CH8_Perfect_Competition

CH8_Perfect_Competition - Intermediate Microeconomics...

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Unformatted text preview: Intermediate Microeconomics Perfect Competition Instructor: Bin Xie Spring 2015 Perfect Competition Perfect competition is a market structure in which: there are a large number of rms rms sell identical products buyers and sellers have full information about prices charged by all rms transaction costs, the expenses of nding a trading partner and completing the trade above and beyond the price, are low rms can freely enter and exit the market Each rm is a price taker and its individual demand curve is a horizontal line at the prevailing market equilibrium price. Perfect competition is rarely a real-world situation. Examples of markets in real economy: Automobile market: Honda; BMW Pharmaceutical market: Roche; Pzer Agricultural commodities markets: wheat; soybeans Assumptions of Perfect Competition 1. Large number of rms No single rm's actions can raise or lower the price. (no rm has market power.) 2. Identical (homogeneous) products If all rms are selling identical products, it is dicult for any rm to raise the price above the current market price. 3. Full information Consumer knowledge of all rms' prices makes and can easily buy elsewhere if any one rm raised its price. 4. Negligible transaction costs It is easy to switch buyers/sellers. 5. Free entry and exit Leads to large number of rms and promotes price taking. All above assumptions reinforce the fact that competitive rms (individually) are price takers and have no inuence on the price. The price is treated as given. Firm's Demand in Competitive Market Are perfectly competitive rms' demand curves really at? A rm's residual demand curve, D r (p), is the portion of the market demand that is not met by other sellers at any given price. D r (p) = D(p) − S o (p) D(p) = market demand S o (p) = amount supplied by other rms The demand elasticity of an individual rm i could be presented as: εi = nε − (n − 1)ηo . Even if not perfectly horizontal, the residual demand curve of an individual rm is much atter than market demand. For simplicity, we assume the residual demand curve (which is the demand curve faced by a single rm) is at in our analysis. Example Suppose there are 100 identical rms in total in the market. If the market demand curve is Q = −2p + 50, the supply curve of any individual rm is S o = 2p − 10. What is the residual demand curve Prot Maximization Maximizing prot involves two important questions: 1. 2. Output decision: If the rm produces, what output level q∗ maximizes its prot (or minimizes its loss)? Shutdown decision: Is it more protable to produce q∗ or to shut down and produce no output? Prot Maximization: Output Rules A rm can use one of three equivalent output rules to choose how much output to produce: 1. A rm sets its output where its prot is maximized. 2. A rm sets its output where its marginal prot is zero. 3. A rm sets its output where its marginal revenue equals its marginal cost. Mathematically, if we take the derivative of π(q) = R(q)C (q) with respect to output and set it equal to zero (output rule #2), we nd: dR(q ∗ ) dC (q ∗ ) dπ(q ∗ ) = − = MR(q ∗ ) − MC (q ∗ ) = 0 dq dq dq MR(q ∗ ) = MC (q ∗ ) Prot Maximization: Shutdown Rule A rm shuts down only if it can reduce its loss by doing so. Shutting down means that the rm stops producing (and thus stops receiving revenue) and stops paying avoidable costs. (q = 0) Only xed costs are unavoidable because they are sunk costs in short run. Firms compare revenue (R ) to variable cost (VC ) when deciding whether to stop operating. Shutting down may be temporary. The rm shuts down only if its revenue is less than its avoidable cost. Example If the rm decides to produce in short run, the revenue will be R = 2000. The variable cost is VC = 1000 and the xed cost is F = 3000. What is the prot π of the rm? Would the rm shut down in short run? Would the rm shut down in long run? Perfect Competition in the Short Run Given this general description of rms' prot maximization decisions, how do perfectly competitive rms maximize prots in the SR? Because it faces a horizontal demand curve, a competitive rm can sell as many units of output as it wants at the market price, p . Revenue is R(q) = pq , thus, q ∗ satises: dpq ∗ dC (q ∗ ) dπ(q ∗ ) = − = p − MC (q ∗ ) = 0 dq dq dq Marginal cost equals the market price MC = p is equivalent to MC = MR because MR = p in perfect competition. Example Suppose a rm has the following cost function C = 100 + 2q 2 . If price equals $20, what is the rm's output decision? What are its short-run prots? Perfect Competition in Short Run (Cont.) Prot is maximized at q where Revenue − Cost is greatest. Prot is the q ∗ (p − AC (q ∗ )). Recall that rms compare revenues to variable costs to determine shutdown: VC (q) pq < VC (q), p < = AVC q Shut down if market price is less than the minimum of its SR average variable cost curve. Thus, our graphical analysis of rm prot maximization decisions requires an AVC curve to address the shut down decision. If AC (q ∗ ) > p > AVC (q ∗ ), then rm operates, but at a loss(smaller than not operating at all). Excercise: Short Run Competitive Market Examples A rm faces a short-run cost function is given by C (q) = q 2 + 25q + 144 a. If the market price is $75/unit, how many units will the rm choose to produce? b. At what price will the rm earn zero prots? c. If the price is below the level you found in b., will the rm shut down? If so, explain. If not, below what price will it shut down? Short-Run Firm Supply Curve Firms will choose to produce as long as market price is above the AVC minimum, so that is where a rm's supply curve begins. As we consider higher and higher market prices, the horizontal rm demand curve rises and intersects MC at higher and higher quantities. In this fashion, the relationship between market price and prot-maximizing quantity is traced out. This is the perfectly competitive rm's supply curve. Short-Run Firm Supply Curve (Cont.) Supply curve S is the section of MC above minimum AVC . Marginal cost function is the inverse supply function (above AVC): p = MR = MC = f (q), so Si = q = f −1 (p). If the prices of inputs (factor prices) increase, a rm's production costs rise and its supply shifts left. The market supply curve is the horizontal sum of the rm supply curves. (For identical rms or dierent rms) Example Suppose that there are 80 rms in a market, each with the following cost function: C (q) = 100 + 4q 2 a. Derive the short-run individual rm supply curve. b. Derive the short-run market supply curve. c. Suppose the market demand is QD = 1280 − 30p . Find the equilibrium market quantity and price. d. How much output will each rm produce? How much prot is each rm making? Perfect Competition in the Long Run Long-Run Output Decision The rm chooses the quantity that maximizes prot using the same rule as in the SR: MC = MR . Long-Run Shutdown Decision Because all costs are variable in the LR, the rm shuts down if it would suer an economic loss by continuing to operate. Graphically, relevant shutdown point is the minimum of the LR average cost curve. Long-Run Firm Supply Curve Firm usually earns higher prots in the LR than in the SR. Reason? The dierence between SRAC and LRAC . Recall the shapes of SRAC and LRAC , LRAC is at least not higher than SRAC at any level of output. For any output produced, π = q(p − AC ), since LRAC SRAC , πLR πSR . Long-Run Market Supply Curve As in the SR, the LR competitive market supply curve is the horizontal sum of individual rm supply curves. In the LR, rms can enter or exit the market swiftly, so the number of rms is not xed as it is in the SR. A rm enters the market if it can make a long-run prot; A rm exits the market to avoid a long-run loss. What will happen is rms ood in when there is prot and ee where there is a loss. (hit and run) Extreme sensitivity to price uctuation: elasticity of supply = innite. With identical rms, free entry into the market, and constant input prices the LR market supply curve is at at the minimum LRAC . Long-Run Market Supply Curve (Cont.) Identical rms, free entry into the market, and constant input prices. The LR market supply is at because unlimited numbers of rms could enter the market to produce. Long-Run Market Supply Curve (Cont.) Three scenarios in which LR market supply is not at: 1. LR market supply when entry is limited Upward-sloping if government restricts number of rms, rms need a scarce resource, or if entry is costly 2. LR market supply when rms dier Upward-sloping if rms with relatively low minimum LRAC are willing to enter market at lower prices than others Only valid when the amount that lower-cost rms can produce is limited. Otherwise higher-cost rms will not produce 3. LR market supply when input prices vary with output In an increasing-cost market input prices rise with output and LR market supply is upward-sloping In a decreasing-cost market input prices fall with output and LR market supply is downward-sloping Long-Run Competitive Equilibrium Equilibrium occurs at the intersection of LR market demand and LR market supply, which is dierent from SR market supply. Example All rms in a competitive industry have the following long-run total cost curve: C (q) = q 3 10q 2 + 36q where q is the output of the rm. a. Compute the long run equilibrium price. What does the long-run supply curve look like if this is a constant cost industry? Explain. b. Suppose the market demand is given by Q = 111p . Determine the long-run equilibrium number of rms in the industry. ...
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