Firm Theory: production functions, cost curves and profit maximization

1. Firm Theory: production functions, cost curves and profit maximization

2. Remarks • Switching gears: “Theory of the Firm” • Embarking on an analysis of the firm. • Note: • There are lots of different types of firms. • There are lots of ways to organize entrepreneurial activity. • There are lots of firm objectives.

3. What We Assume • For our analysis we assume that: • we have an owner manager, • who has a business, • with the primary and only objective to maximize economic profit.

4. What’s a Business? • A business is an organization producing goods or services, also called a firm. • A business, or firm, is assumed to maximize its profits. • Examples of businesses: Microsoft, Kinko’s, the Campus Store (a business within Cornell University). • Examples of organizations that are not businesses in this sense: Cornell University as a whole, US Department of Defense. • Organizations that produce goods and services but are legally prohibited from using the profit motive are excluded from our formal model of a firm.

5. What’s a Market? • A collection of buyers and sellers organized for the purpose of exchanging goods and services for money. • Markets can be global, national, regional, or local depending upon the item being bought and sold.

6. Profit Maximization • profit = total revenue - total cost • total revenue: • determined by the level and nature of competition in your market • total cost: • costs are determined by factor market prices and the firm’s technology or production function

7. Economic Profits • Economic profits are the difference between total revenue and total costs. • Economic total costs include the opportunity costs of all inputs to the production process–in particular, the opportunity costs of the owner’s time and physical capital (equipment and space). • Whenever we talk about profit we mean economic profit.

8. Accounting Profits • Accounting profits are defined as total sales revenue (the same as total revenue in the economic profits definition) minus operating costs (costs of goods sold + administrative and sales costs for those who know some accounting). • Accounting Profits = Sales Revenue - Accounting Costs

9. Production & Cost Structures • There are lots of ways to describe production and costs. • You need to understand them all. • For example: • total, fixed and variable concepts • average and marginal concepts • long run and short run concepts • all related to each other

10. Jonathan’s New York State Apple Farm • The farm is a business organized to grow and sell apples. • The owner/proprietor, Jonathan, tries to maximize his profits from the business.

11. The U.S. Apple Market • Americans consume 19 lbs. of apples per person annually, for a total consumption of 5 billion lbs. • More than 6 billion lbs. of apples are grown in the US each year (mostly in Washington, New York and Michigan). • Only about 234 million lbs. are imported, while more than 1.3 billion lbs. are exported. • There are about 1,700 apple farms in the State of New York, with an average of 96 acres of orchards per farm and about $92,000/year in revenue from apple sales. • 80% of the New York apple farms are individual or family owned. • Markets like the US apple market are classic examples of competitive product markets.

12. Production Functions • The production function shows the input requirements for each level of production. • For some businesses the production function is relatively simple--a few processes with little substitution. • For some businesses the production function involves thousands of different processes and millions of substitution possibilities. • The production function is the economists summary of the input requirements for each level of production.

13. Jonathan’s Apple Farm Production Function • The table describes Jonathan’s inputs for the annual production of apples shown in the first column.

14. Fixed Factors • A fixed factor is one that does not vary as the quantity produced increases or decreases. • Some factors are fixed in the short run (managerial time). • Some factors are fixed in the medium run (cultivated acreage). • No factors are fixed in the long run.

15. Jonathan’s Fixed Factors • Jonathan has two fixed factors • His cultivated acreage (100 acres) • His own managerial time (1,100 hours)

16. Variable Factors • A variable factor is one that must be increased in order to increase output. • The classic variable factor is labor. • Variable factors usually exhibit diminishing marginal productivity--the amount of extra product generated by each additional unit of the input, holding other inputs constant, declines.

17. Jonathan’s Variable Factors • Jonathan must vary his labor input to increase his production of apples. • At first this variation is modest going from 50 tons/year to 100 tons/year requires an additional 1,200 hours • Going from 200 to 250 tons/year requires an additional 3,200 hours. • Jonathan cannot increase the size of his farm, his acreage is fixed.

18. Jonathan’s Marginal Product of Labor • The graph shows how the marginal product of labor rises, then falls for Jonathan’s apple farm. Marginal product is in red. • The marginal product is the extra amount of apple production (pounds/hour worked) that can be produced by an extra hour of work. • Average product (in blue) is the ratio of output to labor used. Average product of labor is usually called “labor productivity” in the business press.

19. The Average/Marginal Relation • For product curves or any other average/marginal pair of curves: • If marginal product is above average product, then average product is rising. • If marginal product is below average product, then average product is falling. • Therefore, marginal product equals average product when average product is at a critical value, in this case a maximum.

20. From Production Curves to Cost Curves • By combining the production function and the factor prices, we produce the business’s cost curves. • The total cost curve is the amount spent on all fixed and variable costs to produce the indicated output. • The average cost curve is the ratio of total costs to units produced.

21. Marginal Cost • The most important cost concept is marginal cost. • Marginal cost measures the amount by which costs increase as output increases by one unit.

22. 7 Short Run Cost Curves • Total values • fc = fixed costs = PK K where K is fixed • vc = variable costs = PLL*(x) • srtc = short run total costs = fc+vc • Average values • afc = average fixed cost = fc/x • avc = average variable cost = vc/x • sratc=short run average total cost=srtc/x=afc+avc • Marginal value • srmc=short run marginal cost = srtc/x = vc/x

23. Short Run Cost Curves • Short run cost curves get their shape from the marginal productivity of the variable factor (except the fixed costs, of course). • If capital is held constant (short run) then the marginal product of labor gives the short run cost curves their shape. • The levels of cost curves are determined by factor market prices along with technology.

24. Jonathan’s Input Prices • Each of the entries in this table represents a price that Jonathan must pay for an input. • Notice that he “pays” for his managerial time because his next best alternative is to earn $12/hour. • He must pay rent for his land. • Jonathan is a “wage taker” as well as “price-taker.”

25. Jonathan’s Cost Curves • When Jonathan faces the technology and input prices shown previously, the table shows his cost structure.

26. Graph of Jonathan’s Cost Curves • The marginal cost of each ton of apples is shown as the red line. • The average total cost curve is shown as the blue line. • Notice that the marginal cost = average cost at minimum average cost.

27. Long Run Cost Curves • Describing the long run cost curves requires a description of all of the technological possibilities for operating in the industry. • Now both labor and capital are considered variable. • There are three long run cost curves for the firm: • long run total cost = lrtc = PLL*(x) + PKK*(x) • long run average total cost = lratc = lrtc/x • long run marginal cost = lrmc = lrtc/x • The most important one for us is the lratc curve. • Choosing L*(x) and K*(x) will depend on the prices of capital and labor relative to the marginal products of capital and labor and what x you expect to produce. The “bang/buck” condition would have to be met. That is, at L* and K*, the (mpL/PL )= (mpK/PK)

28. Example: 3 Potential Technologies • Suppose there are three different ways for a company, System-fixer, to do business. • Firm sizes A, B and C illustrate the possibilities. • Firm A is small, using only $80 in fixed costs. • Firm B uses twice the capital. • Firm C uses three times the capital.

29. Question • What is the best technology for our system-fixer firm?

30. Answer • It depends on how much System-fixer expects to produce and sell in the market.

31. The Firm’s Long Run Average Total Cost Curve • The firm’s long run average total cost curve consists of the minimum of the three curves illustrated on the right. • System-fixer’s long run average total cost curve is size A’s (blue) until 6 units, size B’s (red) from 6 to 10 units and size C’s (brown) from 11 units onward. • The shape of the firm’s lratc curve will be determined by how the technology behaves. • The lratc is the outer envelope of the possible sratc curves.

32. The Firm’s Long Run Average Total Cost Curve and MES • MES = minimum efficient scale • MES = the level of output at the minimum of the firm’s lratc curve. • When there are “economies of scale,” the lratc is declining. • When there are “diseconomies of scale,” the lratc is increasing. • At MES all the economies of scale are exhausted. • In real world empirical analysis, economists often observe a more “L-shaped” lratc curve.

33. Profit Maximization • Profit () = total revenue(tr) - total cost(tc). • Profit depends on the firm’s output level (x). • So…  (x) = tr(x) - tc(x) • Define • marginal revenue (mr) = tr/x • marginal cost (mc) = tc/x

34. Profit Maximization • General rules for profit maximization: • If x* maximizes , then • mr = mc at x* • x* is a profit max and not a profit min • at x* it’s worth operating • If using a short-run perspective use short run cost curves. • If using a long-run perspective uselong run cost curves.

35. Running at a Profit • When the market price exceeds the firm’s average total cost at x*, the firm is running at a profit. • Great.

36. Running at a Loss • When the market price is less than the firm’s average total cost at x*, the business is running at a loss. • What should the firm do in the short run? • produce x* if the firm takes in enough in revenue to cover its variable costs. • shut down and play dead if its revenues at x* don’t even cover variable costs.

37. Running at a Loss • What should the firm do in the long run? • It should plan to go out of business if it does not expect either the market price to rise or its costs to fall or both.

38. Sunk Costs and Avoidable Fixed Costs • In the real world the shut down rule is slightly different. • When the firm actually operates, x>0, it makes sense to only talk about fixed and variable costs. • However, when the firm considers shutting down in the short run (when profits are negative at the profit maximizing output level) then they have to take another look at their fixed costs. • Fixed costs=sunk costs + avoidable fixed costs • Now change the shutdown rule to be: • produce x* if the firm takes in enough in revenue to cover its variable costs + avoidable fixed costs, otherwise shut down.