 – 0.1 L2 , where q represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labor input. (a). Suppose K=5; what is the average productivity of labor (Average product of Labor, MPL) (b). Suppose K=10; at what level of labor input does the total output reach the maximum?3. Consider the production function: Y = F(K, LE) = Kº4 (LE) 0.6 in which output (Y) depends on capital (K) and the number of effective workers (LE), while the number of effective workers depends on the amount of workers (L) and the efficiency of each worker (E). (a) Derive the per effective-worker production function: y = f(k), where y Y LE K & k = LE
- The per-unit cist of an item is its average total cost=(=total cost/quantity). Suppose that a new cell phone application costs $100,000 to develop and only $0.70 per unit to deliver to each cell phone customer. What will be the per-unit coat of the application if it sells 100 units? What will be the per-unit coat of the application if it sells 1,000 units? What will be the per-unit cost of the application if it sells 1 million units?*0.65 0.35 where x is the amount of labor and y is the amount of capital. The productivity of a country is given by f(x,y) = 100x (a) Compute the marginal productivities of labor and capital when x = 300 and y = 500. (b) Use part (a) to determine the approximate effect on productivity of increasing capital from 500 to 502 units, while keeping labor fixed at 300 units. (c) What would be the approximate effect of decreasing labor from 300 to 298.5 units while keeping capital fixed at 500 units? (a) The marginal productivity of labor is (Do not round until the final answer. Then round to two decimal places as needed.) The marginal productivity of capital is (Do not round until the final answer. Then round to two decimal places as needed.) (b) When capital is increased from 500 to 502 units, the approximate change in productivity is (Do not round until the final answer. Then round to two decimal places as needed.) (c) When labor is decreased from 300 to 298.5 units, the approximate change…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.
- A car wash firm calculates that its daily production (in numbers of cars washed) depends on the number of n workers it employs according to the formula P=30n-0.05n^2 cars. (a) Calculate the marginal product of labor at employment level of 50 workers. ___ cars/workers. Interpret the results. This means that, at an employment level of 50 workers, the firm’s daily production will increase at a rate of ____ cars per additional worker it hires.Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t = 50+8e-0.00005y Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If he swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MP) is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ MPy character.)Factory X can produce skis or snowboards. If all factory time is devoted to producing skis, 400 pairs of skis per day are produced. If the factory devotes all time to producing snowboards, 700 snowboards per day are produced. Snowboards 700 400 Pairs of Skis A recent technological advancement has positively impacted factory operations. This has resulted in an increase production of snowboards by 50%. What is the new maximum number of skis that can be produced per day?
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