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- Digging calms by hand in Sunset Bay requires only labor input. The total number of calms obtained per hour (q) is given by :Q = 100√LWhere L is labor input per hour. A. Graph the relationship between q an LB. What the average productivity of labor in Sunset Bay? Graph this relationship and show that output per unit of labor input diminishes for increase in labor input. C. It can be shown that the marginal productivity of labor in Sunset By is given by:MPL =50√LGraph this relationship and show that labor’s marginal productivity is less than average productivity for all values of L . Explain why this is do.D. Explain the concept of diminishing returns to labor and how this concept related to increasing marginal costs.Consider the following production function that depends only on labor:Q = 8L¹/2 1. Write a combination of input and output that are technically efficient. In other words, for what level of L and Q, is the technology efficient? 2. Write a combination of input and output that are technically inefficient. In other words, for what level of L and Q, is the technology inefficient? 3. Write a combination of input and output that are technically unattainable. In other words, for what level of L and Q, is the technology unattainable?The information on three different technologies named as q, v and x is listed in the table below. Note that all of these technologies use different combinations of two types of factors of production, labor and capital, to produce 1000 units of output. Consider the first scenario where the per unit prices of the inputs, labor and capital are $50 and $25 respectively. Technology No of Labors Capital (tons) Cost value ($) A 10 50 B 30 20 C 50 10 Now imagine that a discovery has been made which has led to labor advancements leading to a reduction in per unit price of labor to $10, ceteris paribus. Which technology will a typical firm adopt under these changed circumstances and why? Using the value of costs found, what is the value of the economic rent for this firm?
- Describe where the law of diminishing marginal productivity begins for We R' Write. We R' Write currently uses 75 workers on the production line per day. Given the calculations in the table, is this number optimal? Why, or why not? If you could make a suggestion regarding the optimal number of workers We R' Write should use on the production line, what would it be? Why? Number of Workers per Day Pens Produced per Day Average Product Marginal Product Price per Pen Total Value Product Average Value Product Marginal Value Product Price of Worker per Day 0 0 --- --- $3.50 $0.00 --- --- $560 15 1,000 66.67 67 $3.50 $52.50 $233.33 $233.33 $560 30 2,700 90.00 113 $3.50 $105.00 $315.00 $396.67 $560 45 5,100 113.33 160 $3.50 $157.50 $396.67 $560.00 $560 60 7,900 131.67 187 $3.50 $210.00 $460.83 $653.33 $560 75 12,000 160.00 273 $3.50 $262.50 $560.00…In economics and econometrics, the Cobb-Douglas production function is a particular functional form of ne production function, widely used to represent the technological relationship between the amounts of two r more inputs (particularly physical capital and labor) and the amount of output that can be produced by nose inputs. The function they used to model production is defined by, P(L, K) = 6LªK!-a where P is the total production (the monetary value of all goods produced in a year), L is the amount f labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L nd K represent labor and capital and are therefore never negative. Show that the Cobb-Douglas production function can be written as P P(L, K) = 6LªK1-a → In K L In b+ a ln KProf. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?
- Consider the following production function: q = 9LK + 6L² – Assuming capital is measured on the vertical axis and labor is measured on the horizontal axis, determine the value of the marginal rate of technical substitution when K= 30 and L= 10. MRTS = -. (Enter a numeric response using a real number rounded to two decimal places.) 20 tv MacBook Air F6 FB 10 F3 23 2$ & з 4 6 7 8 { [ E Y U P D F G J K > C V N M command option - .. .- BWe often work with production technologies that give rise to initially increasing marginal product of labor that eventually decreases. Are the following statements then True or False? Explain. For such production technologies, the marginal product of labor is increasing so long as the slope of the production frontier becomes steeper as we move toward more (we are increasing) the labor input.Suppose the production function is given by Q=K1/2L1/2, and that Q=30 and K = 36. How much labor isemployed by the firm?A. 49 B.6 C.36 D.25
- 1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.We often work with production technologies that give rise to initially increasing marginal product of labor that eventually decreases. Are the following statements then True or False? Explain.A negative marginal product of labor necessarily implies a downward sloping production frontier at that level of labor input.Please only do 4 and 5 not 1 2 or 3 Suppose a firm’s production function is K^1/3 L^2/3 Mpk= L^2/3 / 3K^2/3 MpL=2K^1/3 / 3L^1/3 The rental rate of capital is $52, and the wage rate is $13. What is the cost minimizing capital to labor ratio? How many units of capital and labor should the firm use to produce 1200 units of output How much would it cost the firm to produce 1200 units? What is the short run and long run total costs of decreasing output to 1000 units? Assuming relocation is costless, should the firm relocate to a new location where w=15, r=40?