Production Theory. Lesson 7. Ryan Safner 1. Hood College. ECON Microeconomic Analysis Fall 2016

Transcription

1 Production Theory Lesson 7 Ryan Safner 1 1 Department of Economics Hood College ECON Microeconomic Analysis Fall 2016 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

2 Lesson Plan 1 The Basics of Production 2 The Technology of Production 3 Short Run Production Marginal Product Average Product 4 Long Run Production Isoquants Isocost Lines Constrained Optimization: Cost Minimization 5 Returns to Scale Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

3 Producer Behavior How do producers decide which products to produce, and how much of each product? How do producers decide which combination of inputs to use? The answers to these questions are the building blocks for market supply curves Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

4 Production So far, we ve looked at how markets allocate existing goods among consumers But, the vast majority of goods must be produced before we can exchange and consume them Production is the creation of value, by transforming lower-valued goods (resources, inputs, etc) into higher-valued goods (outputs, consumer products, etc) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

5 Production What to Produce? The ultimate goal of all economic activity is consumption so all production must ultimately be calibrated towards those goods that consumers desire (consumer sovereignty) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

6 Consumer Sovereignty The direction of all economic affairs is in the market society a task of the entrepreneurs. Theirs is the control of production. They are at the helm and steer the ship. A superficial observer would believe that they are supreme. But they are not. They are bound to obey unconditionally the captain s orders. The captain is the consumer. Neither the entrepreneurs nor the farmers nor the capitalists determine what has to be produced. The consumers do that. If a businessman does not strictly obey the orders of the public as they are conveyed to him by the structure of market prices, he suffers losses, he goes bankrupt, and is thus removed from his eminent position at the helm. Other men who did better in satisfying the demand of the consumers replace him. The consumers patronize those shops in which they can buy what they want at the cheapest price. Their buying and their abstention from buying decides who should own and run the plants and the land. They make poor people rich and rich people poor. They determine precisely what should be produced, in what quality, and in what quantities. Ludwig von Mises ( ) Human Action (1949), p.270 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

7 Production Relationships Production Function: Transforming Inputs into Outputs Y = f (T, L, K, E) Output (Y ) is a function of inputs (factors of production (FOP)): Factor Owned By Earns Land (T) Landowners Rent Labor (L) Laborers Wages Capital (K) Capitalists Interest Entrepreneurship (E) Entrepreneurs Profits Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

8 Factors of Production - (1) Land Land All the goods provided by nature Not just geographical territory, but also all the minerals beneath and all the vegetation above Supply of land is (overall) fixed Can sell full property rights or only sell temporary use rights in exchange for rent Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

9 Factors of Production - (2) Labor Labor The personal expenditure of energy Opportunity cost of labor is leisure Can sell a temporary property right over the produce of your services in exchange for wages Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

10 Factors of Production - (3) Capital Capital All higher-order goods that are used in the production of lower order goods 1st-Order Goods: Consumer goods (immediately consumed) 2nd-Order Goods: Goods used to produce 1st-order goods n-order Goods: Goods used to produce (n-1) order goods Can sell temporal services in exchange for interest Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

11 Capital & Labor Capital and Labor are often substitutable! Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

12 Capital & Labor Capital and Labor are often substitutable! Say you want to produce 100 copies, 1 worker produces 1 copy/hour, and a copy machine costs $700 and produces 100 copies/hour (and requires 1 worker to operate it) Wages are $5.00/hr: Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

13 Capital & Labor Capital and Labor are often substitutable! Say you want to produce 100 copies, 1 worker produces 1 copy/hour, and a copy machine costs $700 and produces 100 copies/hour (and requires 1 worker to operate it) Cost Function: TC = wl + rk Wages are $5.00/hr: Hire 100 Workers Hire 1 Worker, 1 Copy Machine $5(100) = $500 $5(1) + $700(1) = $705 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

14 Factors of Production Capital and Labor are often substitutable! Say you want to produce 100 copies, 1 worker produces 1 copy/hour, and a copy machine costs $700 and produces 100 copies/hour (and requires 1 worker to operate it) Cost Function: TC = wl + rk Wages are increased to $10.00/hr: Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

15 Factors of Production Capital and Labor are often substitutable! Say you want to produce 100 copies, 1 worker produces 1 copy/hour, and a copy machine costs $700 and produces 100 copies/hour (and requires 1 worker to operate it) Cost Function: TC = wl + rk Wages are increased to $10.00/hr: Hire 100 Workers Hire 1 Worker, 1 Copy Machine $10(100) = $1, 000 $10(1) + $700(1) = $710 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

16 Lesson Plan 1 The Basics of Production 2 The Technology of Production 3 Short Run Production Marginal Product Average Product 4 Long Run Production Isoquants Isocost Lines Constrained Optimization: Cost Minimization 5 Returns to Scale Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

17 Producer Behavior In general, as in many parts of life, what is occurring is constrained optimization We are trying to optimize do the best that we possibly can Subject to our constraints (e.g. limited time, limited income, limited attention) In the case of production, producers want to minimize costs for a given level of output (in order to maximize profit) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

18 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

19 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: 1 Production takes place in firms that produce a single product Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

20 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: 1 Production takes place in firms that produce a single product 2 The firm has already chosen which product to produce Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

21 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: 1 Production takes place in firms that produce a single product 2 The firm has already chosen which product to produce 3 Firms minimize costs Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

22 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: 1 Production takes place in firms that produce a single product 2 The firm has already chosen which product to produce 3 Firms minimize costs 4 There are only two inputs: labor (L) and capital (K) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

23 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

24 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: 5 Capital (K) is fixed in the short run Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

25 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: 5 Capital (K) is fixed in the short run 6 Using more inputs produces more output Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

26 Producer Behavior: Assumptions & Framework We have a number of simplifying assumptions to make our model easy to work with: 5 Capital (K) is fixed in the short run 6 Using more inputs produces more output 7 Inputs experience diminishing returns Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

27 Production Functions Typical Cobb-Douglass production function: Y = AL α K β L: labor K: capital A: total factor productivity (technology) α: output elasticity of labor β: output elasticity of capital Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

28 Production Functions Example Y = 2L 0.5 K 0.5 Total factor productivity: 2 (technology makes L & K produce twice as much output) Output elasticity of capital: 0.5 (as K increases by 1%, output increases by 0.5%) Output elasticity of labor: 0.5 (as L increases by 1%, output increases by 0.5%) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

29 Production Functions Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

30 Production Functions Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

31 Production Functions This is the production function! Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

32 Production Functions This is the production function! Chair = f(screws, Screwdriver, Wood Pieces, Labor) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

33 Short run vs. Long Run The time -frame of production can be divided between short vs. long run Short run: before firms enter/exit market At least one factor of production is fixed (i.e. capital/factories) Long run: after firms enter/exit market All factors of production are variable Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

34 Lesson Plan 1 The Basics of Production 2 The Technology of Production 3 Short Run Production Marginal Product Average Product 4 Long Run Production Isoquants Isocost Lines Constrained Optimization: Cost Minimization 5 Returns to Scale Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

35 Short Run Production In the short run, at least one factor (i.e. capital) is fixed: Q = f ( K, L) e.g. we produce with one factory, but can change the amount of labor used in the factory Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

36 Marginal Product The marginal product of an input is the additional output produced by an additional unit of an input (holding other inputs constant) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

37 Marginal Product The marginal product of an input is the additional output produced by an additional unit of an input (holding other inputs constant) Like marginal utility Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

38 Marginal Product The marginal product of an input is the additional output produced by an additional unit of an input (holding other inputs constant) Like marginal utility Eventually hits diminishing returns Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

39 Marginal Product The marginal product of labor (MP L ) is the additional output produced by adding one additional unit of labor (holding capital constant) MP L = Q L Using calculus, this is the partial derivative of the production function with respect to labor Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

40 Marginal Product The marginal product of labor (MP L ) is the additional output produced by adding one additional unit of labor (holding capital constant) MP L = Q L Using calculus, this is the partial derivative of the production function with respect to labor The marginal product of capital (MP K ) is the additional output produced by adding one additional unit of capital (holding labor constant) MP K = Q K Using calculus, this is the partial derivative of the production function with respect to capital Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

41 Marginal Product Example Consider the production function Q = KL Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

42 Marginal Product Example Consider the production function Q = KL In the short run, capital is fixed at 4 units Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

43 Marginal Product Example Consider the production function Q = KL In the short run, capital is fixed at 4 units So plug 4 in for K Q = 4 L = 2 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

44 Marginal Product Example Consider the production function Q = KL In the short run, capital is fixed at 4 units So plug 4 in for K Q = 4 L = 2 L The short run production function is Q = 2 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

45 Marginal Product Example Consider the production function Q = KL In the short run, capital is fixed at 4 units So plug 4 in for K Q = 4 L = 2 L The short run production function is Q = 2 L The marginal product of labor is the partial derivative: (I would give this to you!) Q L = L = 1 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

46 Marginal Product Goolsbee et. al (2011: 220) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

47 Marginal Product Goolsbee et. al (2011: 222) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

48 Average Product Average product is the total output divided by the number of inputs The average product of labor (AP L ) is the output per worker AP L = Q L This is the slope of a line from the origin (0,0) to the short run production function at L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

49 Average Product Average product is the total output divided by the number of inputs The average product of labor (AP L ) is the output per worker AP L = Q L This is the slope of a line from the origin (0,0) to the short run production function at L Can do the same thing for capital, holding labor constant Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

50 Average Product Goolsbee et. al (2011: 220) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

51 Marginal and Average Product Pindyck (2013: Ch.6) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

52 Marginal and Average Product Point A: MP L = 20 (slope of TP is 20) AP L = 15 (slope of ray) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

53 Marginal and Average Product Point A: Point B: MP L = 20 (slope of TP is 20) AP L = 15 (slope of ray) MP L = 30 (slope of TP is 30) AP L = 20 (slope of ray) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

54 Marginal and Average Product Point B is an inflection point: For L < 3, MP L For L > 3, MP L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

55 Marginal and Average Product Point B is an inflection point: For L < 3, MP L For L > 3, MP L Point C is maximum of APL When MP L > AP L, AP L When MP L < AP L, AP L When MP L = AP L, max AP L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

56 Marginal and Average Product Point B is an inflection point: For L < 3, MP L For L > 3, MP L Point C is maximum of APL When MP L > AP L, AP L When MP L < AP L, AP L When MP L = AP L, max AP L Point D is maximum of TP At L = 8, MP L = 0 L > 8, MP L < 0 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

57 Production Stages Stage I MP L AP L MP L > AP L Increasing marginal returns to L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

58 Production Stages Stage I Stage II MP L AP L MP L > AP L Increasing marginal returns to L MP L AP L MP L < AP L Decreasing marginal returns to L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

59 Production Stages Stage I Stage II Stage III MP L AP L MP L > AP L Increasing marginal returns to L MP L AP L MP L < AP L Decreasing marginal returns to L MP L < 0 AP L Negative marginal returns to L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

60 Lesson Plan 1 The Basics of Production 2 The Technology of Production 3 Short Run Production Marginal Product Average Product 4 Long Run Production Isoquants Isocost Lines Constrained Optimization: Cost Minimization 5 Returns to Scale Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

61 Long Run Production In the long run, all factors of production are variable (can be changed) e.g. can build more factories, rent more space, invest in more machines, etc Q = f (K, L) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

62 Long Run Production Goolsbee et. al (2011: 225) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

63 Long Run Production: Isoquants K We can draw an isoquant curve representing the combinations of labor and capital that yield the same level of output 4 C Similar to indifference curves for consumers 2 1 A B Q = L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

64 Long Run Production: Isoquants K We can draw an isoquant curve representing the combinations of labor and capital that yield the same level of output Similar to indifference curves for consumers Points to the NE are on higher isoquants, yield higher output C 1 A 2 D 3 Q = 3.00 B Q = 2.00 L 4 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

65 Long Run Production: Isoquants K We can draw an isoquant curve representing the combinations of labor and capital that yield the same level of output Similar to indifference curves for consumers Points to the NE are on higher isoquants, yield higher output C 1 A 2 D 3 More Q Q = 3.00 B Q = 2.00 L 4 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

66 Long Run Production: Isoquants K Slope is decreasing as we move (point A) More L, MP L Less K, MP K B slope= 2 A Q = 2.00 slope= 1 2 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

67 Long Run Production: Isoquants K Slope is decreasing as we move (point A) More L, MP L Less K, MP K Slope is increasing as we move to uparrow (point B) More K, MP K Less L, MP L B slope= 2 A Q = 2.00 slope= 1 2 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

68 Marginal Rate of Technical Substitution The slope of an isoquant curve is called the marginal rate of technical substitution (MRTS) K MRTS LK = K L B slope= 2 A Q = 2.00 slope= 1 2 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

69 Marginal Rate of Technical Substitution The slope of an isoquant curve is called the marginal rate of technical substitution (MRTS) K MRTS LK = K L B It is the rate at which a producer is willing to substitute 1 more unit of L for less K and get the same output slope= 2 A Q = 2.00 slope= 1 2 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

70 Marginal Rate of Technical Substitution The slope of an isoquant curve is called the marginal rate of technical substitution (MRTS) K MRTS LK = K L B It is the rate at which a producer is willing to substitute 1 more unit of L for less K and get the same output Consider it the opportunity cost of 1 more unit of L: how many K must be given up? slope= 2 A slope= 1 2 Q = 2.00 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

71 Marginal Rate of Technical Substitution Moving along the curve, as Q is always constant: Q = MP L L + MP K K = 0 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

72 Marginal Rate of Technical Substitution Moving along the curve, as Q is always constant: Q = MP L L + MP K K = 0 MP L L = MP K K Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

73 Marginal Rate of Technical Substitution Moving along the curve, as Q is always constant: Q = MP L L + MP K K = 0 MP L L = MP K K K L = MP L MP K Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

74 Marginal Rate of Technical Substitution Moving along the curve, as Q is always constant: Q = MP L L + MP K K = 0 MP L L = MP K K K L = MP L MP K The MRTS between labor and capital at any point tells you the relative marginal products of labor and capital at that point: MRTS = slope = K L = MP L MP K Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

75 Marginal Rate of Technical Substitution Moving along the curve, as Q is always constant: Q = MP L L + MP K K = 0 MP L L = MP K K K L = MP L MP K The MRTS between labor and capital at any point tells you the relative marginal products of labor and capital at that point: MRTS = slope = K L = MP L MP K MRTS plays a critical role in driving producer behavior Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

76 MRTS and Marginal Products MRTS = slope = K L = MP L MP K Bend of the isoquant curve tells us how these inputs are related Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

77 MRTS and Marginal Products MRTS = slope = K L = MP L MP K Bend of the isoquant curve tells us how these inputs are related Relatively straight curves denote inputs that are more easily substitutable for one another Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

78 MRTS and Marginal Products MRTS = slope = K L = MP L MP K Bend of the isoquant curve tells us how these inputs are related Relatively straight curves denote inputs that are more easily substitutable for one another Relatively bent curves denote inputs that are more easily complementary to one another Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

79 MRTS and Marginal Products MRTS = slope = K L = MP L MP K Bend of the isoquant curve tells us how these inputs are related Relatively straight curves denote inputs that are more easily substitutable for one another Relatively bent curves denote inputs that are more easily complementary to one another Look at extreme cases first to get the idea: Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

80 MRTS and Marginal Products ATMs (K) Consider bank tellers (L) and ATMs (K): 1 ATM can do the work of 2 bank tellers Q = 1 Q = 2 Q = Tellers ( Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

81 MRTS and Marginal Products ATMs (K) Consider bank tellers (L) and ATMs (K): 1 ATM can do the work of 2 bank tellers Always willing to substitute one ATM for 2 tellers no matter the level of output (MRTS=-0.5) Q = 1 Q = 2 Q = Tellers ( Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

82 MRTS and Marginal Products Consider bank tellers (L) and ATMs (K): 1 ATM can do the work of 2 bank tellers Always willing to substitute one ATM for 2 tellers no matter the level of output (MRTS=-0.5) ATMs (K) Perfect substitutes: 3 producer will always trade 2 off ATMs vs Tellers at same 1 fixed rate Q = 1 Q = 2 Q = 3 Tellers ( Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

83 MRTS and Marginal Products Consider busses and bus drivers: Buses (K) Q = 3 2 Q = 2 1 Q = Drivers Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

84 MRTS and Marginal Products Consider busses and bus drivers: Must combine both in constant proportion (1:1) Buses (K) Q = 3 2 A Q = 2 1 Q = Drivers Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

85 MRTS and Marginal Products Consider busses and bus drivers: Must combine both in constant proportion (1:1) Starting with 2 busses and 2 bus drivers (A) Buses (K) Q = 3 2 B A Q = 2 1 Q = Drivers Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

86 MRTS and Marginal Products Consider busses and bus drivers: Must combine both in constant proportion (1:1) Starting with 2 busses and 2 bus drivers (A) Adding 2 more drivers will not increase output (B) Buses (K) C 3 Q = 3 2 B A Q = 2 1 Q = Drivers Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

87 MRTS and Marginal Products Consider busses and bus drivers: Must combine both in constant proportion (1:1) Starting with 2 busses and 2 bus drivers (A) Adding 2 more drivers will not increase output (B) Nor will adding 2 buses instead (C) Buses (K) C 3 Q = 3 2 B A Q = 2 1 Q = Drivers Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

88 MRTS and Marginal Products Consider busses and bus drivers: Must combine both in constant proportion (1:1) Starting with 2 busses and 2 bus drivers (A) Adding 2 more drivers will not increase output (B) Nor will adding 2 buses instead (C) Perfect complements: must always be combined in fixed proportions (a Leontief production function) Buses (K) C 3 Q = 3 2 B A Q = 2 1 Q = Drivers Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

89 MRTS and Marginal Products Goolsbee et. al (2011: 228) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

90 MRTS and Marginal Products Goolsbee et. al (2011: 228) Straighter more substitutable Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

91 MRTS and Marginal Products Goolsbee et. al (2011: 228) Straighter more substitutable Very bent more complementary Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

92 Total Cost and the Isocost Line The isocost line is a line that describes the combinations of inputs that are the same total cost (TC) TC = rk + wl r is the rental rate of capital, w is wage (the prices of each factor of production) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

93 Total Cost and the Isocost Line The isocost line is a line that describes the combinations of inputs that are the same total cost (TC) TC = rk + wl r is the rental rate of capital, w is wage (the prices of each factor of production) To graph, solve for K: K = TC r w r L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

94 Total Cost and the Isocost Line The isocost line is a line that describes the combinations of inputs that are the same total cost (TC) TC = rk + wl r is the rental rate of capital, w is wage (the prices of each factor of production) To graph, solve for K: K = TC r TC r : Y-intercept (using only K) w r L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

95 Total Cost and the Isocost Line The isocost line is a line that describes the combinations of inputs that are the same total cost (TC) TC = rk + wl r is the rental rate of capital, w is wage (the prices of each factor of production) To graph, solve for K: TC K = TC r w r L r : Y-intercept (using only K) w r : slope = (negative) factor price ratio Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

96 Total Cost and the Isocost Line The isocost line is a line that describes the combinations of inputs that are the same total cost (TC) TC = rk + wl r is the rental rate of capital, w is wage (the prices of each factor of production) To graph, solve for K: TC K = TC r w r L r : Y-intercept (using only K) : slope = (negative) factor price ratio : X-intercept (using only L) w r TC w Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

97 Total Cost and the Isocost Line K Suppose: Total Cost = $50 w = $5 r = $ L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

98 Total Cost and the Isocost Line K Suppose: Total Cost = $50 w = $5 r = $10 K = TC r w r L = $50 $10 $5 $10 = L TC r slope = w r = 5 10 = 1 2 TC=$ TC w L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

99 Total Cost and the Isocost Line K Suppose: Total Cost = $50 w = $5 r = $10 K = TC r w r L = $50 $10 $5 $10 = L Vertical intercept: TC r = $50 $10 = 5 TC r slope = w r = 5 10 = 1 2 TC=$ TC w L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

100 Total Cost and the Isocost Line Suppose: Total Cost = $50 w = $5 r = $10 K = TC r w r L = $50 $10 $5 $10 = L Vertical intercept: TC r = $50 $10 = 5 Horizontal intercept: TC w = $50 TC r K slope = w r = 5 10 = 1 2 TC=$50 $5 = 10 L TC w Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

101 Total Cost and the Isocost Line K Any point on the line is the same total cost: TC=$50 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

102 Total Cost and the Isocost Line K Any point on the line is the same total cost: Point A: $5(0L) + $10(5K) = $ A TC=$50 L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

103 Total Cost and the Isocost Line K Any point on the line is the same total cost: Point A: $5(0L) + $10(5K) = $50 Point B: $5(10L) + $10(0K) = $ A TC=$50 B L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

104 Total Cost and the Isocost Line K Any point on the line is the same total cost: Point A: $5(0L) + $10(5K) = $50 Point B: $5(10L) + $10(0K) = $50 Point C: $5(2L) + $10(4K) = $ A C TC=$50 B L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

105 Total Cost and the Isocost Line K Any point on the line is the same total cost: Point A: $5(0L) + $10(5K) = $50 Point B: $5(10L) + $10(0K) = $50 Point C: $5(2L) + $10(4K) = $50 Point D: $5(8L) + $10(1K) = $ A C D 1 TC=$50 B L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

106 Total Cost and the Isocost Line K Any point beneath the line is lower total cost A C D 1 TC=$50 B L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

107 Total Cost and the Isocost Line K Any point beneath the line is lower total cost Point E: $5(3L) + $10(2K) = $ A C 4 3 E 2 D 1 TC=$50 B L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

108 Total Cost and the Isocost Line K Any point beneath the line is lower total cost Point E: $5(3L) + $10(2K) = $35 Any point above the line is higher cost Point F: $5(6L) + $10(4K) = $ A C F 4 3 E 2 D 1 TC=$50 B L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

109 Total Cost and the Isocost Line K Changes in relative factor prices will pivot the isocost line TC r slope = 1 2 TC=$ TC w L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

110 Total Cost and the Isocost Line Changes in relative factor prices will pivot the isocost line Wages double from $5 to $10 Slope steepens, w r = $10 $10 = 1 Horizontal intercept: TC w = $50 TC r K 3 slope = 1 2 slope = 1 2 $10 = 5 1 TC=$50 TC=$50 L TC w TC w Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

111 Total Cost and the Isocost Line K Changes in relative prices will pivot the isocost line TC r slope = TC w L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

112 Total Cost and the Isocost Line K Changes in relative prices will pivot the isocost line The rental rate of capital decreases from $10 to $7.50 Slope steepens, w r = $5 $7.50 = 2 3 Vertical intercept: w r = $50 $7.5 = TC r TC r slope = 1 2 slope = TC w L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

113 Producer s Constrained Optimization We now have the two tools to understand basic producer production choices: Isoquants: combinations of L&K attaining same output Isocost line: combinations of L&K attaining same total cost The producer s constrained optimization problem: minimize total cost subject to a particular level of output min TC = wl + rk s. t. f (K, L) K,L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

114 Producer s Constrained Optimization Find lowest isocost line tangent to isoquant (i.e. lowest total cost for a quantity of output) K Q = 10 L TC = $50 TC = $100 TC = $150 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

115 Producer s Constrained Optimization Find lowest isocost line tangent to isoquant (i.e. lowest total cost for a quantity of output) Point A minimizes total cost and attains 10 units of output K A Q = 10 L TC = $50 TC = $100 TC = $150 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

116 Producer s Constrained Optimization K Find lowest isocost line tangent to isoquant (i.e. lowest total cost for a quantity of output) Point A minimizes total cost and attains 10 units of output Point B attains 10 units of output but costs more A B Q = 10 L TC = $50 TC = $100 TC = $150 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

117 Producer s Constrained Optimization K Find lowest isocost line tangent to isoquant (i.e. lowest total cost for a quantity of output) Point A minimizes total cost and attains 10 units of output Point B attains 10 units of output but costs more Point C costs the same as A but doesn t attain 10 units of output C A B Q = 10 L TC = $50 TC = $100 TC = $150 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

118 Producer s Constrained Optimization Find lowest isocost line tangent to isoquant (i.e. lowest total cost for a quantity of output) At tangency point: Slope of Isoquant = slope of Isocost Line K MRTS LK = MP L MP K MP L MP K = w r = w r Q = 10 L TC = $100 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

119 Producer s Constrained Optimization Find lowest isocost line tangent to isoquant (i.e. lowest total cost for a quantity of output) At tangency point: Slope of Isoquant = slope of Isocost Line K MRTS LK = MP L MP K MP L MP K = w r = w r A Q = 10 L TC = $100 Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

120 Producer s Constrained Optimization MP L MP K = w r Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

121 Producer s Constrained Optimization MP L MP K = w r Rearranging the tangency condition implies that at that tangency: MP L w = MP K r Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

122 Producer s Constrained Optimization MP L MP K = w r Rearranging the tangency condition implies that at that tangency: MP L w = MP K r The producer finds the combination of inputs that provides the most output on a cost-adjusted basis Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

123 Producer s Constrained Optimization MP L w = MP K r Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

124 Producer s Constrained Optimization MP L w = MP K r Equimarginal Principle: Produce where the marginal product per dollar spent is equalized across all n inputs! Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

125 Producer s Constrained Optimization MP L w = MP K r Equimarginal Principle: Produce where the marginal product per dollar spent is equalized across all n inputs! Why is this the optimum? Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

126 Producer s Constrained Optimization MP L w = MP K r Equimarginal Principle: Produce where the marginal product per dollar spent is equalized across all n inputs! Why is this the optimum? Suppose MP L w > MP K r Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

127 Producer s Constrained Optimization MP L w = MP K r Equimarginal Principle: Produce where the marginal product per dollar spent is equalized across all n inputs! Why is this the optimum? Suppose MP L w > MP K r Marginal product per $ spent on labor (wages) is higher than for capital Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

128 Producer s Constrained Optimization MP L w = MP K r Equimarginal Principle: Produce where the marginal product per dollar spent is equalized across all n inputs! Why is this the optimum? Suppose MP L w > MP K r Marginal product per $ spent on labor (wages) is higher than for capital Use more labor and less capital! Getting more for your money! Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

129 Producer s Constrained Optimization MP L w = MP K r Equimarginal Principle: Produce where the marginal product per dollar spent is equalized across all n inputs! Why is this the optimum? Suppose MP L w > MP K r Marginal product per $ spent on labor (wages) is higher than for capital Use more labor and less capital! Getting more for your money! Using more labor will decrease MP L, until MU X w > MP K r This is why the tangency is a stable equilibrium Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

130 Visualizing the Equimarginal Principle Capital Labor MP r MP w MP K K MP L L Suppose you use only capital: Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

131 Visualizing the Equimarginal Principle Capital Labor MP r MP w MP K K Suppose you use only capital: MP L We can earn more utility by switching to hiring a worker instead of a capital! Gain in output from +1 Labor > Loss of output from -1 Capital Employ more Labor because MP L w > MP K r L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

132 Visualizing the Equimarginal Principle Capital Labor MP r MP w MP K K Suppose you use only capital: MP L We can earn more utility by switching to hiring a worker instead of a capital! Gain in output from +1 Labor > Loss of output from -1 Capital Employ more Labor because MP L w > MP K r We can keep doing this so long as MP L w > MP K r L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

133 Visualizing the Equimarginal Principle Capital Labor MP r MP w MP K K Suppose you use only capital: MP L We can earn more utility by switching to hiring a worker instead of a capital! Gain in output from +1 Labor > Loss of output from -1 Capital Employ more Labor because MP L w > MP K r We can keep doing this so long as MP L w > MP K r L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

134 Visualizing the Equimarginal Principle Capital Labor MP r MP w MP K K Suppose you use only capital: MP L We can earn more utility by switching to hiring a worker instead of a capital! Gain in output from +1 Labor > Loss of output from -1 Capital Employ more Labor because MP L w > MP K r We can keep doing this so long as MP L w > MP K r L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

135 Visualizing the Equimarginal Principle Capital Labor MP r MP w MP K K Suppose you use only capital: MP L We can earn more utility by switching to hiring a worker instead of a capital! Gain in output from +1 Labor > Loss of output from -1 Capital Employ more Labor because MP L w > MP K r We can keep doing this so long as MP L w > MP K r L Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

136 Visualizing the Equimarginal Principle Capital Labor MP r MP w MP K K Suppose you use only capital: MP L We can earn more utility by switching to hiring a worker instead of a capital! Gain in output from +1 Labor > Loss of output from -1 Capital Employ more Labor because MP L w > MP K r We can keep doing this so long as MP L w If we kept substituting Labor for Capital, MP L The equimarginal principle: MP L w > MP K r w = MP K r < MP K, should switch back! r Ryan Safner (Hood College) ECON Lesson 7 Fall / 64 L

137 Producer s Constrained Optimization Example A firm is employing 100 workers at $15/hour and is renting 50 units of capital at $30/hour. At these levels, MP L = 45 and MP K = 60 1 Is this firm minimizing costs? 2 If not, what changes should it make? 3 How does your answer to (2) depend on the timeframe of analysis? Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

138 Lesson Plan 1 The Basics of Production 2 The Technology of Production 3 Short Run Production Marginal Product Average Product 4 Long Run Production Isoquants Isocost Lines Constrained Optimization: Cost Minimization 5 Returns to Scale Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

139 Returns to Scale The returns to scale of production refers to the change in output when all inputs are increased in the same proportion Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

140 Returns to Scale The returns to scale of production refers to the change in output when all inputs are increased in the same proportion Constant returns to scale: output increases at the same proportionate rate as inputs increase Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

141 Returns to Scale The returns to scale of production refers to the change in output when all inputs are increased in the same proportion Constant returns to scale: output increases at the same proportionate rate as inputs increase e.g. if you double all inputs, output doubles Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

142 Returns to Scale The returns to scale of production refers to the change in output when all inputs are increased in the same proportion Constant returns to scale: output increases at the same proportionate rate as inputs increase e.g. if you double all inputs, output doubles Increasing returns to scale: output increases more than proportionately to the change in inputs Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

143 Returns to Scale The returns to scale of production refers to the change in output when all inputs are increased in the same proportion Constant returns to scale: output increases at the same proportionate rate as inputs increase e.g. if you double all inputs, output doubles Increasing returns to scale: output increases more than proportionately to the change in inputs e.g. if you double all inputs, output quadruples Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

144 Returns to Scale The returns to scale of production refers to the change in output when all inputs are increased in the same proportion Constant returns to scale: output increases at the same proportionate rate as inputs increase e.g. if you double all inputs, output doubles Increasing returns to scale: output increases more than proportionately to the change in inputs e.g. if you double all inputs, output quadruples Decreasing returns to scale: output increases less than proportionately to the change in inputs Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

145 Returns to Scale The returns to scale of production refers to the change in output when all inputs are increased in the same proportion Constant returns to scale: output increases at the same proportionate rate as inputs increase e.g. if you double all inputs, output doubles Increasing returns to scale: output increases more than proportionately to the change in inputs e.g. if you double all inputs, output quadruples Decreasing returns to scale: output increases less than proportionately to the change in inputs e.g. if you triple all inputs, output doubles Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

146 Returns to Scale Example Does each of the following production functions exhibit constant returns to scale, increasing returns to scale, or decreasing returns to scale? Q = 2K + 4L (1) Q = 2KL (2) Q = 2K 0.3 L 0.3 (3) Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

147 Returns to Scale Again, one reason we often use Cobb-Douglas production functions is to easily determine returns to scale: Q = AL α K β α + β = 1: constant returns to scale α + β > 1: increasing returns to scale α + β < 1: decreasing returns to scale Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

148 Returns to Scale Goolsbee et. al (2011: 239) For each curve, L and K are doubled Ryan Safner (Hood College) ECON Lesson 7 Fall / 64

149 Expansion Paths & Cost Curves Goolsbee et. al (2011: 246) Output Expansion Path: curve illustrating the changes in the optimal mix of inputs for different outputs Total Cost (TC): curve showing the total cost of producing different outputs Ryan Safner (Hood College) ECON Lesson 7 Fall / 64