Lecture 15 ( 15) Feb. 19, 2004

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1 Lecture 5 ( 5) Feb. 9, 004. The Relationship beteen Marginal Product and Marginal Cost curves. In the short run, e assume at least one factor of production is fixed in order to produce output. In a very simple case, if e assume the production function is as follos: () Q = f ( L, K), here Q is output per period, L is amount of labor (in hours or in number of orkers) per period, and K is amount of service provided by capital per period. In the short run, e assume K is fixed such as, () Q = f ( L, K ). Then, the marginal cost of output in an individual firm is defined as, () dtc =, dq here is marginal product of labor. That is, the marginal product of labor is defined as additional units of output due to one additional unit of labor. In equation (), the age rate (payments per man-hour or per labor) is predetermined. Therefore, as labor is added to the production of output holding the amount of capital fixed, the additional output due to an additional unit of labor, i.e., marginal product of labor, ill first increase but eventually decrease. Therefore, the shape of marginal cost is determined the shape of MPL. Since the marginal product eventually decreases as L increases, e can dra the marginal product curve as,

2 Figure marginal product curve, MPL 0 L0 LMax L In Figure, the marginal product curve first increases but decline later. This is because e consider there is the la of diminishing returns (or the la of diminishing marginal productivity). Note, also in Figure, the marginal product is zero at. That is the total product is at the maximum. Therefore, any additional labor ill decrease the total amount of output after L. Thus, the marginal product after L is negative. Max Then, if e accept the la of diminishing returns in the production, the marginal cost should fall and rise as output increases since the marginal cost is the ratio of. MPL maximum MPL L Max Max to e take only the relevant part of MP curve. Figure 0 L L * marginal cost curve minimum 0 Q * Q

3 In Figure, you may see the folloing relation beteen marginal product and marginal cost curves: dq (4) and K dl dtc d( + FC) d dl = = = = dq dq dq dq Therefore, e ill have: (5) =. From Equation (5), e can see the relationship beteen marginal cost and marginal product curves. * As MP rises, decreases. When MP is maximum, is minimum. As L decreases, rises. L Note that e move on the marginal cost curve hen e increase labor, holding all others constant. That is, all others mean such as, r (price of capital per unit), K, technology and so on. Therefore, hen one of these factors changes, the marginal cost curve shifts up or don. This is very important to remember. Figure = = > Firm

4 . Supply curve of product in an individual firm No, e ant to learn ho the supply curve of product in a typical firm can be derived. Figure 4 AC, AFC AC The slope of AC is 0. The slope of is 0. 0 Q the shutdon point The above figure is once shon in my previous note. No, let us consider the firm in a competitive product market accepts the price of its product is determined in the market rather than it determines. This can be sho in the folloing figure: Figure 5 P S i D 0 Q Industry (or Product Market) Firm i in the industry 4

5 In Figure 5, e have to diagrams: one is of the industry and another is the firm s marginal cost curve. The price of product per unit is determined in the industry or product market, e.g.,, hich is the equilibrium price as D=S. Firm i can not P 0 change this price since there are a large number of firms hich are producing identical products as firm i. Therefore, firm i simply accept the price as given. With the price, firm i tries to maximize its profits: Firm i s profit function: (6) π = TR TC = P Q TC. The maximization of profits ill be given as, dπ dtr dtc d( Q) (7) = = = = 0 dq dq dq dq Equation (7) tells us that as long as TR is greater than TC, there ill be positive profits. Then, the output at hich the profits is maximized is q * hen P = 0. Figure 6 P S i P D 0 D 0 Q q * q Industry (or Product Market) Firm i in the industry 5

6 No, suppose that the market demand D decreases. Then, the equilibrium price ill be loer than and the ne lo price is P. Then, firm i ill adjust its output according to the ne price the ne output level for firm is at q. P such as P = i to maximize its profits. Then, Then, the question is: Does the firm produce its output hen P =? The Anser is No! * Firm ill produce output as long as the total revenues exceeds or are equal to the variable costs, hen P =. * Firm ill not produce output hen TR <. Why? Note that if a firm is already in the industry, some costs incurred to the firm even though it produces nothing. The cost is fixed costs. Therefore, fixed costs are the maximum loss the firm can make hen it is already in the industry or market. Therefore, if the firm produces output and make some additional loss to the fixed costs, then it does not make any sense since the firm increases its loss greater than fixed costs. Figure 7 AC, AFC AC P Shutdon point q 0 6

7 In Figure 7, suppose the market price of product P is just at the level of shutdon point. Since the square area belo the average variable cost curve is the variable costs, the total revenues are equal to the total variable costs. = q q = =. =. Therefore, q q q No, the total revenues are the price of product times output: TR = P q TR = P q. Then, at q and P, the total revenues equal the total variable costs: TR = TV. Therefore, hen the price of product is loer than the shutdon point, the total revenues are smaller than total variable costs. Then, the firm ill go out of business and leave the industry. No, let us see here the total costs are in the folloing figure. The total costs are the square area belo the average cost curve at. q Figure 8 AC, AFC AC TC FC P Shutdon point q 0 7

8 Next, hen the price level becomes at, hat is the relationship beteen total revenues and total costs? Figure 9 AC, AFC AC TC FC P AFC q In Figure 9, hen the price of product is at, the total revenues equal the total costs: TR = TC. Hence, there is no loss. By the ay, hen the price of product P is in beteen the shutdon point and s, the total revenues ill be larger than the total variable costs: costs. break-even point. No, it is easy to see the profits are positive, that is P TR >, covering some portion of total fixed TR > TC, hen P > the In sum, if firm i is already in the market, it ill start producing output hen P is at least as high as the shutdon point. If firm is not in the market but considering to join the industry, then the price must be at least as high as. Hence, the supply curve of product in a typical firm is the marginal cost curve but at and above the shutdon point if the firm is already in the firm. If the firm is not in the industry, the supply curve is the marginal cost curve at and above. 8

9 S, S, S A S B B A the shutdon point FirmA FirmB Firm A is already in the industry (or market) so that the supply curve of product is the marginal cost curve at and above the shutdon point and the dark vertical part from the origin to point A. Firm B is not in the industry but considering to join the industry so that the supply curve by firm B is the marginal cost curve at and above and the dark vertical part from the origin to point B. Industry Supply Curve A horizontal summation of supply curves of all potential firms in the industry. 9