Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if TFP declines by 43%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).
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Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if TFP declines by 43%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).
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- Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if TFP declines by 12%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).Returns to scale in production: Recall that a production function F(K, L) exhibits constant returns to scale if doubling the inputs leads to a doubling of output. If it leads to more than doubling of output, there are increasing returns to scale; if it leads to less than doubling of output, there are decreasing returns to scale. The answers to parts (a) and (f) are worked out below. (a) Y = K1/2L1/2. If we double K and L, output is (2K) 1/2(2L) 1/2 = 21/221/2K1/2L1/2 = 21/2+1/2K1/2L1/2 = 2K1/2L1/2. So output exactly doubles, and there are constant returns to scale. (b) Y = K1/3L2/3 + . This production function says you get units of output “for free,” that is, even if there is no capital and no labor. Then you produce on top of that with a Cobb-Douglas production function. If we double K and L, output is Notice that the first term is doubled, but the output we got for free (the A) is left unchanged. Therefore, output is less than doubled, and this…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.)
- 10K L%. 1). Consider the production function Q = (a) What is the output when K = 100000 and L = 243? (b) Use the marginal analysis to estimate Q(99995, 243) and Q(100000, 245). (c) Use a calculator to compute these two values of Q to three decimal places and compare these values with your estimates in (b). (d) How big must AL be in order for the difference between Q(100000, 243+AL) and its linear approximation Q(100000, 245) + -DAL, to differ by more than two units?Returns to scale in production: Do the following production functions exhibitincreasing, constant, or decreasing returns to scale in K and L? (Assume Ais some fxed positive number.)(a) Y = K1/2L1/2(b) Y = K2/3L2/3(c) Y = K1/3L1/2(d) Y = K + L(e) Y = K + K1/3L1/3 (f ) Y = K 1/3L2/3 + A (g) Y = K 1/3L2/3 − AQ2. A firm's production function is Q = 9LZ+1)/10KY+1)/10 %3D • Find out MPL and MPK. • Find out APL when K=16 L= 64.
- 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?Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).How many units of output should each plant produce? Please specify your answer as an integer.
- 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 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?Please no written by hand and no image Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if both capital and labor rise by 42%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).