Week 5A

# Week 5A - COMM/FRE 295 October 4 2010 Competitive Firms...

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COMM/FRE 295 October 4, 2010 Competitive Firms, Markets and Consumer Surplus Sections 8.1 – 8.4

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Topics Examined • Rule for maximizing profits: P = MC result • Derivation of a supply schedule for a competitive firm, including shut-down point – Mathematical analysis – Graphical analysis • Graphical illustration of short run profits for a competitive firm • Long run equilibrium for a competitive industry • Measuring consumer surplus
Where do Supply Curves come from? • Recall the sequence of this course so far – Derivation of consumer demand curves – Market supply and demand; equilibrium – Production theory and cost theory • The market supply curve used previously is the aggregation of the supply curves of many individual competitive producers • We want to formally derive the supply curve for an individual producer

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Method 1: Production Function • Short run production function is Q = f(L) • P = price of output and W = price of labour (both are fixed; they do not change with Q) • Profits are π = Pf(L) – WL • Choose the value of L that maximizes profits: dπ/dL = P[df(L)/dL] – W = 0 solve to obtain L * (P,W) • Substitute L * (P,W) into the production function to obtain the supply schedule Q = f(L * (P,W)) • Firm’s supply schedule depends only on prices
Method 2: MC = P • The cost function, C(q; w, r), tells us the least cost way to produce q units of output given wage rate w and cost of capital r • How much should the firm produce to maximize profits (i.e., optimal q)? • Rather than choosing L as in the previous problem, the firm will choose output, q • To implement this approach, we need a revenue function

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Method 2: MC = P; Cont’n • Revenue function equal to R(q) = P(q)q where P(q) is the firm’s demand schedule • Profit function is π(q) = R(q) – C(q) • Maximum profits requires a zero slope for the profit function: dπ/dq = dR(q)/dq – dC(q)/dq = 0 • Notice that dR(q)/dq – dC(q)/dq = 0 is equivalent to MR = MC • The general rule for profit maximization (assuming shut down is not optimal) is to produce where marginal revenue (MR) is equal to marginal cost (MC)
Method 2: MC = P; Cont’n • A competitive firm is a price taker, which means that P(q) does not vary with q so R(q) = Pq (here P represents a fixed price) • In this case, MR = dR(q)/dq = P • So the MR = MC rule for maximizing profits simplifies to P = MC for a competitive firm

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Week 5A - COMM/FRE 295 October 4 2010 Competitive Firms...

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