Principles of Economics (12th Edition)
12th Edition
ISBN: 9780134078779
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 Economics (12th Edition)
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- The 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_forwardProvide a graph and an explanation to show that the production function Q = L.5K.5 has diminishing marginal product of labor but has constant returns to scale.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
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