6. Duane breeds parrots for a living. He has discovered that the production function forparrot chicks (Q) is: Q = K2 L12 where K is capital (for example nest boxes, cages andthe like) and L is parrot food. The price of K is $8 and the price of L is $2.a. What type of production function is this?b. Does this production function exhibit constant, increasing or decreasing returns to scale?Explain.c. What is the average product of capital?

A firm uses different combinations of factors of production such as labor and capital to produce…

6. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q = K2 L12 where K is capital (for example nest boxes, cages and the like) and L is parrot food. The price of K is $8 and the price of L is $2.

6. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q = K2 L12 where K is capital (for example nest boxes, cages and the like) and L is parrot food. The price of K is $8 and the price of L is $2.

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter7: Production And Cost In The Firm

Section: Chapter Questions

Problem 21PAE

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3. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q=K0.5 p0.5 where K is capital (for example nest boxes, cages and the like) and F is parrot food. The price of K is $8 and the price of F is $2. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Provide a graph of the function using Excel.
3. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks (Q) is: Q=K0.5 p0.5 where K is capital (for example nest boxes, cages and the like) and F is parrot food. The price of K is $8 and the price of F is $2. (a) What type of production function is this? Explain. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Provide a graph of the function using Excel. (c) Find the marginal products of capital and food. (d) Suppose that Duane wants 144 parrot chicks, how much K and F should be employed to minimise costs. What is the cost of producing 144 parrot chicks? 1 1 (e) Suppose that Duane is faced with the same problem as in (e) except that he has a fixed amount of K. In fact, K = 16. How much F should be bought to minimise costs? What is the total cost?
.2. Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her productionfunction for jewelry is given byQ = B0.4C0.4Suppose she can buy beads and copper at prices PB and PC, respectively.(a) Calculate Tiva’s marginal rate of technical substitution between B and C.(b) Does this production function have increasing, constant, or decreasing returns to scale?Explain. (c) Set up the cost minimization problem you would use to calculate Tiva’s cost functionC(Q) in Lagrangian form. (Note: You do not need to solve it or derive first orderconditions.Suppose Tiva decides to branch out in her jewelry offerings by getting a 3D printer. The costof producing new 3D printed jewelry isC(Q) = 25 + Q24For the rest of this problem, assume Tiva can produce fractions of jewelry, don’t worry aboutrestricting your answers to whole numbers.(d) Compute Tiva’s marginal cost and average cost of production for 3d printed jewelry.(e) Explain why she will shut down when the market price falls…
6. The Miller Company is trying to determine the combination of inputs to produce a specific volume of bar stools ordered. The production function for the firm is given: Q = 14LK? The wage of a worker is $80/day and the price of a machine is $240/day. If they need to produce 4,536 bar stools per day: a. What is the optimal combination of Labor and Capital, i.e. find the cost-minimizing combination of inputs to produce 4,536 bar stools? b. What is the total cost of using the inputs found in part a?
1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. - a. Write down the firm's production possibility set, and its input requirement set.“ b. Is this production function concave, quasi-concave? c. Is this production function homogenous, homothetic? + d. Find its returns to scale when x1=1, and x2=1.e
3. Frisbees are produced according to the production function q = 2K+L where q = output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant defined in part a and part b. What is the RTS along this isoquant? Explain why the RTS is the same at every point on the isoquant. d) Graph the q = 50 and q = 200 isoquants for this production function also. Describe the shape of the entire isoquant map. e) Suppose technical progress resulted in the production function for frisbees becoming q = 3K+ 1.5L. Answer part a through part d for this new production function and discuss how it compares to the previous case.
4. A firm producing cars. The production function for shoes (Q) is: Q = K2 L"2 where K is capital and L is labor. The price of K is $8 and the price of L is $2. a. What type of production function is this? b. Does this production function exhibit constant, increasing or decreasing returns to scale? Explain. c. What is the average product of capital, average product of labor, marginal product of capital, and marginal product of labor? d. Does capital obey the "law of diminishing returns?" Explain. e. Suppose that firm wants to produce 144 cars, how much K and L should be employed to minimize costs? f. What is the minimum cost of producing 144 cars? g. Now suppose that firm is faced with the same problem as in (e and f) except that firm has a fixed amount of K. In fact, K = 16. How much L should be employed to minimize costs, and what is the total cost.
4. Show that the law of diminishing marginal productivity holds for the production function Q=6L² - 0.2L'
24. A specific production process can be represented by the production function, f(x1, x2) = (x 1/2 + x 1/3) 3. A. How much x₁ could the firm give up if it wanted to use 1 extra unit of x2 and still wanted to produce an identical level of output? B. Labeling everything and being precise, draw the isoquant corresponding to q = 4. = 9. C. On the same graph, draw the isoquant corresponding to q D. Between the isoquants you just drew, does the production technology display decreasing, increasing, or constant returns to scale? E. Analytically determine whether the production process has global returns to scale that match your local results from part D. Recall that in order to claim global returns to scale, your result must hold for ALL possible values of x1 and x2.
5. Suppose that a hot dog vendor uses a cart (K) and his time (L) to make and sell hot dogs. The vendor's production function is where Q is the number of hot dogs per day. Suppose that the rental on hot dog carts is $50 per day and that the vendor wants to Q = K0.3 10.7 produce 500 hot dogs per day. Use calculus to: a. derive the demand for labor. b. show that the demand for labor satisfies the law of demand. 2
IV. Will can produce a higher grade, Gw, on an upcoming economic exam by studying. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, Gw = 2.5A0.36R 0.64. His roommate David's grade production function is G) = 2.5A0.25R0.75 a. What is Will's marginal productivity from studying supply and demand problems? What is David's? b. What is Will's marginal rate of technical substitution between studying the two types of problems? What is David's?
2. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and fl