Walter Nicholson Christopher Snyder Amherst College Christopher Snyder Dartmouth College PowerPoint Slide Presentation | Philip Heap, James Madison University ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

CHAPTER 6 Production ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chapter Preview We now want to turn to firm behavior, and answer three main questions. What happens to output as a firm increases the number of input(s) it uses? To what degree is a firm able to substitute one input for another? What happens to production as a result of technological change? ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Production Functions A firm is any organization that turns inputs into outputs. A production function is a mathematical relationship between inputs and outputs. q = f( K, L, M, ...) q = f( K, L ) ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Marginal Product Marginal product: The additional output that can be produced by adding one more unit of some input, holding all other inputs constant. What happens to output as we add one more unit of one input (labor) to a fixed amount of another input (capital). ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Total Product and Marginal Product As labor increases output increases but at a diminishing rate. So marginal product decreases as labor increases. Output per week MPL L* L* Labor input per week Labor input per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Average Product Average product is equal to total output divided by the number of workers. Average product tells you how productive all your workers are on average. It does not tell you how productive an extra worker is. Practical difficulty in applying the marginal product concept. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Isoquant Maps How can a firm combine different amounts of capital and labor to produce output? Isoquant: A curve that shows the various combinations of inputs that will produce the same (a particular) amount of output. How does this compare to an indifference curve? Isoquant map is a contour map of a firm’s production function. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Isoquant Map Capital per week KA A q=30 q=20 KB B q = 10 LA LB Labor ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Rate of Technical Substitution Marginal rate of technical substitution (RTS): The amount by which one input can be reduced when one more unit of another input is added while holding output constant. If you used one more worker how much less capital could you use and still produce the same level of output. RTS = - slope of the isoquant RTS = - (change in capital) / (change in labor) ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Rate of Technical Substitution At point A, the slope of the isoquant = RTS = ΔKA/ ΔL Capital per week Along the isoquant. the slope gets flatter and the RTS diminishes At point B, the slope of the isoquant = RTS = ΔKB/ ΔL KA A The amount of capital that can be given up when one more unit of labor is employed gets smaller and smaller ΔKA ΔL KB ΔKB B q = 10 ΔL LA LB Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

The RTS and Marginal Product Why must the slope of the isoquant be negative or the RTS positive? RTS = MPL/MPK If RTS was < 0 either MPL or the MPK would also have to be < 0. But then a firm would be paying for an input that reduced output. Since no firm would do that MP’s > 0 and the RTS > 0. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

The RTS and Marginal Product Why does the slope of the isoquant get flatter or why does the RTS diminish? The less (more) labor is used relative to capital, the more (less) able labor is able to replace capital in production. As the firm uses more and more labor, the MPL falls. Therefore, to maintain the same level of output, the firm would only be able to give up smaller and smaller amounts of capital. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Returns to Scale What would happen to production if a firm increased the number of all inputs? Returns to scale: The rate at which output increases in response to a proportional increases in all inputs. Two opposing effects at work as scale increases: Greater division of labor (specialization). Managerial inefficiencies and coordination problems ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Returns to Scale Constant returns to scale: If inputs increase by a factor of X, output increases by a factor equal to X. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Constant Returns to Scale Capital per week Output increases at the same proportion as inputs 4 q=40 3 q=30 2 q=20 1 q = 10 1 2 3 4 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Returns to Scale Constant returns to scale If inputs increase by a factor of X, output increases by a factor equal to X. Increasing returns to scale If inputs increase by a factor of X, output increases by a factor greater than X. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Increasing Returns to Scale Capital per week Output increases at a rate greater than the increase in inputs 4 Or to increase output by some factor X, inputs would only need to increase by a factor less than X. 3 q=40 2 q=30 1 q=20 q = 10 1 2 3 4 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Returns to Scale Constant returns to scale If inputs increase by a factor of X, output increases by a factor equal to X. Increasing returns to scale If inputs increase by a factor of X, output increases by a factor greater than X. Decreasing returns to scale If inputs increase by a factor of X, output increases by a factor less than X. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Decreasing Returns to Scale Capital per week Output increases at a rate less than the increase in inputs 4 q=30 3 2 q=20 1 q = 10 1 2 3 4 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Input Substitution How is the shape of the isoquant related to how easy it is to substitute one input for another? Fixed proportions production function: A production function in which the inputs must be used in a fixed ratio to one another. Mowing a lawn: one worker and one lawnmower. There is no way to substitute one input for another. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Fixed Proportions Production If you only have K0 machines would only need L0 workers to produce q0. Capital per week If you used L1 workers your output would remain the same. K1 q1 K0 q0 L0 L1 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Input Substitution Why does the degree to which a firm can substitute one input for another matter? Suppose the price of one of the firm’s inputs increases. The firm will want to use less of the relatively more expensive input and more of the relatively less expensive input. A firm that is able to substitute one input for another will be able to keep its costs from rising as much. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Changes in Technology A production function or isoquant reflects a firm’s current technological knowledge. What happens to the production function if there is technological progress? Technical progress: a shift in the production function that allows a given output level to be produced using fewer inputs. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Changes in Technology Capital per week q0 q0’ Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Changes in Technology vs. Input Substitution Capital per week With technological change the firm can produce the same level of output, q0, with K0 but less labor. K0 q0 q0’ L1 L0 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Changes in Technology vs. Input Substitution Capital per week With input substitution the firm would need to use K1 units of capital with L1 units of labor. K1 K0 q0 q0’ L1 L0 Labor per week ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

A Numerical Production Example Production of burgers at Hamburger Heaven Hamburgers per hour: q = 10 x (KL) ½ There are constant returns to scale. K, L = 1, q = 10 K, L = 2, q = 20 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Constant Returns at Hamburger Heaven Grills Workers Hamburgers 1 10 2 20 3 30 4 40 5 50 6 60 7 70 8 80 9 90 100 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Average and Marginal Product at Hamburger Heaven Suppose that Hamburger Heaven uses 4 units of capital q = 10(KL) ½ q = 10(4L) ½ q = 20L ½ ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Q, AP and MP at Hamburger Heaven q = 10 x (4 x 2)1/2 = 28.3 APL = 28.3/2 = 14.1 MPL = 28.3 - 20 = 8.3 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Isoquant for Hamburger Heaven Suppose Hamburger Heaven wants to make 40 burgers. q = 40 = 10(KL) ½ 4 = (KL) ½ 16 = KL So if K = 2 and L = 8, q = 40 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Isoquant for Hamburger Heaven ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Isoquant for Hamburger Heaven Grills 8 2 q = 40 2 8 Workers ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

RTS at Hamburger Heaven RTS = - change in K / change in L = -(4-5.3)/(4-3) = 1.3 RTS = - change in K / change in L = -(1.8-2)/(9-8) = 0.2 ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

RTS at Hamburger Heaven As HH uses more and more workers, the RTS falls. From L =3 to L =4, RTS = 1.3 From L = 8 to L = 9, RTS = 0.2 As more and more workers are used, the firm is less able to reduce the number of grills it uses. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Technological Progress at Hamburger Heaven Suppose that due to genetic engineering hamburgers can flip themselves. Old production function: q = 10(KL) ½ New production function: q = 20(KL) ½ If HH still wants to make 40 burgers 40 = 20(KL) ½ 4 = KL With old technology: 16 = KL ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Technological Progress at Hamburger Heaven Grills With the old technology: 16 = KL With the new technology: 4 = KL 4 q = 40 q = 40 1 4 Workers ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Summary A production function, q = (K,L) shows the relationship between output and inputs. Marginal product is the additional output that can be produced by adding one more unit of some input, holding all other inputs constant. An isoquant shows the possible input combinations that a firm can use to produce a given level of output. The absolute value of the isoquant’s slope is the RTS – the rate at which one input can be substituted for another. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Summary The RTS falls as the firm uses more and more of one input. Production may exhibit constant, decreasing, or increasing returns to scale. With fixed proportions production a firm will not be able to substitute one input for another. With technological progress a firm can produce a given level of output with fewer inputs: the isoquant shifts in. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.