Tunction: P(L, K)=13L0.3K0.7 Find the marginal productivity of labor and marginal productivity of capital functions. Enter your answers using CAPITAL L and K, or your answer will not be recognized. Use the preview button to make sure your answer is entered correctly before you submit any answer(s)! PL PK

Tunction: P(L, K)=13L0.3K0.7 Find the marginal productivity of labor and marginal productivity of capital functions. Enter your answers using CAPITAL L and K, or your answer will not be recognized. Use the preview button to make sure your answer is entered correctly before you submit any answer(s)! PL PK

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?
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.)
This is the answer plz write Clear hand written Y=Sk 0.5 +3L Multiply k & L by X 0.5 5(xk) ⁰.³ + 3 (XL) ⁰.s = = 510.5 40.5 + 3 x 0.5 10.5. k = x0.5 [sk0.5 + 320.5] = X0.5 4 Since power of is less than 1, production function has decreasing returns. Correct: c) Decreasing
Q4 The output of a production process, Q, is given by the function KL Q = K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. Q5 3 The equations defining a simple model of the economy are: C = 0.75Y + 18 I = 22 where C, Y and I denote consumption, national income and planned investment, respectively. Use this model to complete the following table of values and hence draw an accurate graph of C + I plotted against Y on the interval 0 < Y< 200. 100 200 C + I By drawing a second line on the diagram, calculate the equilibrium level of national income. Use your graph to explain what happens to the equilibrium level of national income when the marginal propensity to consume decreases with autonomous consumption fixed.
Write a paragraph to explain to your CEO that based on using regression analysis, through using the solver tool of excel, recalculate the optimum units to produced this month is 800 pro 200 mini to have the maximize revenue of $174,400.00. Explain what/why would it be if you make any changes in the units to stay within the constraints that you have it would produce less money.
A firm's production function is given by Q = 40K0.8L0.2 Each unit of capital costs $40 and each unit of labour costs $80. (a) Find the maximum level of output if the total input costs are $400,000. (b) Estimate the increase in production if an addtional $5,000 is made available. (c) Show that the ratio of marginal product to price is the same for both inputs. (a) Maximum output Q = (Round to the nearest integer as needed.) (b) Increase in output is units (Round to the nearest unit as needed.) (c) The ratio of the marginal product of capital to price is (Round your answer to two decimal places.) The ratio of the marginal product of labour to price is (Round your answer to two decimal places.)
A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?
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(i) Find the rate of change of the function f(x) =x + 2/ 1 − 8x with respect to x when x = 1.(ii) The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) =2t4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
pols Add-ons Help Last edit was seconds ago xt I UA Calibri 11 + 三 2 | 3 II | I 4 II| II6 4. Thanks to years of consistent contracts and an outstanding administration, Crestwood High School has formed one of the best teaching staffs in the State of Michigan. This staff has learned how to work seamlessly with each other and students. They are now able to effectively teach more students in every class than before. *Name the determinant: Automakers have introduced new heating lamps to their paint shops that allow them to dry layers of paint faster than ever before. These newly invented heaters use less energy and have greatly increased output. 5. *Name the determinant: 27°C Rain II 近

c) Assuming that the cost of employing each worker is $220 per day (including wages and materials), and Custom Made Pot has daily fixed costs of $400, fill in Table B given below: Round your AVC and MC answers to one decimal place. Number of TP = WorkersOutput 1 2 3 4 5 6 18 80 180 240 280 294 7 TVC($) 6 220 440 660 880 1100 1320 TFC Table B 400 400 400 400 400 400 TC 620 840 1060 1280 1500 1720 AVC($) 22 5.5 3.67 3.67 G ATC 62 10.5 5.89 5.33 5.33 5.3 3.9 4.5 5.8 d) On the graph given below, plot the following points showing the quantity and dollar amounts. point of diminishing returns (D) most productive point (P) economic capacity (E) Once a point is plotted, a tool icon will pop up. You can use this to enter exact co-ordinates for your points as needed. Tools Question 1- CH 6: In-Class Activity x MC($) 0 220 220 220 220 220 Prev i 1 of 8 Next > O & https://exto.mheducation.com/ext/map/index.html? l
Units of fixed input K Labor Hours (L) Output (Q) TFC TVC TC AFC AVC ATC MC 3 0 0 90 0 90 0 0 0 0 3 1 4 90 20 110 22.5 5 27.5 5 3 2 90 90 40 130 1 0.444 1.444 0.233 3 3 160 90 60 150 0.563 0.375 0.938 0.286 3 4 200 90 80 170 0.45 0.400 0.85 0.5 3 5 230 90 100 190 0.391 0.435 0.826 0.667 3 6 250 90 120 210 0.36 0.480 0.84 1 3 7 260 90 140 230 0.346 0.538 0.885 2 3 8 265 90 160 250 0.340 0.604 0.943 4 If the price of the output is $1, how many units of output should the firm produce to maximize profit? What is the firm’s profit level?