Principles of Microeconomics, Student Value Edition Plus MyLab Economics with Pearson eText -- Access Card Package (12th Edition)
12th Edition
ISBN: 9780134421315
Author: Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher: PEARSON
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Question
Chapter 9, Problem 2.2P
To determine
The production function of a firm exhibiting both increasing and decreasing returns to scale.
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A farm producing wheat has the following production function Q = 4L + 3K. Does the above function exhibit increasing, constant, or decreasing returns to scale? Prove and explain your answer.
Suppose a firm has the following production function Q (K, L) =K0.5 L0.4. Show mathematically whether the firm has increasing, decreasing, or constant returns to scale.
If a firm has economies of scale, it must have increasing returns to scale. True or false? PLEASE EXPLAIN IN DETAIL .
Chapter 9 Solutions
Principles of Microeconomics, Student Value Edition Plus MyLab Economics with Pearson eText -- Access Card Package (12th Edition)
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- Explain how a firm can have constant returns to scale in production and economies of scale in cost.arrow_forwardThe production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?arrow_forwardShow that the elasticity of scale for a homogeneous production function of degree k is precisely k.arrow_forward
- KA. A firm produces output with the production function, Q = F(K, L) = K0.5 L0.5 with r=4 and w= 2. The firm is using K=16 and just enough L to produce 16 units of output in the short run. How much could the firm save if it were producing 16 units in the long run?arrow_forwardDistinguish between economies of scale and constant returns to scale. What shape will the long-run average cost curve have for economies of scale and constant returns to scalearrow_forwardam. 131.arrow_forward
- A firm has a short run production function: Q = 16L^(1/2) where q = units of output, L = units of labor. Write down an expression for the marginal product of labor (MPL) and evaluate q and MPL for L = 9, L = 16, L = 36 and L = 100. On separate graphs, sketch q in terms of L and sketch MPL in terms of L. Confirm that the short run production function satisfies the law of diminishing returns.arrow_forwardA short run production function of a competitive firm is given by Y=6L^(2/3) where Y represents the units of output while L is the labour required. If P = 3 and W = 6. How much of Y will it produce?arrow_forwardIf a firm has economies of scale, it must have increasing returns to scale. True or false?arrow_forward
- A firm’s production function is given by q = min{M, L1/2}, where M is the number of machines and L is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit. a. Is this technology decreasing return to scale? Show your argument. b. Is it true the statement that if average production cost is increasing, a firm’s technology exhibits the decreasing return to scale. (If yes, show the proof. If not, show a counter example) c. Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)arrow_forwardQuestion # 1: Majeda wrote the following answer on her microeconomics examination: “Virtually every production function exhibit diminishing returns to scale because my professor said that all inputs have diminishing marginal productivities. So, when all inputs are doubled, output must be less than double." How would you grade Majeda's answer? Question # 2: Suppose a firm had a production function with linear isoquants, implying that its two inputs were perfect substitutes for each other. What would determine the firm's expansion path in this case? For the opposite case of a fixed-portions production function, what would the firm's expansion path be? Question # 3: Suppose that a firm's production function is q = 30√L. In the short run, where there are fixed costs of $2,200, and labor is the variable input whose cost is $6,300 per units. What is the total cost of producing 20 units of output?arrow_forwardPlease answer fast and Arjent pleasearrow_forward
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