Eco 201 Spring 2009 Lecture 4.2b

1. Eco 201Spring 2009Lecture 4.2b Cost Functions Long-run Cost Curve

2. The marginal cost curve (MC) • A marginal cost represents the relation between marginal cost incurred by a firm in the short-run production of a good and the quantity of output produced. • holding other variables, like technology and resource prices, constant.

3. The marginal cost curve (MC) • Marginal Cost = Difference in total costs in going from producing Q -> Q+1 units

4. The marginal cost curve (MC) • The marginal cost curve is U-shaped. Marginal cost is relatively high at small quantities of output, then as production increases, declines, reaches a minimum value, then rises. • Shape of the marginal cost curve is due: 1) first, increasing; 2) then decreasing marginal returns (and the law of diminishing marginal returns - Diminishing returns).

5. Diminishing Marginal Returns • In economics, diminishing returns is also called diminishing marginal returns or the law of diminishing returns. • In a production system with fixed and variable inputs (say factory size and labor), beyond some point, each additional unit of variable input yields less and less additional output

6. A Little HistoryMalthus • The concept of diminishing returns can be traced back to the concerns of early economists such as Johann Heinrich von Thünen, Turgot, Thomas Malthus and David Ricardo. • Malthus and Ricardo, who lived in 19th centuryEngland, were worried that land, a factor of production in limited supply, would lead to diminishing returns. In order to increase output from agriculture, farmers would have to farm less fertile land or farm existing land with more intensive production methods. In both cases, the returns from agriculture would diminish over time, causing Malthus and Ricardo to predict population would outstrip the capacity of land to produce, causing a Malthusian catastrophe. (Case & Fair, 1999: 790).

7. In Terms of Cost • Producing one more unit of output costs more and more in variable inputs. • Law of increasing relative cost, or law of increasing opportunity cost. • Diminishing marginal returns also implies a technological relationship. • Decreased “specialization” or productivity of an input, e.g., labor • Less well-suited for production of this good

8. An Example • Suppose that one kilogram (kg) of seed applied to a plot of land of a fixed size produces one ton of crop. • You might expect that an additional kilogram of seed would produce an additional ton of output. • If there are diminishing marginal returns, that additional kilogram will produce less than one additional ton of crop (on the same land, during the same growing season, and with nothing else but the amount of seeds planted changing). • “crowding out” from sunlight, competition for water and nutrients – increased “seed density” decreases production • For example, the second kilogram of seed may only produce a half ton of extra output. • Diminishing marginal returns also implies that a third kilogram of seed will produce an additional crop that is even less than a half ton of additional output. Assume that it is one quarter of a ton.

9. Combining cost curves:MC and TC (ATC) • Combine marginal, total cost curves to provide information about firms. • Assume that the firm is in a perfectly competitive market. • Marginal revenue equals market equilibrium price • Marginal cost curve will cut the average cost curve at its lowest point. • In a perfectly competitive market a firm's profit maximizing price would be above the price at which the average cost curve cuts the marginal cost curve. • If the marginal revenue is above the average total cost price the firm is deriving an economic profit.

10. Combining cost curves

11. A good link for cost curves • http://www.whitenova.com/thinkEconomics/lrac.html

12. The long-run average cost curve (LRAC) • LRAC is U-shaped • Since all factors are variable, U-shape reflects (dis)economies of scale or scope

13. Long-run/short-run Cost Curves • Long-run average cost curve is the envelope of an infinite number of short-run average total cost curves, • Each short-run average total cost curve tangent to, or just touching, the long-run average cost curve at a single point corresponding to a single output quantity. • The key to the derivation of the long-run average cost curve is that each short-run average total cost curve is constructed based on a given amount of the fixed input, usually capital. • when the quantity of the fixed input changes, the short-run average total cost curve shifts to a new location.

14. Relationship between SRAC and LRAC curves • In the SR one factor (K) is fixed • Chose K to minimize costs for a given level of output • http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=long-run+average+cost+curve,+derivation

15. Envelope Theorem • Long-run cost curve when K is completely variable

16. Long-run <-> Short-run Cost Curves • Long-run average cost curve is the factory size (or quantity of capital) that can produce each quantity of output at the lowest short-run average total cost. • Five short-run average total cost curves • corresponds to five alternative factory sizes that could be used to produce Stuffed Amigos--10,000 square feet, 20,000 square feet, 30,000 square feet, 40,000 square feet, and 50,000 square feet. These five factors reach minimum short-run average total cost at production levels of 100, 200, 300, 400, and 500 Stuffed Amigos, respectively.

17. The long-run average cost curve (LRAC) • The LRAC curve is U-shaped • As a firm in the long-run increases the quantities of all factors employed, other things being equal: • the output may increase initially at a more rapid rate (economies of scale) than the rate of increase in inputs, • then output may increase in the same proportion of the input (constant returns to scale), • and ultimately, output increases less proportionately (diseconomies). • economies of scale when negatively-sloped • diseconomies of scale when positively sloped. • Constant returns to scale when no slope

18. Review