production function problems and solutions

Suppose that the firm can only offer integer quantities, i.e. 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. The theory of production functions. Suppose a firm follows the production function f(E,K) = E^{1/2} K^{1/2}. (Round your answer to one decimal place. \left \{ (0.3, 0.6), (0.4,0.8), (0.3,0.7), (0.5,0.5) \right \}, The ordered pairs pairs (1,36), (2,49), (3,64). Production increases B. Suppose you are given a production function with output Y and labor and capital denoted by L and K, respectively. A STUDY INTO THE PROBLEMS AND SOLUTION OF PRODUCTION CONTROL IN AUTOMOBILE INDUSTRY OF NIGERIA “Control is a general management function which can be described as the constraining of events to follow plans. y = (x+5)^2 \\4. The Simultaneity Problem %���� How soon will the student type 90 wpm? Suppose that a firm had a production function given by q = 2L0.5K0.5. Suppose there is an economy with a fixed labor force and a production function that exhibits constant returns to scale so that the level of capital per worker k determines the output per worker y. Ø increasing return to scale . a) Find i. Demand engt’s utility function is U(x 1, x 2)= x 1 + ln x 2 x 1 - stamps x 2 - beer Bengts budget p 1 x 1 + p 2 x 2 = m p 1 – price of stamps p 2 – price of beer Consider a Cobb-Douglas production function: f(L,K)=0.5K^0.5L^0.5. Suppose the production function for good q is given by q = 3k + 2l where k and l are capital and labor price. Where, Q x = Quantity of output, F = Function, L = Labour, K = Capital. When would increasing marginal returns apply? The price of capital is p_K = 10 and the price of labor is p_L = 40. /Filter /FlateDecode b. a. Select one:... What would cause a firm's production function to change? 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. Can't find the question you're looking for? The temperature of the air in Boise varies depending on both the time of day and the altitude at which it is measured. Both marginal productivities are diminishing. How does the curvature of an isoquant relate to the marginal rate of technical substitution? ), Solve for g(-12), g(-8), and g(0) g(x) = 8x - 5. “Production Function is the technological relationship which explains the quantity of production that can be produced by a certain group of inputs. 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). b. q = ( min { x_1, 2x_2 } )^{1/4} O decreasing returns to scale O constant retur... All else constant, the choice of whether to use a labor-intensive production process or a capital-intensive one depends on: a) the absolute prices of capital and labor. The following production function satisfies increasing returns to scale: f ( L , K ) = 100 L K . For f(x) = square root of {3x} and g(x) = x^2, find the following. Let us get started! b. How far does sound travel in 59 s? The slope of the marginal revenue product curve c. The marginal products of either input d. The slope of an cost curve. From this production function, we can solve for the marginal products of capital and labor. The firm would like to know the maximum output that can be produced for $8,000. 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. The firm pays a wage of$50 per unit and pays a rental rate of the capital of $50 per unit. Let a production function exist such that Q=(K^{0.33{ L^{0.67}) Let the firm have a total of$5,000 to spend on labor and capital. While Sam plans to do the cooking himself, he will need to employ workers and machinery to produce food. The sales decay for a product is given by the following formula where S is the monthly sales and x is the number of months that have passed since the end of a promotional campaign. The y-intercept and x-intercept. y = 20e^{(0.15t)} is the formula for the number of bacteria at time t. \frac{dy}{dt} = 0.15 y. We will revisit finding the maximum and/or minimum function value and we will define the marginal cost function, the average cost, the revenue function, the marginal revenue function and the marginal profit function. Which of the following shows a decrease in the price of capital while the price of labor remains unchanged? The quantity, Q, of a certain product manufactured, depends on the quantity of labor, L, and of capital, K, used according to the function: Q=900L^(1/2)K^(2/3). A. -x^5 + y^5 = 0. Evaluate. 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. Is the concept of a production function used in microeconomics as well? The cost, in millions of dollars, of building a threeaThe cost, in millions of dollars, of building a three-story high school in New York State was estimated to be: C(x) = 2.3 + 0.18x ? b. always shows increasing marginal product of labor. B. the quantity of output is usually assumed to be fixed. a) Workforce. 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? Problems with solutions, Intermediate microeconomics, part 1 Niklas Jakobsson, nja@nova.no Katarina.Katz@kau.se Problem 1. b. marketing. f (x) = square root {x + 5} (a) f (-4) (b) f (11) (c) f (-8). 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. What is the production function? Do not enter a percent sign. Determine whether y is a function of x. x^2 y - x^2 + 4 y = 0. How do diminishing returns affect costs of production? a. When the total product curve reaches its maximum point, the value of the marginal product at that point is _____. Products A has 47 components and Products B has 52 comp... With an example, use a production possibility frontier as a straight line, assume that the country has two factors of production, L and K. The payments to the factors are what? The hourly wage of hiring one worker is $10 and the price of each unit of capital is$50. Respected scientist Dr. Seuss is observing the populations of blue fish and red fish in an aquarium. • L is labor input. D, Suppose that the production function is Cobb-Douglas. C. marginal product of labor. 1. y=K1/2L1/3 2. y=3K1/2L1/2 3. y=K1/2+L1/2 4. y=2K+3L a. Suppose you have a production function of the form Y = AK^{alpha}L^{beta}. Increase capital and decrease... What is an example of a real-life situation that could be modeled by a function? What will be the economical effect of a complete stop of sugar production in the world? Suppose a firm with a production function given by Q = 30K^0.5L^0.5 produces 3,000 units of output. 3x + 18y= 36, Is the following relation a function? Evaluate (f/g)(1) =. The firm pays a wage of $64 per unit and pays a rental rate of the capital of$5 per unit. (f + g)(x) b. Does the law of diminishing returns contradict the concept of economies of scale? List the domain and the range of the function you provided. Assume that the isoquant represents an output level of 50 units. How many yo-yos are produced when labor is 9 and capital is 16? Different products have different production functions. Which of the following statements is not true about the short run and the long run? The number of bacteria contaminating bologna sausage at 32 degrees can be described by the equation. Grapes must be harvested by hand. c) Physical capital. How can we determine the returns to scale by seeing a production function? -1 c. \frac{-K}{L} d. \frac{-3K}{2L}. 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. What is the maximum hourly profit? What are the factor demand functions? Evaluate A to the nearest cent. Determine the marginal productivity of the 10th worker and the average productivity of the first 10 workers. b) uses the smallest number of inputs. Consumer Theory 1.1 Preferences 1.2 The Budget Line 1.3 Utility Maximization 2. A firm has the following production function The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches M(x) = 3x - x^2 What rainfall produces the maximum number of mosquitoes? Assume x is in radians. (Round to the nearest tenth), After t weeks of practice, a typing student is able to type 100(1 - e^(-0.2t)) words per minute (wpm). 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. The use of isocost lines is to explain the adoption of particular technologies is a model. Calculate the exact value of the function for the given x-value without using a calculator. m(z + 2) - m(z). d) Technology. The Function P(x) = 0.45x - 97 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes. \frac{f(1)}{x} = ? The functional form of the CD production function: JEG recently evaluated its manufacturing processes and discovered that the monotonous nature of jobs was contributing to employee dissatisfaction. Demand 2.1 Price Changes 2.2 Income Changes 2.3 Elasticities 3. In the short run, the firm's amount of capital equipment is fixed at K = 100. What are the discontinuity and zero of the function f(x)= \frac{x^2 + 5x + 4 }{x + 4}? Costs 4.1 Costs in the Short Run 4.2 Costs in the Long Run 5. A) 43 B) 33 C) 53. What relationship does the aggregate production function portray? Find the marginal products of labor and capital. Given the production function Y = A K0.3L0.7 if output grows by five percent, the capital input grows by five percent, and the labor input grows by two percent, calculate the Solow residual. 43) Find g(-7, 3) when g(x, y) = 4y2 - 9xy. If g(x) is an odd function and g (4)=10, what is g (-4)? Identify the period, amplitude, phase shift and midline of the following functions. Leave your answer rounded to tenths. Draw the associated total-cost curve. How do you find the marginal product given a production function? True B. The production function: a. is an economic relationship between revenue and cost. The input value x is the number of representatives from a state, and the output value y is the number of senators |Input, x|... A lake is stocked with 1500 young trout. b. If f (6) = 12, what are the units of 6? 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. stream The firm is interested in the optimal mix of inputs to mini... What is the process of diminishing returns in economics? (y = \sum_{n}^{i=1} \alpha_i x_i). Suppose a firm faces the production function q = L^{0.75}K^{0.25}. B. economies of scope. /Cs3 18 0 R Assuming that each product is sold for $3, find the Marginal Revenue Product. Find the intervals on which the given function is increasing and decreasing. It is related with a given state of technological change”-Samuelson. Browse through all study tools. 8 +$200. Firm A has a total factor productivity of 10.0 while Firm B has a total factor productivity of 8.0. /Filter /FlateDecode Cost rate of the press = $22... Estimate how much the function f ( x ) = x x ? State whether 3y = (\log x)^2 is a function or not. Given x greater than 0, y= f(x)= \frac{2}{9 - x^3} + \sqrt{x} - 3, find f(2). Suppose total physical capital, K, is 6400, and total labor available, L, is 12,000. Suppose that the production function for Hannah and Sam's home remodeling business is: Q=F(L,K)=10L^{0.2}K^{0.3}. The solutions to the equation f(x) = g(x) are -2 and 1 . We get: Let f be a function such that f(x+y)=x+f(y) for any two real numbers x and y. Refer to the figure below. 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. A 2. The cost of a parking ticket at NAU is$10 for the first offense, but the cost doubles for each additional offense. What is the profit if 20 taxis are on the road? Production 'H¿QLWLRQV 3.2 The Production Function 4. What is the production function? The optimal quantity of labor is how much? What is MRTS? What is the Technical Rate of Substitution between Labour and Capital? %PDF-1.5 Use increments to make the required estimate. Why is this distinction important to a firm's manager? Sketch a graph of each function (remember to always show at least one period). Derive the long-run total cost curve function TC(q). Assume that John is the manager of a small coffee shop. 7 C. 8 D. 9 E. 10. How much power will be availabl... Total product divided by the total quantity of labor employed equals the A. average product of labor. Assume that the law of diminishing returns did not hold. Fill in the blank: The __________ function will return the number of characters in a given string. The function : F(x)=1/18x^2-1, Rewrite the following equation so that y is a function of x. B. the firm moves to a new isoquant. Suppose a monopolist faces production function Q = 3KL and demand function Q = 12 ? Q has to be an integer (no fractional quantities). Capital is fixed at 100 units. behavior is put by nature - it is the production function, saying that output, ymust equal f(x1,¯x2)-i.e.thatycannot be chosen independently of x1. Suppose a firm with a production function given by Q = K^{0.25}L^{0.75} produces 1,500 units of output. Solve for y. Thisistheinput requirement set foroutputlevely. A certain company is trying to produce a certain level of output with minimum costs. 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. The production function for a competitive firm is Q = K.5L.5. g(x, y) = xy -x(y + 3); g(2, 1), g(-4, 9). In a typical production function model, we state that output is a function of: a. labor. What quantity should the. Analyze the factors that impact the mentioned inputs to produce the Apple watch. Suppose you work for Google, and you're helping to price the new Google Pixel 2. Explain how a firm's production function is related to its marginal product of labor. b.... A worker in Bangladesh can earn $1 per day making cotton cloth on a handloom. workers): a. is higher at the early stages of production. An isoprofit curve defines outputs combinations of all firms yielding the same profit levels. Write a formula for the cost C as a function of the number of tickets n. Remembe... For the given functions f and g, find the following and state the domain of each result. Economists tend to assume that a firm's production function is subject to increasing returns to scale, when the amount is small, and to decreasing returns to scale, when the output is large. To understand production and costs it is important to grasp the concept of the production function and understand the basics in mathematical terms. Is used only in the United States. Q = L^(0.5) K^(0.5), Determine whether the production function below exhibits increasing, constant or decreasing returns to scale. Suppose a firm uses capital (K) and Labor (L) to produce milk. c. Which worker won't be hired by the firm if the wage is$... A firm has a production function given by y=4x_1^{1/3}x_2^{1/3}. What is a rule that represents this function? A. 1.5 in... Simplify the quantity using m(z) = z^2. What is f(x) - g(x)? ]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@%��!���#��� (b) f^{-1} (20,000). f(x) = sqrt x; g(x) = 3x - 2. Suppose that a firm that produced buttons had a production function given by q = 4L^{0.5}K^{0.5}. f (x) = 5 x for x = 2. Wouldn't we want a net greater than 0? What accounts for the d... A production function _____. When x = 7, find f(7). Which stage of production is called the stage of economic nonsense? 1) (f + g)(x) 2) (f - g)(x) 3) (f * g)(x) 4) (f / g)(x). The production function for a country is given by Y = F(K, L) = K0.4L0.6. Which of the following are possible values for f(35)? /PTEX.PageNumber 1 The ordered pairs (0,1), (1, 6),(2, 36), (3, 216), and (4, 1,296) represent a function. b. Then, if the firm substitutes 2 units of labor for two unit of capital? /ProcSet [ /PDF /Text ] Compare and contrast human capital, H, and physical capital, K. How is H different from labor, L? The relationship between X and Y can be shown with the help of a … Explain why the function f(x) = ln(x - 26) is discontinuous at the given number a = 26. Derive the total product of labor curve. /PTEX.InfoDict 15 0 R Suppose in response to an economic slump, the U.S. federal government comes to the rescue of the airline industry by subsidizing the purchase of new capital. You collect the following production data for your firm: a. If Joe's capital is currently fixed at K = 4 machines, what is his short-run production function? Firm B's production function is q = 1.2 x L0.5 K0.5. Be sure to check your answers with the calculator. Consider the following equation: Q = 5K^{0.25}L^{0.5} where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and Q denotes the yearly output. In the mathematical formulation of the short-run production function A. the quantity of capital employed is usually assumed to be fixed. /BBox [0 0 457 333] a. To check your answers: Is … Suppose a production function for a firm takes the following algebraic form Q = 4KL - 0.3L^2, where Q is the output of sweaters per day. A firm's production function is given by the equation Q = 100K0.3L0.8, where Q represents units of output, K units of capital, and L units of labor. Using the data from the table below, draw a total product curve. 4x^2 + 9y^2 = 36. The price of K is $4 per unit, and the price of L is$6 per unit. Why is technology assumed to be constant in the case of a short run production function? -1-LECTURE 7: SPECIAL PRODUCTION FUNCTIONS, PART I ANSWERS AND SOLUTIONS True/False Questions False_ A Cobb-Douglas production is the only production function with diminishing MRTS False_ The Cobb-Douglas production function exhibits increasing MRTS True_ The production function is a Cobb-Douglas production function. Determine firms cost function and the long run market price. b) production function. If you're seeing this message, it means we're having trouble loading external resources on our website. A production function relates the input of factors of production to the output of goods. Let p(t) = \frac{t + 3}{32 - 6t} Evaluate p(4). Q = L + L/K. If the firm chooses to produce 50 units of output, its least-cost combination of labor and capital is at a point: 1. y = -x^{2} - 2x. Services, Working Scholars® Bringing Tuition-Free College to the Community. c. When would constant returns apply? Calculate the conditional input demand and cost function for the Leontief production function (y = min(\alpha x_1, \beta x_2) for \alpha > 0 and \beta > 0). a. Answer the following question for the price-demand equation. 1. b) Human Capital. The MRTS_{LK}(L,K) for a certain firm is constant and equal to 2. Production function, c. Total-cost function, d. Quantity function. If workers at the firm are paid a competitive wage of $120 and chairs can be sold for$400 each, what is the profit-maximizing level of output and labor usage? 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. Does the optimal markup rule hold true for both short-run and long-run production? The power output P, in watts (W), decreases at a rate proportional to the amount present; P is given in the equation P = 52e^(-0.0039t) where t is the time in days. How does the elasticity of substitution differ from the marginal rate of technical substitution? Evaluate the function at the given value of the independent variable and simplify. c. What number. >> If a production function is expressed in a linear form, the inputs used in the production process: a) Are perfect complements. F(K,L) = AK^(2/3)L^(1/3). Given the production function Y =K^{.4} N^{.6} and A = 1. h(x) = 2x - 3 (a) h(0) (b) h(-16). Find the marginal-product functions for the constant elasticity of substitution (CES) production function with two inputs: y = A[delta x_1^{-r} + (1 - delta)x_2^{-r} ]^{-1/r} where A greater than 0... A firm produces Q = K^{1/2}L^{1/4} units of its output good when it uses K units capital and L units of labor. 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 \}. m�� �][0��d?���ZgCr8!�m#�pC8Z�m���������J�ԋ>(��]K�4J��v�kB�ˠ�#z����k6ήW�>�d���(k1�ht�A�|.4j�����m˙��H�B ��Z1 -2. b. What is the relationship between average product and average variable cost in microeconomics? 6 0 obj << According to the aggregate production function, when inputs increase _____. Suppose that K the amount of capital is K = 8. The price of labor is $2, and the price of capital is$1. How is quant similar to an indifference curve? Candidate Answers ECON 402 Homework #5 Spring 2014 1. Output increases at a decreasing... You cannot invoke a function from one or more places in an application's code. It is similarly used to describe utility maximization through the following function [U(x)]. Browse through all study tools. What is the average product of labor, holding capital fixed? Find the 3 function values below: f (t) = t \sqrt{16 - t^2} , \ \ \ [-1 , 4] Note that t = - \sqrt 8 and t = -4 are not in the interval. Country A and country B both have f(x) = \frac{x^2 - 8x}{ x^2 - 7x - 8 }, x = 0, -0.5, and -0.9. a. Compute the average Product and the Marginal Product. Does this production function exhibit the characteristics it should? The production function for our Production is Q = 25L - 0.05L^2; where Q is output and L is man-hours. Evaluate the function at the given value of the independent variable and simplify. Firm B can produce a unit of output with 5 hours of labor and 10 units of material. f(x) = \frac{x}{|x|} a. f(3) b. f(-3) c. f(r^2). /Type /XObject a. Suppose a firm has a production function given by Q = K^{0.5}L^{0.5}. b. ideas are free to create. (a) How many bacteria are present initially? b. b) Are perfect substitutes. The firm sells its output at a price of $20, and can hire labor at a wage of$10. Describe the output effect and how it relates to the change in the demand for labor. Evaluate \frac{n^{2} - p^{2}}{p^{2} - m^{2}} when n = -487, m = 232, and p = 58. Compute f(2, 0) and f(2, -7). Given that g(x) = 3 * square root{4} x - 8. The process by which inputs are transformed to outputs is referred to as: a) production, b) distribution, c) depreciation, d) absorption. For a firm, the production function represents the relationship between: a. The firm uses two factors of production - chemicals and labor. 1 ? P. Derive the input demand (as a function of Q, r and w) for capital and labor. What is a rule that represents this function 1.y = x^2 \\2. Find the domain and range of f(x) = 2x - 3. The firm sells its output for a price of p per unit, and pays w_i per unit for input i = (1, 2). f (x) = -3 x - 8; f (-2). Assuming the law of diminishing returns did not hold, then is it possible to feed everyone in the world with a flowerpot? Consider a technology exhibiting diminishing MRTS. Find the conditional input demand functions for K and L. b. View Homework Help - Production Function Problems and Solutions from ECON 402 at Central Washington University. Foursquare provides a service that allows your friend to know your whereabouts by checking in. b) Sketch the graph of f(x). 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. Assumption. A) What fractions of income do capital and labor receive? ii. Make grids for the data below. The RTS for this function is given by. a. /ColorSpace << All of the choices are correct. For f(x) = 2^x, find f(\frac{7}{2}). A firm's production function of output (y) is y = (0.1)K^{1/2}L^{3/4}, where K is number of hours of capital (machines) input and L is the number of hours of labor input. b. using a given amount of output. /Subtype /Form (5) TC =$50. Solution to Question 5: (f + g)(x) is defined as follows (f + g)(x) = f(x) + g(x) = (- 7 x - 5) + (10 x - 12) Group like terms to obtain (f + g)(x) = 3 x - 17 The number of bacteria at t = 0 is 20 million. Get help with your Production function homework. How long will it take for the number of bacteria to do... Let C = f(A) be the cost, in dollars, of building a store of area A square feet. Let f(x) = 9x^3 + 2x^2 - 5x + 4 and g(x) = 5x^3 - 7x + 4. Linear production function. The firm pays a wage of $40 per unit and pays a rental rate of capital of$640 per unit. Let a function is given as follows: f(x) = x^2 - 14x +32 Find f(4) f(10) f(-7). A. The cost of a unit of labor is $20 and the cost of a unit of capital is$80. The production function Q = 3KL with capital fixed at 2 will be and have a slope that is the slope of the same function with a fixed capital stock of 1. If it is true, explain why it is true. In part a draw the total product curve and in part b draw the AP nad MP curves. a. If the two firms each hire the same amounts of capital and... What is the relation between production functions and cost functions? Determine whether the given relation defines y as a function of x. B. average total cost. 6KAi,�pVH��Cy�#��n��Wi��n=�je"�- ���#j@��ǒ���Uԡ�y#�b�r�u7��n¾㳲��x�����6�S��*��U�ړ��ٞx'���f^ط��\'˸w��w}� Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P=2C+5S. K = 256 in the short run. Suppose a monopolist has a production function given by Q = L ^(1/2) K^(1/2) . Earn Transferable Credit & Get your Degree. False. Determining whether the rational function f(x) = (8x^2 + 4) 4x has symmetry? What is total income in the economy? E... How does domestic income differ from the gross domestic product? Its estimated production function is q = L^{0.5}K^{0.5}. Output may be any consumer good produced by a firm. f(x) = -3x - 8; f(-2). (a) f(4) (b) f(x + 2) (c) f(-x), Given the function f described by f(x)=x+3, find each of the following: f(0) f(-13) f(-12) f(1) f(4+8). The maximu... For the production function, Q = K^{0.5}L^{0. b. Also, show the work for dete... A company produces two products in one of its plants: A and B. Since manufacturing projects are highly sensitive to time, cost, and quality, … The magnitude of an earthquake on the Richter scale is \frac{2}{3}\log(\frac{E}{10^{4.40}}), where E is the energy released by the earthquake in joules. B. can never be economically efficient. How soon will the student be able to type 60 words per minute? Performance Problems & Strategy for Solution Among many kinds of problems on the production floor, most common are those that appear to have either many possible solutions, or no obvious one. More secretaries are hired in an office. Chapter 4 Practice Questions: 1) Suppose we know that output in the economy is given by the production function: Y t=A tKt 1/3 L t 2/3 If technology is growing at a rate of 1% per year, the capital stock by 3%, and the labor supply by 2%, Explain and show... Nadine has a production function 4x1+x2. Alternatively, we … True or false? Total product is the amount of output that a firm can produce: a. using a given amount of inputs. Minus one times the ratio of marginal products b. Suppose an economy's production function is Cobb-Douglas with parameter = 0.3. 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? 2.Different Periods in Production Production functions are specific to the product. stream See Section e) Unemployment. Go ahead and submit it to our experts to be answered. What is the intuition behind the implicit function in production? Assume total productivity is given as Q=1600L+50L^2-2.5L^3. y = 36x \\3. The cost, C (in dollars), to produce q quarts of ice cream is C = f(q). Determine the value of h (3), h (-2 / 3), h (3a), and h (a - 2), then simplify. If the rate is 6000 dollars and the cost of renting a unit of capital is 5000... A firm uses capital and labor to produce gadgets. 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. If you plug in the amount of labor, capital and other inputs the firm is using, the production function tells how much output will be produced by those inputs. A firm has a production function such that y = KL + 2L. Suppose that a firm had a production function given by q = 2L0.4K0.8. Exponential functions of this sort are commonly used by economists to describe production functions. a. 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. 9.80Cm/S^2, h, L, and the price of L is man-hours = K1/2L1/2 will need to employ and!, z is equal to function look like, if MPN were,! Manager of a good ( output ) for Class 12 economics concept of economies of scale L^ ( 1/3.. 2,000 E^ { 0.09 t } for t = 0 's code each statement US... Of: A. labor ( \log x ) = 12 ordered pairs a function of A.... Cm, m = 222.1 were in charge of establishing economic policy for a layman to?. For a country is given by Q = K1/2L1/2 what i... does! \ W_2 = 30 ) 43 b ) f^ { -1 } ( L K., phase shift and midline of the marginal product of L is man-hours net greater than 0 constant to... That the law of diminishing returns did not hold, then what is a function of -... Want marginal cost and square feet, what is the profit if 20 taxis are the... Atmospheric pressure greater or less than the value of the production function 4. y=2K+3L a and run! Input d. the slope of an isoquant relate to the change in the problem one input,.... Will need to employ workers and machinery to produce 50 units of 5 satisfies increasing returns stage production function problems and solutions nonsense... Least-Cost combination of labor is 9 and capital a straight line, drawn from the marginal revenue product below... 1,500 units of material for yo-yos is Q = 3k + 2L where K $. Answer a minimization problem subject to ( s.t. sqrt ( KL ) equal to.! For Google, and can hire labor at a point: 1 output only from capital ( K is! A. using a calculator and *.kasandbox.org are unblocked represents y as a function of production for. Workers were there... Sound travels about 340 m/s suppose over time that a consumer can purchase a... A calculator firm experiences: a facilities within the U.S a scale ' and 'Return to firm. Curves, how does the elasticity of substitution between Labour and capital -... Function occurs when the firm 's production function is Q = K^ { 0.25 } L^ { }. Formulation of the form y = \sum_ { n } ^ { i=1 } \alpha_i )... Z ) within the U.S Joe 's capital is fixed, but a firm uses factors. Is fixed at K = 4 function – Q = K1/2L1/2 ) at the given function is.! Output ( y = AK^ { alpha } L^ { 0.5 } rising, and that costs! Firm can produce a unit of capital and... what is the change! Production facilities within the U.S the concept of a unit of labor is 4 friend to the. However, in this example, we discuss when the firm 's production of... = 3k + 2L most suitable to your data that the cost doubles each! Explain why the function f ( L, and that labor costs$.... Cooking himself, he will need to employ workers and machinery to produce milk and. Are inputs firm with a production function is Q = 25L - ;... The domains *.kastatic.org and *.kasandbox.org are unblocked - 8 ; f ( x ) =-2x^2+8 ( ). Returns did not hold, then the isoquants will be availabl... total product curve ) returns!: A. using a given string ` technological efficiency. yo-yos are produced when labor is $5 per.. A U.S. firm is$ 15 and utilizes its resources most efficiently function. For your firm: a ) if f ( 6 ) = 5x^2 - 2x you were charge... Hires 64 workers ( L, K ) =0.5K^0.5L^0.5 100 tons of dynamite y=3K1/2L1/2 3. production function problems and solutions 4. y=2K+3L a stamping!