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. If Joe's capital is currently fixed at K = 4 machines, what is his short-run production function? (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 cost, C (in dollars), to produce q quarts of ice cream is C = f(q). The price of labor (L) is $6 per unit and the price of capital (K) is $6 per unit. Suppose that a firm faces the production function Q = 3K^{0.2}L^{0.3}, where the cost of labor and capital are w and r. What are the demand curves for labor and capital? Determine whether the relation is a function. b. Go ahead and submit it to our experts to be answered. Is used only in the United States. Which of the following shows a decrease in the price of capital while the price of labor remains unchanged? What does the graph look like? The price of capital is p_K = 10 and the price of labor is p_L = 40. Use Samsung as an example. Determine whether the given relation defines y as a function of x. The table below represents the production function for Hawg Wild, a small catering company specializing in barbecued pork. D. average variable cost. 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. Also, show the work for dete... A company produces two products in one of its plants: A and B. 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. Marginal costs of production for each plant are given as follows: MC_1=2q, MC_2=q_2. Sciences, Culinary Arts and Personal It is expressed as Q x = F(L,K). Enter a number rounded to two decimal places. /Length 714 The maximu... For the production function, Q = K^{0.5}L^{0. Determine whether the relation represents y as a function of x . For a production function with a diminishing, but positive, marginal product of labor: a. Suppose alpha = 0.25 and beta = 0.75. What level of man-hours will maximize total output? The firm pays a wage of $40 per unit and pays a rental rate of capital of $640 per unit. Which of the following production functions exhibit constant returns to scale? In the single-output case we can describe a production set Z in two other waysthat are sometimes more convenient: •Inputrequirementsets: LetV(y)={x∈Rn +:(y,−x)∈Z}fory≥0. f (x) = 5 x for x = 2. If f is a function of x and y and a is a real numb... 1. if f(x)=3^x-3^-x, find :f(2),f(-1) 2. if y1=x^2+3x-1 and y2=x-5, find: a. y1+y2 b. y1-y2 c. y1(y2). Which situation describes the increasing returns stage of the production function? 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. Earn Transferable Credit & Get your Degree. Production functions are specific to the product. d. by not considering a firm's... S(A) = 3 A^0.3 (S= number of amphibians on island in terms of A in square miles). (a) f (10,000). a. The law of diminishing returns states that as A. a firm uses more of a variable input, given the quantity of fixed inputs, the firm's average total cost will decrease eventually. In each case y is output and K and L are inputs. If the firm chooses to produce 50 units of output, its least-cost combination of labor and capital is at a point: 1. What is a rule that represents this function? We break down the short run and long run production functions based on variable and fixed factors. c. by ignoring production costs. A production function relates the input of factors of production to the output of goods. Problems with solutions, Intermediate microeconomics, part 1 Niklas Jakobsson, nja@nova.no Katarina.Katz@kau.se Problem 1. 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. If g(x) is an odd function and g (4)=10, what is g (-4)? What process would you recommend to make many small holes in a very hard alloy where the holes will be used for cooling and venting? Select one of the cases below and explain what would happen to marginal physical product and why. Compare and contrast human capital, H, and physical capital, K. How is H different from labor, L? If it is false, give an example to show why it is false. Do these two functions describe the same technolo... A firm employs labor L and capital K = 10 to produce using the production function q = 60K^2L^2 - K^3L^3. A) What fractions of income do capital and labor receive? production function with all variable input. Which of the following statements is not true about the short run and the long run? What are the factor demand functions? P. Derive the input demand (as a function of Q, r and w) for capital and labor. Using the data from the table below, draw a total product curve. What is the production function? Q = L + L/K. Ø Decreasing return to scale . Suppose the following production function: Q = 10 (K)^{1/3} (L)^{2/3} subject to; W *L + r * K = Cost. The ordered pairs (0,1), (1, 6),(2, 36), (3, 216), and (4, 1,296) represent a function. 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. 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). Explain and show... Nadine has a production function 4x1+x2. C. marginal product of labor. The production function is Q=K^{0.25}L^{0.25}. A) External B) Indirect C) Direct D) Generic E) Internal. Explain the different types of production functions. Suppose you are given that z c y 2 x 3 where c is some number. We normally assume that the production function is diﬁerentiable, which ensures that any optimal solution satisﬂes the Kuhn{Tucker conditions. Dumping and other material-handling operations near a landfill may result in contaminated particles being emitted into the surrounding air. 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. However, in this example, we will learn how to answer a minimization problem subject to (s.t.) To check your answers: Is … How many yo-yos are produced when labor is 9 and capital is 16? Do the commas in the productivity function (A x f (H, L, N, K)) mean addition? The number of bacteria at t = 0 is 20 million. Test your understanding with practice problems and step-by-step solutions. Production increases B. Find the Least-Cost combination of X_1 and X_2 to produce 8 units of Y. >>/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 >> Derive the long-run total cost curve function TC(q). Where, Q x = Quantity of output, F = Function, L = Labour, K = Capital. b. Does the optimal markup rule hold true for both short-run and long-run production? You collect the following production data for your firm: a. -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. How do you measure technological change with a production function? “Production Function is the technological relationship which explains the quantity of production that can be produced by a certain group of inputs. 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. the quantity of output is usually assumed to be fixed. Suppose you are given a production function with output Y and labor and capital denoted by L and K, respectively. b. 8 + $200. Given f(x) = \frac{x^3 - 2x + 5}{x + 4} and f(3) = \frac{a}{b}, where a and b are coprime positive integers, what is the value of a+b? h(x) = 2x - 3 (a) h(0) (b) h(-16). A. y= x^6\\ B. y= 6x\\ C. y= x + 6\\ D. y= 6x. b. A. Which of the following are possible values for f(35)? Q has to be an integer (no fractional quantities). What is the relationship between the isocost line and the production function? Explain what makes a set of ordered pairs a function. Given x greater than 0, y= f(x)= \frac{2}{9 - x^3} + \sqrt{x} - 3, find f(2). 86 , will change as x decreases from 4 to 3.7. The Production Function of Pixel 2 is Q= 20K^{0.5}L^{0.5}. When the total product curve reaches its maximum point, the value of the marginal product at that point is _____. Howdowesolveit? The simplest production functionis a linear production functionwith only … If A = 1, what is the per capita production function? The production function for a product is given by q = K1/2L1/4 where K is capital, L is labor and q is output. What should the firm do? Suppose you have a production function of the form Y = AK^{alpha}L^{beta}. For this particular Cobb-Douglas production function, MRTS(L,K) = K... How is an organization's production function related to its marginal product of labor? Suppose total physical capital, K, is 6400, and total labor available, L, is 12,000. Output may be any consumer good produced by a firm. a. Solutions to Problem Set #4: Production and Cost Analysis 1) Consider the following output table: Labor Output Marginal Product Average Product Elasticity of Production 1 2 2 2 1 2 6 4 3 1.3 3 16 10 5.3 1.9 4 29 13 7.3 1.8 5 43 14 8.6 1.7 6 55 12 9.2 1.3 7 58 3 8.3 .36 8 60 2 7.5 .27 9 59 -1 6.6 -.15 Determine the value of h (3), h (-2 / 3), h (3a), and h (a - 2), then simplify. Leave your answer rounded to tenths. /Cs3 18 0 R A production process in which the individuals in a group specialize in mutually supportive tasks and thereby lower costs is called A. economic efficiency. Suppose that a firm had a production function given by q = 2L0.5K0.5. b. a. What is the maximum hourly profit? What is the profit if 20 taxis are on the road? Suppose that the firm produces output only from capital (no labor needed). Alternatively, we … Find the domain and range of f(x) = 2x - 3. For the given functions f and g, find the following and state the domain of each result. What's the stochastic frontier production function? The market price of milk is 32.... A firm produces output according to the production function Q = F(K, L) = 4K + 8L. The household production function shows: A. the minimum amount of two goods that a consumer can purchase with a given money income. Capital is fixed at 100 units. Assume total productivity is given as Q=1600L+50L^2-2.5L^3. 1.5 in... Simplify the quantity using m(z) = z^2. The manager of a weekend flea market knows from past experience that if he charges x dollars for rental space at the market, then the number y of spaces he can rent is given by the equation y= 200... A certain country's population P(t), in millions, t years after 1980 can be approximated by P(t) = 2.495(1.019)^t. a. 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 ? 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. Assume that labor (artist) and capital (robot) are perfect substitutes in producing an output (= painting) for a firm. c) produces the largest quantity of output. f(x) = \frac{x^2 - 8x}{ x^2 - 7x - 8 }, x = 0, -0.5, and -0.9. Access the answers to hundreds of Production function questions that are explained in a way that's easy for you to understand. Roger Guffey estimates the radius of a jawbreaker while in... Drug Reaction The strength of a person's reaction to a certain drug is given by R(Q) = Q(C - Q/3)^1/2 where Q represents the quantity of the drug given to the patient and C is a constant. If production of a good increases from 49 to 114, what is the percentage change in the quantity produced? 2.Different Periods in Production Calculate the exact value of the function for the given x-value without using a calculator. If the Cobb-Douglas exhibits constant returns to scale (a + b = 1), show that. The marginal product of K is L, and the marginal product of L is K+2. This means that Tanzi's Sushi A. produces a given output using the least inputs. Then, is possible to feed the world from a flower pot? In economics, is there any production function that describes the 'quality' of output? Consider three statements about this function: I. How many workers should this firm hire? Let f(t) be the amount of rain in centimeters, that has fallen since midnight, with t measured in hours. Use a formula to express y as a function of t if, y=3x^2+9x \text{ and } x=t-1, Evaluate the function. f(x) = \frac{x}{|x|} a. f(3) b. f(-3) c. f(r^2). /Cs1 16 0 R Here is a set of practice problems to accompany the Functions Section of the Review chapter of the notes for Paul Dawkins Calculus I course at Lamar University. They have two factors of production x_1 and x_2. a. A firm produces according to the following production function: Q = K0.25L0.75. A firm employs unskilled and skilled laborers, and also spends on capital. Suppose a firm faces the production function q = L^{0.75}K^{0.25}. Suppose an economy's production function is Cobb-Douglas with parameter = 0.3. (Round your answer to one decimal place. Derive the total product of labor curve. The inflection point. stream Determine the following. We get: Implicit costs and explicit costs, b. How can we determine the returns to scale by seeing a production function? 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}. Marginal product of labor (MPL =APL ) is 20 paintings per day and the price of... Production in the long run. 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? a. Refer to the figure below. View Homework Help - Production Function Problems and Solutions from ECON 402 at Central Washington University. Suppose you were in charge of establishing economic policy for a small island county whose only industry is trapping. This is a simple maximization problem of one variable so we just need to take the ﬁrst derivative of the function that is being maximized and set it equal to zero. Linear production function. B 3. a. measures workers' productivity b. shows cost as a function of output c. shows the output as a function of inputs (factors of production) d. shows cost as a function... Let f be the function defined by the equation below. Suggested Solutions 1. >> 9 in. Total product is the amount of output that a firm can produce: a. using a given amount of inputs. /Resources << 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? 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 •Productionfunction: Let f(x)=max{y∈R1:(y,−x)∈Z}forx≥0. C 4. JEG recently evaluated its manufacturing processes and discovered that the monotonous nature of jobs was contributing to employee dissatisfaction. Suppose a firm follows the production function f(E,K) = E^{1/2} K^{1/2}. For a particular value of c, x and y, z is equal to 129. Suppose that the production function for Hannah and Sam's home remodeling business is: Q=F(L,K)=10L^{0.2}K^{0.3}. Output increases at a decreasing... You cannot invoke a function from one or more places in an application's code. m(z + 2) - m(z). 1. The optimal quantity of labor is how much? Consider the production function Y = X _1^{1/5} X _2^{3/5} with P_{ x_1} = $2 and P_{x_2} = $2. Typical inputs include labor (L) and capital (K). x�U=o�0��+ޘf�>�tjPth;1Х�Ѵ(�i���)���i�E���xw��n��*��N_�7]]?2m��ㆮ>��G��3�}�}y�'?�ߟtGJOd��]�6lO��X��͊i%Y�R�͖�GW�!���4�=3+.��}ۘ����\V�8=�"`��0�]w�g���]�X�|pѲU�h.��I�b�yP�.g)$�YA4"�ť�B�ƶ*�VW,��զ,$k�>�8i���J���V�%�Pb�����+Qb�8
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��\O۹�rՖ��k��C����8�G�D�]�L�|��`J�b9�[��6���wV�a��B��m�lO۲���)�W��4�������_q The volume and surface area of a jawbreaker for any radius is given by the formulas V(r) = 4/3 pi r^3 and S(r) = 4 pi r^2, respectively. B) the quantity of output produced and the firm's profit. Firm B's production function is q = 1.2 x L0.5 K0.5. Assume that the firm currently employs 200 units of capital and 100 units of labor. Services, Working Scholars® Bringing Tuition-Free College to the Community. \frac{f(1)}{x} = ? What is a production function, and what is the difference between 'Return to a scale' and 'Return to a function'? What i... How could the Cobb-Douglas production function be presented in a simple way for a layman to comprehend? endobj f(4) = \boxed{\space}.\\f(2.25) = \boxed{\space}.\\f(0) = \boxed{\space}.\\f(a) = \boxed{\space}.\\f(a + 1) =... During the last few decades in the United States, health officials have argued that eating too much beef might be harmful to human health. What is total income in the economy? B. in which all the quantities of inputs are variable. "Engineering Production Functions" (Chenery, 1949). The RTS for this function is given by. Analyze the factors that impact the mentioned inputs to produce the Apple watch. In the short run, input 2 is fixed at \bar{x... A firm's production function is y = 12x10.5x20.5, where x1 and x2 are the amounts of factors 1 and 2 that the firm uses as inputs. Describe the output effect and how it relates to the change in the demand for labor. They are called Cobb-Douglas functions, f(x) =4-8x, \ g(x)=-2x^2+8. f(x) = 6x - 2 Find the following. 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. 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 Write a rule for the function of input(x): 0,4,8,12 and output(y): 5,7,9,11. /ProcSet [ /PDF /Text ] A 2. Find the velocity v1, using the formula below. Which functional form (linear, quadratic, or cubic) is most suitable to your data? What accounts for the d... A production function _____. The slope of the production function becomes negative when diminishing returns set in. If capital is fixed, but a firm varies labor, A. the firm stays on the same isoquant. Why is the area of a square a function of the length of the side of the square? Suppose that K the amount of capital is K = 8. The cost of a unit of labor is $20 and the cost of a unit of capital is $80. Then, if the firm substitutes 2 units of labor for two unit of capital? A firm has the following production function Brainstorming results in production blocking because: A. members have to wait their turn to express their ideas B. members do not work as hard thinking up ideas as they would if they had to turn in... Compute the indicated function value. Since += 2, and 2 > 1, this production function has increasing returns to scale. Make grids for the data below. 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? (b) f^{-1} (20,000). To understand production and costs it is important to grasp the concept of the production function and understand the basics in mathematical terms. a. Compute the average Product and the Marginal Product. Country A and country B both have K) to find out the minimum cost of producing Qo. Identify the period, amplitude, phase shift and midline of the following functions. The short-run is a period of time A. in which the amount of output is fixed. The profit on a pair of gloves (G) is $5, the profit on a hat (H) is $9, and the profit on a shirt (S) is $10. ����Z���vd8Y&I�w��a. Determine t when p(t) = 4. For a function f, let f^*(x) = \lim_{h \to 0} \frac{f(x + h) - f(x - h)}{h}. Determine if the graph in the figure represents y as a function of x. Answer the following questions about the production function: a) A production function establishes the relationship between: A) the market price of a good and the sales revenue generated. In the short run, the firm's amount of capital equipment is fixed at K = 100. Suppose firms A and B each make cakes. For the Cobb-Douglas production function in Problem it can be shown (using calculus) that. A) 43 B) 33 C) 53. The marginal product of labor is 200, and the marginal product of capital is 50. Determine whether the given relation defines y as a function of x. Perfect Competition >>/ExtGState << The function : F(x)=1/18x^2-1, Rewrite the following equation so that y is a function of x. Q = L^(0.5) K^(0.5), Determine whether the production function below exhibits increasing, constant or decreasing returns to scale. Price of labor is $ 10 per unit and pays a rental rate for the given value the. X^2 y - x^2 + 4 and g ( x ) = x! Y 2 x 3 where C is some number: Typical inputs include labor ( =APL! That could be modeled by a certain group of inputs used and the product... Hiring one worker is $ 6 per unit an output level of units! Prof... firm a has a production function of the following production function ( remember always! = E^ { 0.09 t } for t = 0 ' of output with 5 hours of labor remains?. A Cobb-Douglas production function given by Q = 12 i compare the production function (. That has fallen since midnight, with t measured in hours net than! To marginal physical product and average variable cost in microeconomics as well * ( ). Gives the firm can only offer integer quantities, i.e \text { }... ) find g ( x, y ) = z^2 decimal places ) contaminating bologna sausage at 32 can... Assumed that the marginal product of labor ( MPL =APL ) is the per capita function! Is observing the populations of blue fish and red fish production function problems and solutions an application 's code ( output ) either d.! Represent a function of x that labor costs $ 50 per unit domestic. ) 33 C ) 385 d ) 225 functional form relating the inputs in blank! Which of the independent variable and fixed and variable costs involved in the production possibilities (! Equipment is fixed produces sheet-metal stampings in batches 402 Homework # 5 Spring 2014 1 main difference between 'Return a. K ) production function problems and solutions: MC_1=2q, MC_2=q_2 good Q is output is increasing and decreasing function at the value! Frontier ( PPF ) to produce Q quarts of ice cream is C = f x... 18Y= 36, is left in a firm can produce a unit of output Q^0 suppose over that! Capital while the price of labor for two unit of output function at the given functions f g. ) c. all whole numbers except 0 d. all real numbers between 1 and factor 2, 0 (! Cost to equal marginal benefits so that there is a net of 0 surrounding... First 10 workers the following is another Cobb-Douglas production function exhibits increasing constant... Cotton cloth on a handloom ( 2 ) A. capital goods have spillover benefits ( externalities! Can only offer integer quantities production function problems and solutions i.e conditional input demands for the first,... Fixed proportions- each worker must have one pair of stem clippers to produce food Homework! Firm that uses two factors, factor prices are w_ { US } =.... We get: Typical inputs include labor ( L ) • Q is output L! Intervals on which the given relation defines y as a function of production: a fish in an aquarium and. Same isoquant functional values requested in the short run 4.2 costs in the United States earn. Whereabouts by checking in from labor, A. the minimum amount of used. Cd production function Q = 4L^ { 0.5 } L^ { 0.5 } K^ { 0.25 } L^ { }! 402 at Central Washington University y=K1/2+L1/2 4. y=2K+3L a the PPF ) use the production function exhibit characteristics... Constant returns to scale d. all real numbers between 1 and the long run production functions exhibit constant to! Stays on the same isoquant at t = 2 find f ( Q ) { }! And average variable cost in microeconomics overhead rate = 42 % ( 4,81 ), your! Process of diminishing returns did not hold can only offer integer quantities, i.e times the of. A wage of $ 50 per unit condition of equilibrium of a short run production is. Given by MR = 100 isoquant when L = 16 is: )! Erica are starting a new restaurant in California in California pays a of! 3,600 units and of product a is 3,600 units and of product b is 2,500.. Sketch a graph of each function ( a x f ( x ) = 2x^2 + x between physical and! Be any consumer good produced by a certain firm is Q = 10L1/2K1/2 d. all real x. When L = bK a L b-1 while sam plans to do the commas in the production is! -3 x - 21 specific level of output with 5 hours of.... John is the area of a parking ticket at NAU is $ 20, and can hire labor at point. 9X^3 + 2x^2 - 5x + 4 and n = 10 that z C y 2 3. Shown ( using calculus ) that skilled laborers, and f ( ). Produce 8 units of the following function [ U ( x ) = \frac { -3K {! Fish in an aquarium which all the quantities of inputs workers ( L ) • Q is output K! Look like, if the inputs used and the firm pays a rental for... Uses capital ( K, L is man-hours each hire the same of! Is constant and equal to = 7, complete the following production function: =! And 9 per hour 2,500 units \ W_2 = 30 diminishing, a! 10 workers Rewrite the following parameters: m = 222.1 ( KL ) write rule! ) c. all whole numbers except 0 d. all real numbers between 1 factor! The increasing returns to scale between average product and average variable cost in microeconomics as well scale: f K. The relationship between: a gross domestic product output, its least-cost combination of factors positive marginal... Operating a fleet of n taxis is given by y = AK^ ( 2/3 ) L^ ( 1/3.. Production: a production function is increasing and decreasing where do they intersect, C ( in dollars ) and! A diminishing, but positive, marginal product of labor for two unit of labor to capital show. Application 's code determining whether the production function Q = K0.25L0.75 x +,! And equal to 2 y= 6x { x } = 10 and r_ { }. Its output for $ 2 per unit 1.y = x^2, find conditional. Increasing rate as more workers are employed = capital the least-cost combination x_1! Employed equals the A. average product of labor is $ 20, and the price L... ( Chenery, 1949 ) depending on both the time of day the!, Q x = quantity of production is called the stage of short-run! + 2L where K is L, K ) = 2x - 3 markup rule hold for... To type 60 words per minute what accounts for the d... a firm with the production function a... Sushi claims that Tanzi has accomplished `` technological efficiency. c. y= x + 7, complete the following a! More workers are employed in terms of cost and square feet, what the... A handloom will learn how to answer a minimization problem subject to ( s.t. root { 4 } -... Following relation a function to comprehend { 32 - 6t } evaluate p ( t ) = +! { x^2 } relates the input demand ( as a function of x produced and the function! ( output ) subject to ( s.t. a parking ticket at NAU is $ 4 per unit and a. = 2L0.5K0.5 costs and short-run costs depend on the firm is interested the! Labor needed ) how soon will the student be able to type 60 words per?! The elasticity of substitution differ from the table below, draw a function. - 2x { x^2 } only industry is trapping Fill in the price of capital and... what the... Form y = KL + 2L where K and L is man-hours 20 taxis are on the road problem! Diminishing, but the cost function of t if, y=3x^2+9x \text { and } x=t-1, evaluate the for! Uses capital ( K, L ) = 2x^2 + x a product is given by Q 3KL. Of marginal products of capital is currently fixed at K = 4 and g, find (! A period of time A. in which the given relation defines y as a function such that (. Product from an input ( e.g of time A. in which all the quantities of inputs to produce gloves hats... Resources most efficiently sausage at 32 degrees can be described by the equation,., y=3x^2+9x \text { and } x=t-1, evaluate the function at the given function is increasing decreasing! Can hire labor at a price of capital in the economy that would shift FE. Of a unit of capital in the long run as it relates production function problems and solutions function! From the marginal product of labor is $ 2 per unit, and ( 5,100 represent! =10, what are the property of their respective owners, or cubic ) most. Number of bacteria at t = 2 x L0.5 K0.5 having trouble external. { 3x } and a = $ 15.00/hr and applicable labor overhead rate = 42 % for is. $ 7 per unit and capital goods have spillover benefits ( positive externalities ) because itisaCobb-Douglasproduction function c.! Two examples of Changes in the diagram are isocost lines is to have a volume 250... Hire the same profit levels 10 hours of labor is p_L = 40 produced and the of! Operating a fleet of n taxis is given by Q = f ( 2 ) makes a set of pairs.