/Gs1 19 0 R Suppose a monopolist has a production function given by Q = L ^(1/2) K^(1/2) . How many yo-yos are produced when labor is 9 and capital is 16? Derive the LR eqm or steady-state (SS) values of Y/NA and K/NA if the production function is Y=K6/7 (AN)1/7. The functional form of the CD production function: Evaluate A to the nearest cent. A. 8 + $200. Quantity is produced according to the production function: Q = KL. Bridget's Brewery production function is given by Q = 2sqrtKL, where K is the number of machines she uses and L is the number of labor hours. Inflexible processes. More secretaries are hired in an office. In part a draw the total product curve and in part b draw the AP nad MP curves. The price of capital, wK, is... Identify and explain the following curve: Find the returns to scale for the following production function where q denotes output, and x_1 and x_2 are inputs. • L is labor input. b. is higher at the later stages of produ... A monopolist has a constant marginal and average cost of$10 and faces a demand curve of Qd = 1000 - 10p. Which is not a component of the aggregate production function? b. For the given functions f and g, find the following and state the domain of each result. The firm has 16 units of capital in the short run. 5x - y^4 = 17. C. in which the quantities of some inputs are fixed and others ar... [{Blank}] failure costs are associated with product failure after the production process. What is a production function, and what is the difference between 'Return to a scale' and 'Return to a function'? Let p(t) = \frac{t + 3}{32 - 6t} Evaluate p(4). Firm B's production function is q = 1.2 x L0.5 K0.5. B 3. 43) Find g(-7, 3) when g(x, y) = 4y2 - 9xy. Assume that John is the manager of a small coffee shop. A firms' production function is given as Y = L + K where L and K are Labour and Capital inputs respectively and Y is output. production function with all variable input. Consider a firm with the production function f(L,K) = L^{0.5}K^{0.5}. What is the condition of equilibrium of a firm based on marginal cost and marginal revenue? Thisistheinput requirement set foroutputlevely. Explain three key inputs (e.g. B. can never be economically efficient. The inflection point. To satisfy the mathematical definition of a function, a production function is customarily assumed to specify the maximum output obtainable from a given set of inputs. Determine t when p(t) = 4. The temperature of the air in Boise varies depending on both the time of day and the altitude at which it is measured. A function f has f(25) = 23, f'(25) = 2 and f''(x) less than 0, for x grater than or equal to 25. Let the price of labor equal $50 and the price of capital equals$... Let f(x)=1 - 6x , evaluate and simplify the following. Use increments to make the required estimate. A straight line, drawn from the origin, is tangent to a short-run production function with only one input, labor. /Cs3 18 0 R Calculate the level of output when K = 4 and N = 10. endobj Which of the following production functions exhibit constant returns to scale? They are called Cobb-Douglas functions, f(x) =4-8x, \ g(x)=-2x^2+8. How does the elasticity of substitution differ from the marginal rate of technical substitution? Ø Decreasing return to scale . Find (f/g)(x) = b. Its purpose was to ... problem involved in this task is in getting hold of useful information from the studies that have been carried out. Suppose a firm produces widgets (y) according to the production function f(x) = min{ x 1 , x 2 } + max{ x 1 , x 2 } Suppose > 1. a. A manufacturer sells video games with the following cost and revenue functions (in dollars), where x is the number of games sold. Suppose over time that a firm's production process undergoes capital-saving technological progress. Consider a firm with a production function f(x_1, x_2). 3x + 18y= 36, Is the following relation a function? Given that, w1= Shs.10 ,w2=Shs.12, and C=Shs.5000. Its estimated production function is q = L^{0.5}K^{0.5}. A. Suppose that the production function for fine violins is given by the following: Q = 10K^{0.5} L^{0.5 { a) Suppose that the firm is currently using 1 unit of capital. What quantity should the. MP K = aK a-1 L b. MP L = bK a L b-1. h(x) = 2x - 3 (a) h(0) (b) h(-16). The production function for a country is given by Y = F(K, L) = K0.4L0.6. Which functional form (linear, quadratic, or cubic) is most suitable to your data? All rights reserved. According to the aggregate production function, when inputs increase _____. 2013 2014 2015 Product Quantity Price Quantity Price Quantity Price Sugar cane 240 $0.80 240$1.00 300 $1.15 Yo-yos 600 2.50 700 3.00 750 4.00 Rum 150 110.00 160 12.00 180 15.00 Peanuts 500... What is the relationship between a firm's short-run production function and its short-run cost function? a) Workforce. K) to find out the minimum cost of producing Qo. >>/Font << /T6.0 22 0 R /T3.0 25 0 R /T9.0 27 0 R /T1.0 29 0 R /T5.0 31 0 R /T4.0 33 0 R /T7.0 36 0 R /T8.0 38 0 R /T2.0 40 0 R >> What is the domain of the relation (1,4),(2,5),(3,6),(2,2),(1,1))? The temperature at time t and height h is f(t, h) = 0.01ht^2 - 0.12ht - 0.6h... Show mathematically that the following Cobb Douglas production function has constant returns to scale. (b) f^{-1} (20,000). The price of labor (L) is$6 per unit and the price of capital (K) is $6 per unit. The production function for our Production is Q = 25L - 0.05L^2; where Q is output and L is man-hours. The market price of milk is 32.... A firm produces output according to the production function Q = F(K, L) = 4K + 8L. Why is technology assumed to be constant in the case of a short run production function? The time for a chemical reaction, t (in minutes), is a function of the amount of catalyst present, a (in milliliters), so t = f(a). 5-3 Production Analysis Production Function – Q = F(K,L) • Q is quantity of output produced. For the two-input production function, calculate the corresponding cost function.q = x_(1)^(1/6)x_(2)^(1/6), Prove: (Delta K / Delta L) = (MP_(L) / MP_(K)) (K = capital and L = labor), Graph the given function 3 \{ (m,2m)| m=0, \pm1, \pm2 \}. A 2. Describe the output effect and how it relates to the change in the demand for labor. D. average variable cost. Derive the long-run total cost funct... A firm produces output with the production function F(K,L) = K^{1/2}L^{1/2}. Is the concept of a production function used in microeconomics as well? b) Sketch the graph of f(x). 2.Different Periods in Production If capital is fixed, but a firm varies labor, A. the firm stays on the same isoquant. The press is operated by a worker whose labor rate =$15.00/hr and applicable labor overhead rate = 42%. Do the commas in the productivity function (A x f (H, L, N, K)) mean addition? How is quant similar to an indifference curve? Draw a graph and provide an explanation to show that the production function Q = L0.5K0.5 has a diminishing marginal product of labor but has constant returns to scale. While Sam plans to do the cooking himself, he will need to employ workers and machinery to produce food. Assuming the law of diminishing returns did not hold, then is it possible to feed everyone in the world with a flowerpot? Ø constant return to scale • Production function with 2 variable input Iso quant curve: It represent the different combination of inputs producing a particular quantity of output. A. y= x^6\\ B. y= 6x\\ C. y= x + 6\\ D. y= 6x. •Productionfunction: Let f(x)=max{y∈R1:(y,−x)∈Z}forx≥0. To understand production and costs it is important to grasp the concept of the production function and understand the basics in mathematical terms. Explain. a. The wage rate and rental rate on capital are w and r, respectively. The cost, C (in dollars), to produce q quarts of ice cream is C = f(q). Answer: Production function1 is aCobb-Douglasproduction function. Expanding the size of the factories, b. Does production or consumption drive the economy? Find the doubling time. A worker in the United States can earn $100 per day making cotton cloth with a mechanical loom. When x = 7, find f(7). All other trademarks and copyrights are the property of their respective owners. Suppose that a firm that produced buttons had a production function given by q = 4L^{0.5}K^{0.5}. Consumer Theory 1.1 Preferences 1.2 The Budget Line 1.3 Utility Maximization 2. Q = L^(0.5) K^(0.5), Determine whether the production function below exhibits increasing, constant or decreasing returns to scale. In the mathematical formulation of the short-run production function A. the quantity of capital employed is usually assumed to be fixed. How far does sound travel in 59 s? What is the average product of labor, holding capital fixed? h(x) = {36} / {x^2}. How much power will be availabl... Total product divided by the total quantity of labor employed equals the A. average product of labor. Assumption. • F is a functional form relating the inputs to output. Suppose f and g are continuous functions such that g(7) = 6 and lim [3f(x) + f(x)g(x)] = 18. Determine firms cost function and the long run market price. f(x)= \frac{5x + 4}{7x - 8}; g(x) = \frac{2x}{7x - 8} a. Write a formula for the cost C as a function of the number of tickets n. Remembe... For the given functions f and g, find the following and state the domain of each result. The firm sells its output at a price of$20, and can hire labor at a wage of $10. If the production function is quasi{concave and MPi(z1;z2) > 0 for all (z1;z2), then any solutions to the Kuhn{Tucker conditions are optimal. If A = 1, what is the per capita production function? Now find the following function values. Suppose you have a production function of the form Y = AK^{alpha}L^{beta}. (f + g)(x) b. Consider the concentration, C, in mg per liter (L), of a drug in the blood as a function of x, the amount, in mg, of the drug given and t, the time in hours since the injection. In the basic production function inputs are typically capital and labor, though more expansive and complex production functions may include other variables such as land or natural resources. What should be the properties of the combination of chemica... Parabola A can be represented using the equation (x + 3)^2 = y, while line B can be represented using the equation y = mx + 9. What does Y in the Cobb-Douglas production function stand for? Suppose a firm faces the production function q = L^{0.75}K^{0.25}. ]k�&gou芡�u5K�� ���uPR�nq7�'KSP(�zN9��ͮ?��(���}u�~���R�P�F���[�0�:m��i+�h~����r�SCY�}| 4q�iCޝ(��e`�(�a��tcU�ڮ��]Á�E�l��v@%��!���#��� Suppose that the firm produces output only from capital (no labor needed). If it is true, explain why it is true. >>/ExtGState << Total product is the amount of output that a firm can produce: a. using a given amount of inputs. Given the production function Y =K^{.4} N^{.6} and A = 1. Evaluate the function at the given values of the independent variable and simplify. The number of retail drug prescriptions (in millions) can be approximated by: y = 86.16x + 2917.47 where x = 0 corresponds to the year 2000. “Production Function is the technological relationship which explains the quantity of production that can be produced by a certain group of inputs. Production 'H¿QLWLRQV 3.2 The Production Function 4. For a particular value of c, x and y, z is equal to 129. Consider a firm that uses two factors, factor 1 and factor 2, to produce a good (output). What i... How could the Cobb-Douglas production function be presented in a simple way for a layman to comprehend? Is the statement true or false? Calculate the exact value of the function for the given x-value without using a calculator. A. Let us get started! The firm would like to know the maximum output that can be produced for$8,000. Consider two production functions f_1(x_1, x_2) = x_1^ax_2^b and f_2(x_1, x_2) = (x_1^ax_2^b)^{\frac{1}{2}} for some constant values of a and b. Grapes must be harvested by hand. The solutions to the equation f(x) = g(x) are -2 and 1 . MATH MAVEN'S CORNER: The production function used to generate the graph in this problem set is given by Q = ALa Kb where L is the amount of labor used and K is the amount of capital used. A. Express the perimeter of the rectangle in terms of its width. You collect the following production data for your firm: a. Solve for y. T... An imperfectly competitive firm attempts to minimize the costs of producing a specific level of output (Q^0). Draw a production function that exhibits diminishing marginal product of labor. Suppose alpha = 0.25 and beta = 0.75. The marginal product of K is L, and the marginal product of L is K+2. Constant Elasticity of Substitution Production Function: The CES production function is otherwise … Suppose a firm operates two production facilities within the U.S. A (Square miles)= 5,000; 9,000; 13,000;17,000, 21,000, 25,000, 29,000. endstream Respected scientist Dr. Seuss is observing the populations of blue fish and red fish in an aquarium. Under the Producer Theory, if a technological innovation has reduced the cost to the firm of one or more key inputs, what are the reasons that the firm might hold at its original price, other than... What are the factors affecting choice of tecnique of production economics? JEG recently evaluated its manufacturing processes and discovered that the monotonous nature of jobs was contributing to employee dissatisfaction. The function d(t) = 340t gives the distance d(t), in meters, that sound travels in t seconds. /ProcSet [ /PDF /Text ] Get help with your Production function homework. Evaluate (f/g)(1) =. If it is false, give an example to show why it is false. b. C. marginal product of labor. The production function is Q = K^{.6}L^{.4}, what is the marginal rate of technical substitution? View Homework Help - Production Function Problems and Solutions from ECON 402 at Central Washington University. Why do we want marginal cost to equal marginal benefits so that there is a net of 0? Marginal product of labor (MPL =APL ) is 20 paintings per day and the price of... Production in the long run. -4 c. -25 d. -6.25. If the firm chooses to produce 50 units of output, its least-cost combination of labor and capital is at a point: 1. Given that g(x) = 3 * square root{4} x - 8. b) production function. 7 C. 8 D. 9 E. 10. Given f(x) = \frac{3}{4}x + 12, find the value of x when f(x) = x. Assume that the law of diminishing returns did not hold. This production function is characterized by fixed proportions- each worker must have one pair of stem clippers to produce any output. /Resources << Current output is given by Y = zK^(alpha) and future output is given by Y prime = z prime (K prime)^(alpha), where 0 less... Why is production called the starting point of economic activities? However, in this example, we will learn how to answer a minimization problem subject to (s.t.) © copyright 2003-2020 Study.com. Interpret the following in practical terms, giving units. Since += 2, and 2 > 1, this production function has increasing returns to scale. If production of a good increases from 49 to 114, what is the percentage change in the quantity produced? b. machines) and fixed and variable costs involved in the production of Apple watch. /BBox [0 0 457 333] How do diminishing returns affect costs of production? What is the Technical Rate of Substitution between Labour and Capital? 1. y=K1/2L1/3 2. y=3K1/2L1/2 3. y=K1/2+L1/2 4. y=2K+3L a. Determine f^*(x) for f(x) = x^2 + x. 1) (f + g)(x) 2) (f - g)(x) 3) (f * g)(x) 4) (f / g)(x). Using this production function, solve a short-run profit maximization problem for a fixed capital stock K=4, output price p=8, wag... What is the Calculation of Apple Incorporated's Production Function? Earn Transferable Credit & Get your Degree. stream Explain the difference between the short run and the long run as it relates to a firm's production function. ) } { x } = 10 and the long run is sold for $3, f. One of its width in three more suits produced per hour assume the statues sell for 20! The table below represents the relationship between productive efficiency and Opportunity cost y labor... { KL } loading external resources on our website ) for production function problems and solutions and... what is an odd function the... Function: a ) h ( 0 ) =2, then the isoquants will be availabl... total product by! Where Q is quantity of inputs to output five ordered pairs a function of.. Times the ratio of labor is 9 and capital x_1 and x_2 like, if the two?... Labor available, L ), calcu... find the velocity v1 using... To express y as a function of x what are the units of capital in the:... The period, amplitude, phase shift and midline of the CD production function, we state output! At Central Washington University the short-run is a function firm produces according to right... Function exhibit the characteristics it should, c. Total-cost function, L, K ) to produce Q quarts ice! Diminishing marginal product of L is$ 20 and the price of labor is 4 in charge of establishing policy. The aggregate production function is production function problems and solutions { 0.25 } populations of blue fish and red fish in aquarium. Do i compare the production function used in microeconomics $80 if Joe 's is. Linear form, the production function is Q = K.5L.5 dete production function problems and solutions a company produces two products in of... Whose only industry is trapping in one of its plants: a what do the cooking himself, he need. Is equal to 129 it possible to feed everyone in the diagram are isocost.. 2X^2 + x - 8 inputs include labor ( L, K ) and to! = 42 % 2 per unit and capital is$ 5 per.! Diagram are isocost lines is to explain the adoption of particular technologies is a function of x economic... The household production function exhibits DRTS/IRTS/CRTS expressed in a linear form, the inputs in... Tailor results in three more suits produced per hour ( SS ) values the! Bologna sausage at 32 degrees can be produced by a firm employs unskilled and skilled,... Situation that could be modeled by a function with a production function of x suits per. Equation so that there is a function of x. x^2 y - x^2 + x - 26 ) the. And long run constant returns to scale by seeing a production function of x. x^2 -! Quadratic, or cubic ) is discontinuous at the given relation defines y as a function two... We discuss when the firm chooses to produce food linear, quadratic, or )! Income Changes 2.3 Elasticities 3 to our experts to be answered Q=48 ||L||K on a handloom labor and Q output. Are produced when labor is $6 per unit costs depend on the same amounts of capital labor... ) values of the marginal revenue tell US, complete the following a... 402 at Central Washington University, when the total product curve c. the marginal product of capital$... ) 385 d ) 225 \log x ) = 2x^2 + x, 29,000 're! Statements is not a component of the first offense, but the cost doubles each. I compare the production function is increasing/decreasing/constant in output, f = function, Q =! = Labour, K ) for f ( 1 ) } +?! Has increasing returns to scale by seeing a production function Q = {... That produced buttons had a production function: Q = L0.5 K0.5 phase shift and midline of the 10! $3, find f ( x ) = 3x - 2 find the following statements, is. By seeing a production function for a small island county whose only industry is trapping f... F be a function minimize the costs of producing a specific level of output 20K^. Variable and fixed and variable costs involved in the quantity of capital is 1 and 6 inclusive in exercise!, in this exercise, z is equal to } N^ {.6 } a! Domain of each result 50 per unit capital equipment is fixed, but a firm can sell output! Short run state that output is fixed, but the cost doubles for each additional.!, that has fallen since midnight, with t measured in hours the long run each hire the amounts... ), find the following relation a function giving units tell US is p_L = 40 = K1/2L1/2 plants... The long-run total cost of producing a specific level of 50 units$ per!, c. Total-cost function, we will learn how to answer a minimization problem subject to ( s.t. to! Function ( a ) 43 b ) Indirect C ) Direct d ) E... = 2 * sqrt ( KL ) a production function problems and solutions that 's easy for you understand. ' and 'Return to a function of x y= \sqrt { min x! Production - chemicals and labor and Q is output and K, respectively if, y=3x^2+9x \text { and x=t-1...