The Costs of Production Principles of Microeconomics Boris Nikolaev

Brainstorming costs You run Ford Motor Company. List three different costs you have. List three different business decisions that are affected by your costs.

In this chapter What is a production function? What is marginal product? How are they related? What are the various costs? How are they related to each other and to output? How are costs different in the short run vs. the long run? What are “economies of scale”?

It’s business time. Firms are in the business of making profits. Profit = Total Revenue (TR) – Total Cost (TC) the amount a firm receives from the sale of its output the market value of the inputs a firm uses in production

Sneak Preview MR=MC

Profits Are profits bad? What is the function of profits in a free market economy? In a competitive market profits come not from increase in price, but from decrease in the cost of production. Why? Fortune 500 most profitable companies [see here]

The Weed Trail [read here]

Profits and Insurance Recollect risk-aversion & uncertainty.

Corporate Profits after tax

CP/GDP

Marxist View The stagnating wages since the 1970s Technology World war II Outsourcing Women in the labor force Immigration Problem of effective demand Work more hours Borrowing binge (mortgage debt, credit cards) Greatest profit boom (in the history of the world) Marginal productivity, wages, and profits

Productivity vs Wages

What do you do with the profits? CEO salaries [Forbes list] Mergers & Acquisitions Lend to employees (e.g. GM, IBM, etc.)

Costs Resources are scarce, productive, and have alternative uses. Explicit costs are the direct cash payments you make to use resources you don’t own such as wages, rent, insurance, taxes, etc. Implicit costs is the opportunity cost of the resource you own (the benefit you could have extracted from it from its next best use). Do not require direct cast payments.

Example You need $100,000 to start your business. The interest rate is 5%. Case 1: borrow $100,000 explicit cost = $5000 interest on loan Case 2: use $40,000 of your savings, borrow the other $60,000 explicit cost = $3000 (5%) interest on the loan implicit cost = $2000 (5%) foregone interest you could have earned on your $40,000.

Economic vs Accounting Profit = total revenue minus total explicit costs Economic profit = total revenue minus total costs (including explicit and implicit costs) Accounting profit ignores implicit costs, so it’s higher than economic profit.

Example 1 The equilibrium rent on office space has just increased by $500/month. Determine the effects on accounting profit and economic profit if: a. you rent your office space b. you own your office space

Answers The rent on office space increases $500/month. a. You rent your office space. Explicit costs increase $500/month. Accounting profit & economic profit each fall $500/month. b. You own your office space. Explicit costs do not change, so accounting profit does not change. Implicit costs increase $500/month (opp. cost of using your space instead of renting it) so economic profit falls by $500/month.

Practice Question Your current job pays $50K/year. You have $20K savings that earn you $3K interest a year. You own a garage, which you rent for $12K/ year. You decide to invest your savings and use your garage to start your own business. Did you make a good economic decision? Total Revenue $105K Explicit Costs labor $21K food $20K Total Cost $41K Accounting Profit _____ Implicit Costs salary _____ interest _____ rent _____ Total Implicit Cost _____ Economic Profit / Loss ______ Depreciation or opportunity cost of capital

Production in the Short Run Q= f(L,K) A production function shows the relationship between the quantity of inputs used to produce a good and the quantity of output of that good.

EXAMPLE 1: Production Function 500 1,000 1,500 2,000 2,500 3,000 1 2 3 4 5 No. of workers Quantity of output Q (bushels of wheat) L (no. of workers) 1000 1 1800 2 2400 3 2800 4 3000 5 21

Marginal Product (MP) If you hire one more worker, your output rises by the marginal product of labor. The marginal product of any input is the increase in output arising from an additional unit of that input, holding all other inputs constant. Notation: ∆ (delta) = “change in…” Examples: ∆Q = change in output, ∆L = change in labor Marginal product of labor (MPL) = ∆Q ∆L 22

EXAMPLE 1: Total & Marginal Product 3000 5 2800 4 2400 3 1800 2 1000 1 Q (bushels of wheat) L (no. of workers) MPL ∆Q = 1000 ∆L = 1 1000 ∆Q = 800 ∆L = 1 800 ∆Q = 600 ∆L = 1 600 ∆Q = 400 ∆L = 1 400 ∆Q = 200 ∆L = 1 200 23

EXAMPLE 1: MPL = Slope of Prod Function 500 1,000 1,500 2,000 2,500 3,000 1 2 3 4 5 No. of workers Quantity of output L (no. of workers) Q (bushels of wheat) MPL MPL equals the slope of the production function. Notice that MPL diminishes as L increases. This explains why the production function gets flatter as L increases. 1000 1 1000 800 2 1800 600 3 2400 400 4 2800 200 5 3000 24

Why MPL Is Important your costs rise by the wage he pays the worker Recall one of the Ten Principles: Rational people think at the margin. When you hire an extra worker, your costs rise by the wage he pays the worker your output rises by MPL Comparing them helps you decide whether he should hire the worker. 25

Class demonstration

The Law of Diminishing Marginal Returns Diminishing marginal product: The marginal product of an input declines as the quantity of the input increases (other things equal). Why does it decline?

Practice Question # fishermen Fish caught MP of labor MRP 1 15 2 35 3 58 4 80 5 95 6 105 7 108 8 Input (L) TP = f(L) Assume that only one input (L) is relevant in production. The wage / worker = $175 and one pound of fish is selling for $10

Let’s go back to our farm example… You must pay $1000 per month for the land, regardless of how much wheat you grow. The market wage for a farm worker is $2000 per month. Your cots are related to how much wheat you produce…

EXAMPLE 1: Your Costs L (no. of workers) Q (bushels of wheat) L (no. of workers) Q (bushels of wheat) Cost of land Cost of labor Total cost $1,000 $10,000 $8,000 $6,000 $4,000 $2,000 $0 $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 1 1000 2 1800 3 2400 4 2800 5 3000 30

EXAMPLE 1: Total Cost Curve Q (bushels of wheat) Total Cost $1,000 1000 $3,000 1800 $5,000 2400 $7,000 2800 $9,000 3000 $11,000 31

Marginal Cost Marginal Cost (MC) is the increase in Total Cost from producing one more unit: ∆TC ∆Q MC = 32

EXAMPLE 1: Total and Marginal Cost $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 Total Cost 3000 2800 2400 1800 1000 Q (bushels of wheat) Marginal Cost (MC) ∆Q = 1000 ∆TC = $2000 $2.00 ∆Q = 800 ∆TC = $2000 $2.50 ∆Q = 600 ∆TC = $2000 $3.33 ∆Q = 400 ∆TC = $2000 $5.00 ∆Q = 200 ∆TC = $2000 $10.00 33

EXAMPLE 1: The Marginal Cost Curve Q (bushels of wheat) TC MC MC usually rises as Q rises, as in this example. $1,000 $10.00 $5.00 $3.33 $2.50 $2.00 1000 $3,000 1800 $5,000 2400 $7,000 2800 $9,000 3000 $11,000 34

Why MC Is Important You are rational and want to maximize your profits. To increase profit, should you produce more or less wheat? To find the answer, you need to “think at the margin.” If MC > MR then producing one more unit will decrease profits. 35

Fixed and Variable Costs Fixed costs (FC) do not vary with the quantity of output produced. In our example, FC = $1000 for land Other examples: cost of equipment, loan payments, rent Variable costs (VC) vary with the quantity produced. In our example, VC = wages you pay workers Other example: cost of materials Total cost (TC) = FC + VC 36

EXAMPLE 2: Costs Q FC VC TC 100 $100 520 380 280 210 160 120 70 $0 620 EXAMPLE 2: Costs $800 FC Q FC VC TC VC $700 100 $100 520 380 280 210 160 120 70 $0 620 480 380 310 260 220 170 $100 TC $600 1 $500 2 Costs $400 3 $300 4 $200 5 $100 6 $0 7 1 2 3 4 5 6 7 Q 37

EXAMPLE 2: Marginal Cost Q TC MC Recall, Marginal Cost (MC) is the change in total cost from producing one more unit: $100 $70 1 170 ∆TC ∆Q MC = 50 2 220 40 3 260 Usually, MC rises as Q rises, due to diminishing marginal product. Sometimes (as here), MC falls before rising. (In other examples, MC may be constant.) 50 4 310 70 5 380 100 6 480 140 7 620 38

EXAMPLE 2: Average Fixed Cost Q FC AFC Average fixed cost (AFC) is fixed cost divided by the quantity of output: AFC = FC/Q $100 14.29 16.67 20 25 33.33 50 $100 n/a 1 100 2 100 3 100 Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units. 4 100 5 100 6 100 7 100 39

EXAMPLE 2: Average Variable Cost Q VC AVC Average variable cost (AVC) is variable cost divided by the quantity of output: AVC = VC/Q $0 74.29 63.33 56.00 52.50 53.33 60 $70 n/a 1 70 2 120 3 160 As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. 4 210 5 280 6 380 7 520 40

EXAMPLE 2: Average Total Cost EXAMPLE 2: Average Total Cost Average total cost (ATC) equals total cost divided by the quantity of output: ATC = TC/Q Q TC ATC 74.29 14.29 63.33 16.67 56.00 20 52.50 25 53.33 33.33 60 50 $70 $100 n/a AVC AFC $100 88.57 80 76 77.50 86.67 110 $170 n/a 1 170 2 220 3 260 Also, ATC = AFC + AVC 4 310 5 380 6 480 7 620 41

EXAMPLE 2: Average Total Cost $0 $25 $50 $75 $100 $125 $150 $175 $200 1 2 3 4 5 6 7 Q Costs Q TC ATC Usually, as in this example, the ATC curve is U-shaped. $100 n/a 1 170 $170 2 220 110 3 260 86.67 4 310 77.50 5 380 76 6 480 80 7 620 88.57 42

EXAMPLE 2: The Various Cost Curves Together $0 $25 $50 $75 $100 $125 $150 $175 $200 1 2 3 4 5 6 7 Q Costs ATC AVC AFC MC 43

Fill in the blank spaces of this table. Calculating costs Fill in the blank spaces of this table. Q VC TC AFC AVC ATC MC $50 n/a n/a n/a $10 1 10 $10 $60.00 2 30 80 30 3 16.67 20 36.67 4 100 150 12.50 37.50 5 150 30 60 6 210 260 8.33 35 43.33

Answers Use AFC = FC/Q Use ATC = TC/Q First, deduce FC = $50 and use FC + VC = TC. Use relationship between MC and TC Use AVC = VC/Q Q VC TC AFC AVC ATC MC $0 $50 n/a n/a n/a $10 1 10 60 $50.00 $10 $60.00 20 2 30 80 25.00 15 40.00 30 3 60 110 16.67 20 36.67 40 4 100 150 12.50 25 37.50 50 5 150 200 10.00 30 40.00 60 6 210 260 8.33 35 43.33

EXAMPLE 2: ATC and MC ATC When MC < ATC, ATC is falling. MC $0 $25 $50 $75 $100 $125 $150 $175 $200 1 2 3 4 5 6 7 Q Costs ATC When MC < ATC, ATC is falling. When MC > ATC, ATC is rising. The MC curve crosses the ATC curve at the ATC curve’s minimum. MC 46

Cost in the Long Run Short run: Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC. Long run: All inputs are variable (e.g., firms can build more factories or sell existing ones).

EXAMPLE 3: LRATC with 3 factory sizes Firm can choose from three factory sizes: S, M, L. Each size has its own SRATC curve. The firm can change to a different factory size in the long run, but not in the short run. Q Avg Total Cost ATCS ATCM ATCL 48

A Typical LRATC Curve In the real world, factories come in many sizes, each with its own SRATC curve. So a typical LRATC curve looks like this: Q ATC LRATC 49

How ATC Changes as the Scale of Production Changes Economies of scale: ATC falls as Q increases. Constant returns to scale: ATC stays the same as Q increases. Diseconomies of scale: ATC rises as Q increases. Q ATC LRATC 50

Sources of Economies of Scale Spread of “overhead,” fixed cost over bigger production. Labor specialization. Technology. Learning by doing. Agglomeration economies.

Note on International Trade What goods are produced and where? David Ricardo (1800’s) – comparative advantage. Heckscher & Ohlin (1920-30’s) – differences in factor endowments. Example: Developed countries export more capital intensive goods (cars, airplanes, etc…) and import from developing countries more labor intensive goods (clothing, agricultural products, etc…) Empirical studies.

Krugman’s Model Uses economies of scale to explain international trade. Mass production decreases average cost (ES) Consumers prefer diversity of products Each country specializes and then trades. This is how countries with similar factor endowments engage in trade (e.g. Japan sells Toyota to US, US sells GM to Germany, etc…)