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1、1,Chapter 9,PROFIT MAXIMIZATION,Copyright 2005 by South-Western, a division of Thomson Learning. All rights reserved.,2,The Nature of Firms,A firm is an association of individuals who have organized themselves for the purpose of turning inputs into outputs Different individuals will provide differen
2、t types of inputs the nature of the contractual relationship between the providers of inputs to a firm may be quite complicated,3,Contractual Relationships,Some contracts between providers of inputs may be explicit may specify hours, work details, or compensation Other arrangements will be more impl
3、icit in nature decision-making authority or sharing of tasks,4,Modeling Firms Behavior,Most economists treat the firm as a single decision-making unit the decisions are made by a single dictatorial manager who rationally pursues some goal usually profit-maximization,5,Profit Maximization,A profit-ma
4、ximizing firm chooses both its inputs and its outputs with the sole goal of achieving maximum economic profits seeks to maximize the difference between total revenue and total economic costs,6,Profit Maximization,If firms are strictly profit maximizers, they will make decisions in a “marginal” way e
5、xamine the marginal profit obtainable from producing one more unit of hiring one additional laborer,7,Output Choice,Total revenue for a firm is given by R(q) = p(q)q In the production of q, certain economic costs are incurred C(q) Economic profits () are the difference between total revenue and tota
6、l costs (q) = R(q) C(q) = p(q)q C(q),8,Output Choice,The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the function with respect to q equal to zero,9,Output Choice,To maximize economic profits, the firm should choose the output for w
7、hich marginal revenue is equal to marginal cost,10,Second-Order Conditions,MR = MC is only a necessary condition for profit maximization For sufficiency, it is also required that,“marginal” profit must be decreasing at the optimal level of q,11,Profit Maximization,output,revenues & costs,R,C,12,Marg
8、inal Revenue,If a firm can sell all it wishes without having any effect on market price, marginal revenue will be equal to price If a firm faces a downward-sloping demand curve, more output can only be sold if the firm reduces the goods price,13,Marginal Revenue,If a firm faces a downward-sloping de
9、mand curve, marginal revenue will be a function of output If price falls as a firm increases output, marginal revenue will be less than price,14,Marginal Revenue,Suppose that the demand curve for a sub sandwich is q = 100 10p Solving for price, we get p = -q/10 + 10 This means that total revenue is
10、R = pq = -q2/10 + 10q Marginal revenue will be given by MR = dR/dq = -q/5 + 10,15,Profit Maximization,To determine the profit-maximizing output, we must know the firms costs If subs can be produced at a constant average and marginal cost of $4, then MR = MC -q/5 + 10 = 4 q = 30,16,Marginal Revenue a
11、nd Elasticity,The concept of marginal revenue is directly related to the elasticity of the demand curve facing the firm The price elasticity of demand is equal to the percentage change in quantity that results from a one percent change in price,17,Marginal Revenue and Elasticity,This means that,if t
12、he demand curve slopes downward, eq,p 0 and MR p if the demand is elastic, eq,p -1 and marginal revenue will be positive if the demand is infinitely elastic, eq,p = - and marginal revenue will equal price,18,Marginal Revenue and Elasticity,19,The Inverse Elasticity Rule,Because MR = MC when the firm
13、 maximizes profit, we can see that,The gap between price and marginal cost will fall as the demand curve facing the firm becomes more elastic,20,The Inverse Elasticity Rule,If eq,p -1, MC 0 This means that firms will choose to operate only at points on the demand curve where demand is elastic,21,Ave
14、rage Revenue Curve,If we assume that the firm must sell all its output at one price, we can think of the demand curve facing the firm as its average revenue curve shows the revenue per unit yielded by alternative output choices,22,Marginal Revenue Curve,The marginal revenue curve shows the extra rev
15、enue provided by the last unit sold In the case of a downward-sloping demand curve, the marginal revenue curve will lie below the demand curve,23,Marginal Revenue Curve,output,price,D (average revenue),MR,q1,p1,As output increases from 0 to q1, total revenue increases so MR 0,As output increases bey
16、ond q1, total revenue decreases so MR 0,24,Marginal Revenue Curve,When the demand curve shifts, its associated marginal revenue curve shifts as well a marginal revenue curve cannot be calculated without referring to a specific demand curve,25,The Constant Elasticity Case,We showed (in Chapter 5) that a demand function of the form q = apb has a constant price elasticity of demand equal to b Solving this equation for p, we get p = (1/a)1/bq1/b = kq1/b where k = (1/a)
