10) Suppose that a firm uses both labor (L) and capital (K) as inputs. The firm's long-run production function is Q = F( L,K) = 5√ L√ K. The firm has 100 units of capital. If the firm uses an efficient production method, how much output does it produce in the short run if it hires 25 workers? A) 250 units B) 1,250 units C) 2,500 units D) 50 units

10) Suppose that a firm uses both labor (L) and capital (K) as inputs. The firm's long-run production function is Q = F( L,K) = 5√ L√ K. The firm has 100 units of capital. If the firm uses an efficient production method, how much output does it produce in the short run if it hires 25 workers? A) 250 units B) 1,250 units C) 2,500 units D) 50 units

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.4P

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Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Herproduction function is given by: Q(T,D) = (T1/2 D1/2)1/2*For this problem, assume F, T, and D are infinitely divisible so you don’t need to worryabout restricting to whole-number answers. a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns toscale? Explain. b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputsrequired to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)
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6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?
Lesson 7- Production Question 9
1. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5,where q is the number of computers produced per day, K is hours of machine time, and L ishours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4. a. If both companies use the same amounts of capital and labor, which will generatemore output?b. Assume that capital is limited to 9 machine hours, but labor is unlimited in supply. Inwhich company is the marginal product of labor greater? Explain.
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4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
13. Suppose you have a production technology given by f(x1, x2) = min{2x1, x2} and you are producing at the point where a1 = 10 and x2 = 20. what we mean (generally) by the 'marginal product' of an input in (a production.
II. Helping Conchita-Crem to minimize costs Suppose that the labor cost of Conchita-crem is $20 USD per hour, and the cost of capital is $5 USD per hour. Suppose the production function for conchas is q = 10L/2K2 a) José Antonio produces 1000 conchas. He is currently using 100 workers and 100 ovens. Is he optimizing his use of inputs of production? b) What is the rule to optimize the use of inputs of production? c) Find the optimal level of labor and capital for Conchita-Crem. What is its total cost? d) Now suppose that the rental price of ovens for Conchita-Crem increases 100%. Would the production change? What would be now the rule to efficiently use inputs of production? How much labor and capital be used? What is the total cost now? Compare it to your answer in c. e) Find the input demand functions for capital and labor. Remember these functions specify the amount of labor or capital that Conchita-Crem will use as a function of production level q. f) Suppose now that José Antonio…
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Ebba Kantzen says the following: "I am currently producing 10,000 pizzas per month at a total cost of $50,000. If I produce 10,001 pizzas, my total cost will rise to $50,011. Therefore, my marginal cost of producing pizzas must be increasing." ( 1.) Using the point drawing tool, indicate the point of marginal cost. Label this point "Marginal cost." 2.) Using the point drawing tool, indicate the point of average total cost. Label this point "Average total cost." Carefully follow the instructions above, and only draw the required objects. Costs(dollars per pizza) (5.95,0) MC Quantity (pizzas per month) points ATC