Business 33001: Microeconomics

Transcription

1 Business 33001: Microeconomics Owen Zidar University of Chicago Booth School of Business Week 4 Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 1 / 93

2 Exam Logistics In-class exam next week First 90 minutes of class No problem set this week, but today s material will be covered on the exam Practice exam and solutions available on my website Exam prep: Problem set questions + practice midterm Calculators allowed. Formula sheet provided (see practice exam). Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 2 / 93

3 Today s Class 1 What is Cost? 2 Types and Measures of Cost 3 The Firm s Decision 4 Factor Demand 5 Productivity and Technological Change Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 3 / 93

4 Motivation: why should you care? 1 Main Goal: understand where supply comes from 2 Understand the economics of production 3 Clarify/reinforce your understanding of key concepts (e.g. comparative advantage, productivity, marginal cost, etc.) 4 Build tools for analyzing costs Relevant for cost containment, hiring, and investment Relevant for understanding behavior of suppliers Provides simple benchmarks to keep in mind when negotiating contract terms 5 Deepen your insight into productivity and technological change Build a framework to think intelligently about the rise of robots Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 4 / 93

5 The supply side and differences in price changes by sector Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 5 / 93

6 What is cost? Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 6 / 93

7 Introductory Example: Comparative Advantage and Cost The goal of this example is to illustrate the true nature of cost and the problem society faces when deciding how much of each good to produce Begin with two goods, bananas and oranges and Tom Hanks Tom has two plots of land of equal size (say 1 acre each) 1 Plot 1 can yield 6 oranges per acre or 4 bananas per acre 2 Plot 2 can yield 2 oranges per acre or 3 bananas per acre How much of each crop should Tom produce and how should he divide this production between the two plots? We must determine his opportunity set from which we can determine the costs of production 1 1 In particular we be able to determine marginal cost which will be relevant for Tom s decision Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 7 / 93

8 Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 8 / 93

9 Introductory Example: Comparative Advantage and Cost Where should he produce his first banana? Even though plot 1 can produce 4 per acre, plot 2 is better On plot 1, an increase of 1 banana costs 6/4 = 1.5 oranges On plot 2, the cost of a banana is simply 2/3 =.67 oranges Even though plot 2 is less productive in absolute terms (i.e., plot 1 can produce more of either fruit), plot 2 is still the low-cost producer of bananas Bananas should be produced first on plot 2 until that plot is entirely used for banana production Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 9 / 93

10 Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 10 / 93

11 Introductory Example: Comparative Advantage and Cost Tom s opportunity set is called the production possibility set The slope of the opportunity set (in absolute value) gives the cost of an additional orange, i.e., the marginal cost of an orange Tom s optimal choice sets the marginal cost of an orange to his marginal value of an additional orange Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 11 / 93

12 Other examples Say I want to produce sheep, where is least cost place? Oil drilling Basketball Others? Takeways: 1 The key to the production possibilities set is that underlying assets are heterogeneous. This heterogeneity can manifest itself in terms of what you have to give up (e.g., sheep farmland) or in terms of what you get (e.g., Lebron). 2 The cost of a good is what you give up to get it Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 12 / 93

13 Types and Measures of Cost Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 13 / 93

14 Cost Definitions related to level of output produced 1 Fixed Cost FC: costs that are independent of the output level (given some production). This could be the cost of renting a plot or warehouse 2 Variable Cost VC(q): The part of costs that depend on the chosen level of production (such as the number of workers hired or the amount of inputs). 3 Total Cost TC(q): Fixed Cost + Variable Cost. 4 Sunk Cost: The part of fixed cost which must be paid whether production occurs or not. These are generally present after some initial investment or commitment has been made 5 Salveable Cost: The part of fixed costs that can be recovered if one decides not to produce after making the initial fixed-cost investment or commitment Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 14 / 93

15 Definitions of Measures of Cost 1 Average Cost: AC(q) = TC(q)/q or the cost per unit of producing q units of output 2 Average Salvageable Cost: ASC(q) = (Salvageable Cost + Variable Cost)/q, which is the opportunity cost of production once the fixed-cost investment has been made 3 Marginal Cost: dtc(q)/dq or the ratio of the change in total cost divided by the change in output q. Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 15 / 93

16 Example Cost Functions Consider a firm with the following total costs: TC(q) = }{{} q 8q 2 +.5q 3 }{{} Fixed Costs Variable Costs Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 16 / 93

17 Example Cost Functions Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 17 / 93

18 Example Cost Functions Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 18 / 93

19 Example Cost Functions We can also view ATC and MC graphically ATC is the slope of the ray drawn from the origin to the point (Q, TQ(Q)). Why? Slope of Ray = TC(Q) 0 Q 0 = TQ(Q) Q MC is the slope of the line tangent to the TC curve at point (Q, TQ(Q)) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 19 / 93

20 Example Cost Functions Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 20 / 93

21 Example Cost Functions Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 21 / 93

22 Application: New car plant Suppose you are Elon Musk and run a large automobile manufacturer. You have just opened up a new plant in Oakland that is state-of-the-art. You also have an old plant that is less productive. The Average Cost Curves for the two plants look like the following slide You need to produce 7 cars per month. How would you go about doing so while minimizing total costs? Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 22 / 93

23 Application: New car plant Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 23 / 93

24 New car plant: quantitative example Suppose TC new = 3q 2 new + 3q new + 12 TC old = 4q 2 old + 2q old + 20 How do we think about this problem? If there is positive production at both plants, we want to minimize the total cost of producing 100 cars: min 4q q old,q old 2 + 2q old qnew 2 + 3q new + 12 s.t. q old + q new = 100 new You can plug in old production as total production less new production, i.e., q new = 100 q old, and then minimize costs by optimally picking new production. Or you could set up the Lagrangian as follows: L(q old, q new, λ) = TC old + TC new + λ(100 q new q old ) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 24 / 93

25 New car plant: key idea is to equalize marginal costs FOC: Equating the first two FOCs yields: 8q old + 2 = λ 6q new + 3 = λ q old + q new = 100 8q old + 2 = 6q new + 3 q old = 6q new Plugging this expression into the third FOC yields: ( 6q new 8 q old + q new = ) + q new = 100 q new 57 q old 43 Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 25 / 93

26 The Firm s Decision Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 26 / 93

27 Firm production problem Profit = Revenue Cost π = PQ TC(Q) = PQ VC(Q) FC Pick quantity to produce that maximizes profit dπ dq = dpq dq dvc(q) dq dπ dq = P MC 0 = 0 P = MC dfc dq The firm maximizes profits by equating marginal value, i.e., price, equal to marginal cost Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 27 / 93

28 Principles: firm behavior in a competitive market 1 The firm will produce at the output level where price equals marginal cost so long as at this output level the firm makes positive profits. If the firm cannot make a profit at the point where price equals marginal cost, then the firm s best choice is not to produce at all. Profit = Pq TC(q) > 0 P > AC(q) 2 The firm will produce where price equals marginal cost after making a fixed investment so long as at this output level the firm can cover its cost (i.e. price exceeds average salvageable cost). If not, then the firm will shut down and not produce. Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 28 / 93

29 Firm Production Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 29 / 93

30 Notes on Firm Production Graph 1 AC has a U-shape Initial decline due to amortizing FC over a greater number of units As output rises, firms experience diminishing returns. These increased costs may be due to: lower efficiency large-scale production reaching capacity of fixed inputs like plant size the fact that fewer and fewer productive inputs must be used up (e.g., our two plot example; after using up the capacity of the low-cost plot, the marginal cost of bananas increased) 2 MC vs AC 3 Output decisions X m is the lowest-per-unit cost of production With price at P 0, MC(q) = p X 0 With price at P 1, MC(q) = p X 1 but not profitable This is how we can find the firm s supply curve Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 30 / 93

31 Firm Supply Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 31 / 93

32 What if a firm made sunk investments? The firm will produce as long as profits from producing exceed sunk costs Pq (FC + VC(q)) > Sunk Costs Pq > FC Sunk Costs + VC(q) Salageable Costs + VC(q) P > q P > ASC(q) Firms will produce at prices below AC(q) so long as they can cover the opportunity or salvageable cost Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 32 / 93

33 Firm Production with Salvageable Costs Note: P M is firm s entry price and P s is firm s exit price. Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 33 / 93

34 Example: Firm production problem Suppose total cost is TC(q) = 30 + q q Suppose price is $16 How much should the firm produce? Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 34 / 93

35 Example: Firm production problem Steps 1 Get the marginal cost by differentiating total cost 2 Set marginal cost equal to price 3 Solve for q 2q + 10 = MC 2q + 10 = 16 2q = 6 q = 3 4 Confirm that this level of production is more attractive than not producing at all Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 35 / 93

36 Example: Firm production problem Questions 1 What would happen if the price were higher? 2 What would happen in the firm got more productive (i.e., they could produce more at a given cost)? Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 36 / 93

37 Factor Demand Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 37 / 93

38 Factor demand Thus far, we have mostly focused on the choice of output given the cost conditions of the firm These cost conditions are a result of an underlying optimization process in which the firm chooses the best mix of inputs to produce its output These inputs are called factors of production 1 Labor: the services of people 2 Capital: the services of physical assets The demand for these factors comes from the demand for the goods and services that are produced by the firms that hire these inputs Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 38 / 93

39 Factor demand example: Oil Price Shock Oil Jobs Squeezed as Prices Plummet, The Wall Street Journal, 12/26/2014 U.S. oil and gas companies have been a job engine through much of an otherwise lackluster economic expansion. Now, after a roughly 50% plunge in oil prices, companies are cutting capital budgets and weighing layoffs. One company caught in the industry downturn is Hercules Offshore Inc. The Houston-based firm is laying off 324 employees, roughly 15% of its workforce, because oil companies aren t renewing contracts for its offshore drilling rigs in the Gulf of Mexico while crude prices are depressed. It s been breathtaking, said Jim Noe, executive vice president of Hercules, which was founded in We ve never seen this glut of supply and dislocation in oil markets. So we re not surprised to see a significant decline in demand for our services. Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 39 / 93.

40 A Production Function To understand the nature of derived demand for factors, let s introduce the production function Consider a firm that produces good Y using only labor A production function F (L) gives the amount of the good produced as a function of labor employed Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 40 / 93

41 Production Function: Y = F (L) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 41 / 93

42 Marginal Product of Labor The marginal product of labor MPL = F L gives the rate of change of output with respect to the quantity of labor MPL, i.e. the slope of F (L), decreases with the quantity of labor. Since other factors such as capital (i.e., the size of the plant) are being held constant, output increases at a decreasing rate as the quantity of labor is increased Note that unlike utility, output is a thing we can actually measure For instance, we can reasonably ask how many hours of work does it take to make a TV or a haircut Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 42 / 93

43 Marginal Product of Labor Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 43 / 93

44 Marginal Product of Labor Firms will employ labor to the point where the marginal gain to adding additional labor is exactly equal to the cost of an additional unit of labor The return to additional labor is the amount of output that labor can produce times the price of output MPL P Value marginal product of labor or VMP The cost of labor is the the wage w. Hence the optimal choice of labor by the firm will be where P MPL = w When goods prices P are high, it pays for the firm to use more labor Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 44 / 93

45 Marginal Product of Labor (calculus) If we denote non-labor costs as C, then the firm s profits are: P F (L) C wl }{{} Revenues FOC: P F L w = 0 P MPL = w Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 45 / 93

46 Example: Marginal Product of Labor Suppose p = 10, F (L) = L.5, and non-labor costs are zero How many people should we hire if wages are $1? $5? } 10L {{.5 } wl Revenues P F L w = L.5 w = 0 L.5 = w 5 ( ) 5 2 L = w ( ) 5 2 L(1) = = 25 1 ( ) 5 2 L(5) = = 1 5 Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 46 / 93

47 Marginal Product of Labor Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 47 / 93

48 Long-Run Factor demand (two-inputs) Firms generally use multiple inputs to produce output (e.g., a manufacturing firm may use labor together with plant and equipment to produce its output). Our discussion thus far is short-run because the size of the plant and the amount of equipment can be regarded as fixed The VMP schedule can be thought of as the marginal product of labor holding the level of these other inputs (which we collectively call capital) fixed at the current level The level of capital strongly influences the demand for labor as a given worker can produce more with capital In the long-run, firms decide on the optimal level of labor and capital jointly Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 48 / 93

49 Long-Run Factor demand (two-inputs) Firms make their choice of capital and labor in two stages: 1 The firm decides the mix of labor and capital that can produce a given level output at the least cost 2 The firm makes calculates this cost for different amounts of output and then determines the optimal level of output by producing where price equals the marginal cost of production The optimal levels of labor and capital are then the cost-minimizing levels for this chosen level of output Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 49 / 93

50 Cost Functions - Cake Example, 3 levels of capital For any desired quantity, find lowest cost mix of inputs to produce it Example: How much does it cost to bake 100 cakes? Option 1: 100 Ingredients ($2 each), spoon and bowl (free), 50 hours of labor ($10/hr) Cost: = $700 Option 2: 100 Ingredients ($2 each), electric mixer ($100), 25 hours of labor ($10/hr) Cost: = $550 Option 3: 100 Ingredients ($2 each), cake robot ($10000), 1 hour of labor ($10/hr) Cost: = $10,210 Lowest Cost: Option 2 C(100) = 550 C(100) = 550 Now repeat for every Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 50 / 93

51 Cost Functions - Cake Example, 3 levels of capital Cost function for cake production: C Robot Mixer Hand Q For higher quantities: use more intensive capital and less labor per unit Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 51 / 93

52 Cost curves for a given level of capital What does cost curve look like if... No Diminishing Marginal Product of Labor Constant slope of cost curve Cost $ Fixed K Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 52 / 93

53 Cost curves for a given level of capital What does cost curve look like if... No Diminishing Marginal Product of Labor Constant slope of cost curve Complementarity of labor and capital Slope is flatter for higher levels of capital Cost $ High K robot Low K mixer Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 53 / 93

54 Cost curves for a given level of capital What does cost curve look like if... No Diminishing Marginal Product of Labor, up to capacity Constant slope of cost curve up to capacity Capacity constraint No additional production at any cost (without more capital) Cost $ Fixed K Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 54 / 93

55 Cost curves for a given level of capital What does cost curve look like if... Diminishing Marginal Product of Labor Curve is steeper at higher quantity Cost $ Fixed K Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 55 / 93

56 Cost curves for a given level of capital What does cost curve look like if... Diminishing Marginal Product of Labor Curve is steeper at higher quantity Complementarity of labor and capital Curve is flatter for higher levels of capital Cost $ K3 K2 K1 K0 Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 56 / 93

57 Minimizing costs over choice of capital C With a few choices of capital: Check cost of producing Q units at each possible capital level ˆK Find minimum over all possible capital levels With continuous choice of capital: Can t check costs for every possible capital level! Graphical approach to get optimality condition Use calculus Cost $ Hand K1 Mixer K2 K3 Robot Q K0 Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 57 / 93

58 Isoquants and the Marginal Rate of Substitution If we graph all of the combinations of L and K that can be used to produce a given level of output, we get a curve that resembles an indifference curve In this case, the curve is called an isoquant (for equal quantity) Isoquants slope downward due to the fact that in order to keep the level of output constant a decrease in K must be accompanied by an increase in L As K becomes more scarce, the amount of L we need to substitute for a unit of K will increase The amount of labor needed to substitute for a unit of capital (i.e., the amount labor must increase to maintain the current level of output) is called the marginal rate of substitution of labor for capital. Similarly, the MRS of capital for labor is just the slope of the following isoquant Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 58 / 93

59 Isoquants and Isocost curves Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 59 / 93

60 Isoquants and Isocost curves Isoquants determine the ability of the firm to substitute K and L in production The rate at which K and L can be substituted in the market is determined by the prices of capital and labor With the price of capital of r and a price of labor of w, one unit of labor can be substituted for w/r units of capital This ability to substitute was depicted by the isocost curve, which is the combinations of K and L that have equal costs The cost-minimizing solution is to find the lowest possible isocost curve At this point, the isoquant and isocost curves will be tangent The cost to produce X 0 is C(X 0 ) = L(X 0 )w + K(X 0 )r Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 60 / 93

61 Cost Minimization Solution How do we actually do this? Given technology f (L, K) and input prices w, r, how to find cost function C(Q): Given Q, want to solve for minimum cost L and K 2 Equations: MPL w Q = f (L, K) = MPK r Solve for two unknowns L and K (given Q) Plug in to get C(Q) = wl + rk Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 61 / 93

62 Cost Minimization Math Example Output: Q = f (L, K) = 6 L K Input prices: w = 10, r = 40 To find cost function C(Q): 1 Find MPK, MPL: df (L, K) L MPK = = 3 dk K df (L, K) K MPL = = 3 dl L 2 Plug into bang-for-the-buck optimality condition MPL 3 K L L K 10 = 3 = 4K = L 40 3 To solve for L and K, we now have two equations: w = MPK r : Q = 6 LK L = 4K Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 62 / 93

63 Cost Minimization Math Example Output f (L, K) = 6 L K; Prices w = 10 and r = 40 3 Two equations, two unknowns L and K: ( Q ) 2 6 Q = 6 LK, i.e. Iso-Output K = L L = 4K Cost-Minimization Condition 4 Plug in and solve to get K Q12 IsoOutput C80 L4 K CostMinimization K = Q 12 5 Cost is wl + rk: L = Q L C(Q) = 10 Q Q 12 = 20 3 Q Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 63 / 93

64 Cost Minimization Math Example Output f (L, K) = 6 L K; Prices w = 10 and r = 40 $ Cost 1000 $ Cost K K1 C Q Q Min costs C(Q) = 20Q/ Q Costs for each capital level Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 64 / 93

65 Cost and Production Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 65 / 93

66 Cost and Production Firms will choose higher levels of output when the price of output is high Higher output increases the amount of labor employed (at fixed prices of labor and capital,i.e., w and r) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 66 / 93

67 JULY 2008 IEEE SPECTRUM NA 27 THREE ENGINEERS, HUNDREDS OF ROBOTS, ONE WAREHOUSE Kiva Systems wants to revolutionize distribution centers by setting swarms of robots loose on the inventory BY ERICO GUIZZO NO HANDS: Machines do the heavy lifting at a Staples Denver facility. Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 67 / 93

68 Robots and the price of capital What happens when capital (robots) gets cheaper? Will firms hire fewer workers? Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 68 / 93

69 Impact of a change in a factor price Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 69 / 93

70 Impact of a change in a factor price An increase in the wage causes the isocost curve to be steeper and leads to a substitution of capital for labor, holding the level of output fixed as shown in the prior figure The reduction in labor from L 0 to L 1 is called the substitution effect and always leads to less labor employed as the wage increases The rise in the wage will change the marginal cost and lead to a change in output which is called the scale effect Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 70 / 93

71 Impact of a change in a factor price Marginal cost at a level of output X is simply the change in total cost for an increase in output to X + 1 (approx). MC(X ) = L(X + 1)w + K(X + 1)r (L(X )w + K(X )r) MC(X ) = w(l(x + 1) L(X )) + r(k(x + 1) K(X )) Hence, an increase in the wage will increase MC as long as L(X + 1) > L(X ), i.e., as long as labor is a normal factor of production. Same for K. This increase in MC will reduce output and lead to a further reduction in the use of labor. Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 71 / 93

72 Impact of a change in a factor price on other factor The effect on capital is ambiguous because the substitution and scale effects go in opposite directions Higher wages cause firms to substitute towards capital at any given level of output (thus increasing capital usage) But the higher wage also raises marginal cost of output (assuming labor is a normal factor of production) which will reduce the use of capital (assuming capital is a normal factor) So are cheaper robots reducing employment? Unclear. It depends on magnitude of substitution and scale effects. A separate channel is through technological change. Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 72 / 93

73 Productivity and Technological Change Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 73 / 93

74 Roadmap 1 Definitions 2 Labor Productivity 3 Labor Share 4 Multiple Inputs 5 Biased Technological Change Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 74 / 93

75 Productivity and Technological Change Definition Productivity is the amount of output that can be produced from a given set of inputs Definition Technological change refers to changes in the production process that increase (or decrease) the amount of output that can be produced from a given quantity of inputs and/oralter the optimal mix of inputs used to produce a given level of output Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 75 / 93

76 Average Labor Productivity Labor productivity is output Y per man-hour L The average product of labor APL = Y L % APL = % Y % L For instance, if output is growing at 4% per year while labor input is growing at only 3% per year, then labor productivity must be growing at 1% = 4% 3% per year Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 76 / 93

77 Marginal Labor Productivity We can also examine productivity growth for a competitive industry using the VMP theory of demand Recall W = P MPL, which gives us: % MPL = % w % P Since % w % P is growth in the real wage rate (where real is defined relative to the price of output), this equation tells us that we can measure growth in marginal productivity by growth in the real wage For instance, if the price of output for a competitive industry is growing at 5% per year while the wage rate is growing at 6% per year, then the marginal productivity must be growing at 1% per year Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 77 / 93

78 Relating Average and Marginal Labor Productivity The average product of labor is Y L The marginal product of labor is w p The ratio is Y /L w/p = PY WL = 1 s L where s L is the share of income that goes to labor, i.e., labor s share Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 78 / 93

79 Declining Labor Share in US Manufacturing Labor Share as % of GDP of Manufacturing Year Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 79 / 93

80 Historically, labor s share had been pretty stable at 66% Nonfarm Business Sector: Labor Share, 1980:Q1= (Index) Source: US. Bureau of Labor Statistics Shaded areas indicate US recessions research.stlouisfed.org Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 80 / 93

81 Changes in the Labor Share The ratio expression, i.e. w/p Y /L = s L, implies: % MPL % APL = % s L Hence, labor s share falls when average productivity grows faster than marginal productivity Growth in Y L reflects growth in other inputs besides labor Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 81 / 93

82 Total Factor Productivity Total Factor Productivity (TFP) takes account of the growth in all inputs. TFP growth measures how much output actually goes up relative to how much we expect it to go up based on changed in inputs With two inputs, labor and capital, TFP growth is: % TFP = % Y (s L % L + s K % K) where (s L % L + s K % K) is referred to as the growth in total inputs since it combines the growth in labor and capital to get a measure of the inputs overall (note that the weights are the cost shares of the two inputs) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 82 / 93

83 Striking Productivity Growth: Milk Production per Cow Milk Production per Cow (lbs/year) Year Source: Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 83 / 93

84 Total Factor Productivity based on Prices We can also measure TFP growth using prices % TFP = (s L % w + s K % r) }{{} % P }{{} Predicted cost Actual cost Note that this approach is analogous to how we measured labor productivity using the real wage Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 84 / 93

85 Productivity Growth after deregulation of rail industry Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 85 / 93

86 Average Labor Productivity We can use what we have done so far to revisit why Y L is growing % Y = % TFP + s L % L + s K % K % Y % L = % TFP + s L % L + s K % K % L % Y % L = % TFP + s K (% K % L) % Y /L = % TFP + s K (% K/L) Note we used s L = 1 s K in the third line Takeaway: Y L increases with TFP growth and capital deepening (i.e., growth in the capital to labor ratio) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 86 / 93

87 Biased Technological Change Technological progress can also change the relative demands for capital and labor (or skilled and unskilled labor) We refer to this type of change as biased technological change Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 87 / 93

88 The Impact of Biased Technological Change These figures illustrate the impact of biased change in favor of labor Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 88 / 93

89 Biased Technological Change All three figures show the same shift in the unit isoquant Figure A shows that at the same relative price of capital and labor (i.e., w/r fixed) the firm would switch to using relatively more labor (i.e., K/L would fall) Figure B shows that at the same factor ratio (i.e., along the same ray from the origin), the relative price of labor would have to go up (i.e., w/r would have to rise) Figure C shows that with technological change biased in favor of labor, the rate of technological improvement is greatest at higher L/K (i.e., lower K/L ratios) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 89 / 93

90 Measuring Biased Technological Change % L/K σ% r/w Technological bias This is the actual change in the labor to capital ratio less the predicted change given the change in prices This idea is analogous to shifts in the intercept and then movement along the demand curve from consumer theory Need σ, which is the elasticity of substitution between labor and capital, (think the slope of demand) to measure technological bias However, we can sign the direction of bias by seeing if L/K shifts at every price (analogous to a demand shift % D) Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 90 / 93

91 Q: What caused the global decline of the labor share? United States Japan Labor Share Labor Share China Germany Labor Share Labor Share FIGURE II Declining Labor Share for the Largest Countries Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 91 / 93

92 A: A decline in cost of capital Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 92 / 93

93 Q: What caused the global decline of the labor share? According to an important new paper 2 by Karabarbounis and Neiman A: Decline in cost of capital (i.e., lower price of computers, lower corporate income taxes, lower interest rates) induced firms to substitute sufficiently from labor toward capital, causing s L to go down Bottom Line: Implies decline in cost of capital explains roughly half of the decline in the labor share 2 The Global Decline in the Labor Share The Quarterly Journal of Economics, Owen Zidar (Chicago Booth) Microeconomics Week 4: Cost and Technology 93 / 93