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QUESTION 1
Consider the following production functions, where q is the quantity produced of the good, K
is the quantity of capital used, and L is the quantity of labor used:
Production function 1
q (K, L) = K^αL^β
Production function 2
q (K, L) = K^α + L^β
a) What is production function? Explain by providing appropriate graph.
b) Does Production function 1 have decreasing, constant, or increasing returns to scale?
Explain.
c) Suppose that α = 1 and β = 1. Does Production function 2 have decreasing, constant,
or increasing returns to scale? Explain.
d) Suppose that α = 1/2 and β = 1/2. Does Production function 1 have decreasing,
constant, or increasing returns to scale? Explain
Step by step
Solved in 3 steps with 3 images
- What is a production function?Give only typing answer with explanation and conclusion Consider a production function with two inputs: f(x1,x2) = (x1)a(x2)b Suppose that a = 0.7 and b = 0.7. What type of returns to scale does this production function exhibit? Type 1 for increasing, 0 for constant, and -1 for decreasing.Question B1 A firm produces a good, q according to the production function q = 2K0:2 L°0.8. The cost of a unit of labor is £5 and the cost of a unit of capital is £40. The firm is currently producing 160 units of output and has determined that the cost- minimizing quantities of labor and capital are 160 and 5 respectively. a. Graphically illustrate this situation on a graph using isoquants and isocost lines. Explain intuitively why there is such a difference between the capital input and labour input. b. The firm now wants to double output to 320 units. If capital is fixed in the short run, how much labor will the firm require? Illustrate this point on your graph and find the new cost associated with this level of labour and capital. c. Graphically illustrate how the cost-minimizing level of capital and labor will differ from your answers in a. d. If the marginal rate of technical substitution is 4K/L , find the optimal level of capital and labor required to produce the 320 units of…
- 1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.10. Do the following production functions have increasing, decreasing, or constant returns to scale? Show work.(i) Q = 3K+2L (ii) Q = 6KL
- 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) Suppose you are a hard-working software engineer that works 2000 hours a year, which you allocate between meetings (m), learning activities (I) and working effort (e) doing actual coding tasks (m + 1 + e = 2000). a. Write down your personal production function f (m, 1, e). Briefly describe how your output depends on the three activities. b. Does your production function exhibit increasing, decreasing or constant returns to scale (at all or some output levels)? Explain. c. Suppose a new technology doubles the productivity of your coding hours but requires you to spend X hours to adopt the technology (reducing your available work hours to 2000-X). What is the maximum X that makes adopting the technology worthwhile in the first year?Aplia Homework: Production and Cost in the Firm Underground Sandwiches, a sandwich shop, has the following marginal product curve (labeled MP) for its hourly production. (?) 20 18 16 MP LABOR (Workers) When labor increases from two to three workers, total product increases by per hour. Use the orange points (square symbol) to plot the production function on the following graph. Assume that if there are no workers, Underground Sandwiches does not have any output. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. 80 72 Production Function 64 56 48 32 24 16 MARGINAL PRODUCT (Sandwiches per worker)
- Microeconomics - Production FunctionA firm produces shoes using labor (L) and machinery (K) as factors of production. Its production function is Q = K1/3 * L2/3. Answer:(a) is the marginal product of labor (MPL) decreasing?b) is the average product of labor (APL) decreasing?c) what is the relationship between the average product (AP) and marginal product (MP) curves?d) what type of returns to scale does Q exhibit?Exercise A.5 A company operates with production function q-K¹/2 [1/2 a) What type of returns to scale does this production function present? As production varies, how would you expect long-term average costs to evolve? b) Assume that the firm's capital equipment is fixed and equal to K = 100 units. Find the firm's short-run production function and the marginal productivity of labour and graph these functions. As production varies, how would you expect marginal costs to evolve in the short term? c) If the prices of capital and labour are r = 8€ and w = 2€ respectively, obtain the expression of the short-run total cost function of the firm. b) Obtain the expressions of the functions of short-term average total costs, average variable costs and marginal costs of this company. Find the production level for which the average total cost is minimized and the corresponding average total cost level. d) Indicate the value of the average total cost, the average variable cost and the marginal cost…