Lecture Notes: Econ 203 Introductory Microeconomics Lecture/Chapter 13: Costs of Production M. Cary Leahey Manhattan College Fall 2012

2 Goals Introduction to the theory of the firm New “buzz words” developed here: Production function Price and marginal revenue (MR) and cost (MC) Marginal costs and average total costs (ATC) Classification of costs: Fixed versus variable Implicit versus explicit Distinction between short- and long-runs Economies of scale

3 Introduction: what do firms want to do? Review of what are firm’s costs in your opinion (e.g. Ford) Company goal – profit maximization Profit = Total revenue – total costs Total revenue – total amount received from sale of output Total costs – market value of the inputs used to produce output Alternatives – revenue maximization (ML) market share maximization (Japan) social profit/sustainability

4 Costs: explicit or implicit; profit: economic or accounting Explicit costs are money costs (determined by the market) Usually largest costs are wages/benefits followed by IT Implicit costs do not require a cash outlay Opportunity cost of the owner’s time Example: Interest costs Explicit: borrow $100K at 5% interest with a cash cost of $5K Explicit: borrow $60K at 5% interest with a cash cost of $3K Implicit: borrow $40K from yourself at an implicit 5% cost for $2K Costs are the case in two examples = $5K Profits: Accounting profit = revenues less explicit costs Economic profit = revenues less explicit and implicit costs Economic profit usually lower than accounting profit

5 The production function The production function shows the relationship between inputs and outputs-specifically the quantity of inputs needed to produce a quantity of output Can be displayed as an equation, table or graph Best-known (macro) production function is Cobb-Douglas Y = AF(K,L), where Y – output. L – labor, K – capital, and A is unexplained residual The residual is the amount of output that cannot be attributed to labor or capital, such as the layout of the factory floor

,000 1,500 2,000 2,500 3, No. of workers Quantity of output Production function: an example Q (bushels of wheat) L (no. of workers)

7 Marginal product In the previous example, hiring the next incremental worker increases output by the marginal product of labor The marginal product of any input is the increase in output arising from the additional unit of that input, holding all other inputs constant ∆ (delta) = “change in…” Examples: ∆Q = change in output, ∆L = change in labor Marginal product of labor (MPL) = ∆Q / ∆L

Q (bushels of wheat) L (no. of workers) Example: Total and marginal product MPL ∆Q = 1000 ∆L = 1 ∆Q = 800 ∆L = 1 ∆Q = 600 ∆L = 1 ∆Q = 400 ∆L = 1 ∆Q = 200 ∆L = 1

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 ,000 1,500 2,000 2,500 3, No. of workers Quantity of output Example: MPL = slope of production function MPL Q (bushels of wheat) L (no. of workers)

10 Importance of the concept of (diminishing) marginal product Allows the producer to think along the margin and help make the decision to hire another worker or add another input Why does the marginal product of labor decline Additional worker in the agricultural example has less land to cultivate and is hence less productive In general, the more intense use of labor with any fixed input such as capital, land etc mans diminishing MPL So diminishing MP is that the MP of an input declines as the quantity of the input increases (other things equal)

Example 1: Costs $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 Total Cost $10,000 $8,000 $6,000 $4,000 $2,000 $0 $1, Cost of labor Cost of land Q (bushels of wheat) L (no. of workers)

Example 1: Total cost curve Q (bushels of wheat) Total Cost 0$1, $3, $5, $7, $9, $11,000

13 Marginal costs Marginal cost (MC) is the increase in total costs from producing one more unit MC = ∆TC/ ∆Q If marginal cost in less than the incremental revenue obtained, the additional use of the input is not profitable or makes sense.

Example 1: Total and marginal cost $10.00 $5.00 $3.33 $2.50 $2.00 Marginal Cost (MC) $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 Total Cost Q (bushels of wheat) ∆Q = 1000 ∆TC = $2000 ∆Q = 800 ∆TC = $2000 ∆Q = 600 ∆TC = $2000 ∆Q = 400 ∆TC = $2000 ∆Q = 200 ∆TC = $2000

MC usually rises as Q rises, as in this example. Example 1: The marginal cost curve $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 TC $10.00 $5.00 $3.33 $2.50 $2.00 MC Q (bushels of wheat)

16 Fixed and variable costs Fixed costs (FC) do not vary with the quantity of output produced Examples: land, capital, loan payment, rent Variable costs (VC) vary with the quantity produced Examples: cost of labor and materials Total cost (TC). TC = FC + VC Marginal cost (MC) is the increase in total costs from producing one more unit MC = ∆TC/ ∆Q If marginal cost in less than the incremental revenue obtained, the additional use of the input is not profitable or makes sense.

Example 2: Costs $ $0 100 $1000 TCVCFCQ $0 $100 $200 $300 $400 $500 $600 $700 $ Q Costs FC VC TC

Recall, Marginal Cost (MC) is the change in total cost from producing one more unit: 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.) Example 2: Marginal costs $1000 MCTCQ $70 ∆TC ∆Q∆Q MC =

Example 2: Average fixed cost $100 n/a$1000 AFCFCQ Average fixed cost (AFC) is fixed cost divided by the quantity of output: AFC = FC/Q Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units.

Example 2: Average variable cost $70 n/a$00 AVCVCQ Average variable cost (AVC) is variable cost divided by the quantity of output: AVC = VC/Q As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises.

Example 2: Average total cost (cost per unit, or unit cost) $170 n/a ATC $ $70$100 n/a AVCAFCTCQ Average total cost (ATC) equals total cost divided by the quantity of output: ATC = TC/Q Also, ATC = AFC + AVC

Usually, as in this example, the ATC curve is U-shaped. $0 $25 $50 $75 $100 $125 $150 $175 $ Q Costs Example 2: Average total cost $170 n/a ATC $1000 TCQ

Example 2: The cost curves, ATC, AFC, AVC and MC AFC AVC ATC MC $0 $25 $50 $75 $100 $125 $150 $175 $ Q Costs

$0 $25 $50 $75 $100 $125 $150 $175 $ Q Costs Example 2: Why ATC Is usually u-shaped As Q rises: Initially, falling AFC pulls ATC down. Eventually, rising AVC pulls ATC up. Efficient scale: The quantity that minimizes ATC.

EXAMPLE 2: ATC and MC and profit maximization ATC MC $0 $25 $50 $75 $100 $125 $150 $175 $ Q Costs 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.

26 Costs in the short- and long-run Short-run Some inputs are fixed (land, capital) Long-run: All inputs are variable, as more land can be bought, etc Fixed costs (FC) do not vary with the quaintly of output produced The long-run ATC is a succession of short-run ATC curves.

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

ATC Changes as 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. LRATC Q ATC

29 ATC and production scale Economies of scale occur when increasing production allows greater specialization. Workers can be more productive focused on a narrow task. More common when quantity supplied is low. Diseconomies of scale develop due to coordination problems in large organizations (stretched management) More common when output supplied is high

30 Summary and conclusion Costs are both explicit (in cash) or implicit (no cash outlay but an opportunity cost). Both are important to the firm’s decision making Accounting profit is revenue less cash outlays; economic profit is revenue less all (explicit and implicit) costs Production function shows relationship between inputs and output. Marginal production is the increase in output coming from one additional input. Labor is the most common example. Marginal product usually diminishes with insensitivity of use. As output rise the production function becomes flatter (the delta declines) and the total cost curve becomes steeper (delta increases) Variable costs vary with output; fixed costs do not Marginal costs is the increase in total cost from an extra (incremental) unit of production,. The MC curve is usually upward sloping.

31 Summary and conclusion Average variable cost is variable costs divided by output Average fixed cost is fixed cost divided by output. AFC always falls as output rises. Average total cost (cost per unit or unit cost) is total costs divided by the quantity of output. ATC curve is usually U-shaped. The MC curve intersects the ATC curve at the minimum average total cost MC < ATC, ATC fall as Q rises MC > ATC, ATC rises as Q In the long-run, all costs are variable Economies of scale: ATC falls as Q rises Diseconomies of scale: ATC rises as Q rises Constant returns to scale: ATC remains the same as Q rises