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Week 9: Perfectly Competitive Markets
PERFECTLY COMPETITIVE MARKETS
What is it, exactly, that makes a market perfectly competitive? And what, if anything, is special about a perfectly competitive firm?
Perfectly competitive markets have four characteristics:
The industry is fragmented. It consists of many buyers and sellers. Each buyer’s purchases are so small that they have an
imperceptible effect on market price. Each seller’s output is so small in comparison to market demand that it has an imperceptible
impact on the market price. In addition, each seller’s input purchases are so small that they have an imperceptible impact on input
prices.
Firms produce undifferentiated products. That is, consumers perceive the products to be identical no matter who produces them.
Consumers have perfect information about prices all sellers in the market charge.
The industry is characterized by equal access to resources. All firms—those currently in the industry, as well as prospective entrants—
have access to the same technology and inputs. Firms can hire inputs, such as labor, capital, and materials, as they need them, and they
can release them from their employment when they do not need them.
These characteristics have three implications for how perfectly competitive markets work:
The first characteristic—the market is fragmented—implies that sellers and buyers act as price takers. That is, a firm takes the market
price of the product as given when making an output decision, and a buyer takes the market price as given when making purchase
decisions. This characteristic also implies that a firm takes input prices as fixed when making decisions about input quantities.
The second and third characteristics—firms produce undifferentiated products and consumers have perfect information about prices—
implies a law of one price: Transactions between buyers and sellers occur at a single market price. Because the products of all firms are
perceived to be identical and the prices of all sellers are known, a consumer will purchase at the lowest price available in the market.
No sales can be made at any higher price.
The fourth characteristic—equal access to resources—implies that the industry is characterized by free entry. That is, if it is profitable
for new firms to enter the industry, they will eventually do so.
ECONOMIC PROFIT VERSUS ACCOUNTING PROFIT
A distinction between economic profit and accounting profit: economic profit is the difference between a firm’s sales revenue and the
totality of its economic costs, including all relevant opportunity costs.
economic profit = sales revenue - economic costs
accounting profit = sales revenue - accounting costs
THE PROFIT-MAXIMIZING OUTPUT CHOICE FOR A PRICE-TAKING FIRM
Assuming that the firm produces and sells a quantity of output Q, its economic profit (denoted by π) is π = TR(Q) - TC(Q), where
TR(Q) is the total revenue derived from selling the quantity Q and TC(Q) is the total economic cost of producing the quantity Q. Total
revenue equals the market price P multiplied by the quantity of output Q produced by the firm: TR(Q) = P x Q. Total cost TC(Q) is the
total cost of producing Q units of output.
Because the firm is a price taker, it perceives that its volume decision has a negligible impact on market price. Thus, it takes the market
price P as given. Its goal is to choose a quantity of output Q to maximize its total profit.
For any firm (price taker or not), the rate at which total revenue changes with respect to a change in output is called marginal revenue
(MR). It is defined by ΔTR/ΔQ. For a price-taking firm, each additional unit sold increases total revenue by an amount equal to the
market price—that is, ΔTR/ΔQ = P. Thus, for a price-taking firm, marginal revenue is equal to the market price, or MR = P.
Marginal cost (MC), the rate at which cost changes with respect to a change in output, can be defined similarly to marginal revenue:
MC = ΔTC/ΔQ. Figure 1 shows that for quantities between Q = 60 and the profit-maximizing quantity Q = 300, producing more roses
increases profit. Increasing the quantity in this range increases total revenue faster than total cost: ΔTR/ΔQ > ΔTC/ΔQ, or P > MC. When
P < MC, each time the rose producer increases its output by one rose, its profit goes up by P – MC the difference between the marginal
revenue and the marginal cost of that extra rose .
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Week 9: Perfectly Competitive Markets
Figure 1: Profit Maximization by a Price-Taking Firm Panel (a) shows that the firm’s profit is maximized when Q = 300,000 roses per year. Panel (b)
shows that at this point marginal cost is MC = P. Marginal cost also equals price when Q = 60,000 roses per year, but this point is a profit minimum.
If the producer can increase its profit when either P > MC or P < MC, quantities at which these inequalities hold cannot maximize its
profit. It must be the case, then, that at the profit-maximizing output,
(1) P =MC
Equation (1) tells us that a price-taking firm maximizes its profit when it produces a quantity Q* at which the marginal cost equals the
market price. This shows that there are two profit-maximization conditions for a price-taking firm:
• P = MC.
• MC must be increasing.
If either of these conditions does not hold, the firm cannot be maximizing its profit. It would be able to increase profit by either
increasing or decreasing its output.
HOW THE MARKET PRICE IS DETERMINED: SHORT-RUN EQUILIBRIUM
The short run is the period of time in which (1) the number of firms in the industry is fixed and (2) at least one input, such as the plant
size (i.e., quantity of capital or land) of each firm, is fixed.
THE PRICE-TAKING FIRM’S SHORT-RUN COST STRUCTURE
Now we can construct an individual firm’s short-run supply curve. To do this, we need to explore the cost structure of a typical firm in
the industry.
The firm’s short-run total cost of producing a quantity of output Q is
𝑆𝐹𝐶 + 𝑁𝑆𝐹𝐶 + 𝑇𝑉𝐶(𝑄) 𝑤ℎ𝑒𝑛 𝑄 > 0
𝑆𝑇𝐶 (𝑄) = {
𝑆𝐹𝐶 𝑤ℎ𝑒𝑛 𝑄 = 0
TVC(Q) represents total variable costs. These are output-sensitive costs—that is, they go up or down as the firm increases or decreases
its output. Total variable costs include materials costs and the costs of certain kinds of labor (e.g., factory labor). Total variable costs are
zero if the firm produces zero output and thus are examples of non-sunk costs.
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Week 9: Perfectly Competitive Markets
SFC represents the firm’s sunk fixed costs. A sunk fixed cost is a fixed cost that a firm cannot avoid if it temporarily suspends
operations and produces zero output. For this reason, sunk fixed costs are often also called unavoidable costs.
NSFC represents the firm’s non-sunk fixed costs. A non-sunk fixed cost is a fixed cost that must be incurred if the firm is to produce
any output, but it does not have to be incurred if the firm produces no output. Non-sunk fixed costs, as well as variable costs, are also
often called avoidable costs. The firm’s total fixed (or output-insensitive) cost, TFC, is thus given by TFC = NSFC + SFC. If NSFC = 0,
there are no fixed costs that are non-sunk. In that case, TFC = SFC. This is the case that we consider in the next section.
SHORT-RUN SUPPLY CURVE FOR A PRICE-TAKING FIRM WHEN ALL FIXED COSTS ARE SUNK
Figure 2 depicts the short-run marginal cost curve, SMC, short-run average cost curve, SAC, and average variable cost curve, AVC, for
a firm in the fresh-cut rose industry. Consider three possible market prices for fresh-cut roses: $0.25 per rose, $0.30 per rose, and $0.35
per rose. If we apply the P = MC profit-maximization condition from the previous section, the firm’s profit-maximizing output level
when the price is $0.25 is 50,000 roses per month (point A in Figure 2). Similarly, when the market price is $0.30 and $0.35 per rose, the
profit-maximizing output levels are 55,000 and 60,000 roses per month (points B and C, respectively). Each of these quantities
represents a point at which the firm’s short-run marginal cost SMC equals the relevant market price P, or P = SMC.
The firm’s short-run supply curve tells us how its profit-maximizing output decision changes as the market price changes. Graphically,
for the prices $0.25, $0.30, and $0.35, the firm’s short-run supply curve coincides with the short-run marginal cost curve SMC. Thus,
points A, B, and C are all on the firm’s short-run supply curve.
However, the firm’s short-run marginal cost curve and the firm’s short-run supply curve do not necessarily coincide at all possible
prices. To see why, suppose the price of roses is $0.05. To maximize its profits at this price, the firm would produce at the point at
which price equals marginal cost, an output of 25,000 roses per month. But at this price, the firm would earn a loss: It would incur its
total fixed cost TFC, and, on top of that, it would lose the difference between the price of $0.05 and the average variable cost, AVC25, on
each of the 25,000 roses it produces. That is, the firm’s total loss would be TFC plus 25,000(AVC25 = 0.05) (the shaded region in Figure).
Figure 2: Short-Run Supply Curve for a Price-Taking Firm Whose Fixed Costs Are All Sunk The firm’s short-run supply curve is the portion of its shortrun marginal cost (SMC) above the minimum level of average variable cost, denoted by PS. This is the firm’s shutdown price. For prices below the
shutdown price, the firm supplies zero output, and its supply curve is a vertical line coinciding with the vertical axis.
If the firm did not produce, its loss would only be its (sunk) total fixed cost TFC. At a price of $0.05, then, the firm cuts its loss by not
producing. More generally, the firm is better off cutting its losses by temporarily shutting down if the market price P is less than the
average variable cost AVC(Q*) at the output level Q* at which P equals short-run marginal cost, or P < AVC(Q*).
We can now draw the firm’s short-run supply curve. We have seen that:
A profit-maximizing price-taking firm, if it produces positive output, produces where P = SMC and SMC slopes upward.
A profit-maximizing price-taking firm never produces where P < AVC.
Thus, the firm would never produce on the portion of the SMC curve where SMC < AVC. This is the portion below the minimum level
of the AVC curve. It then follows that if price is below the minimum level of AVC, the firm will produce Q = 0.
In light of this, the firm’s supply curve has two parts:
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Week 9: Perfectly Competitive Markets
Problem -- Deriving the Short-Run Supply Curve for a Price-Taking Firm
Suppose that a firm has a short-run total cost curve given by STC = 100 + 20Q + Q2, where the total fixed cost is 100 and the total
variable cost is 20Q + Q2. The corresponding short-run marginal cost curve is SMC = 20 + 2Q. All of the fixed cost is sunk.
(a) What is the equation for average variable cost (AVC)?
(b) What is the minimum level of average variable cost?
(c) What is the firm’s short-run supply curve?
Solution
(a) Average variable cost is total variable cost divided by output. Thus, AVC= (20Q+Q 2)/Q = 20 + Q.
(b) We know that the minimum level of average variable cost occurs at the point at which AVC and SMC are equal—in this case,
where 20 + Q = 20 + 2Q, or Q = 0. If we substitute Q = 0 into the equation of the AVC curve 20 = Q, we find that the minimum
level of AVC equals 20.
(c) For prices below 20 (the minimum level of average variable cost), the firm will not produce. For prices above 20, we can find
the supply curve by equating price to marginal cost and solving for Q: P = 20 + 2Q, or Q = -10 + P/2. The firm’s short-run
supply curve, which we denote by s(P), is thus:
𝑆(𝑝) = {
0 𝑤ℎ𝑒𝑛 𝑃 < 20
𝑃
−10 + , 𝑤ℎ𝑒𝑛 𝑃 ≥ 20
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SHORT-RUN MARKET SUPPLY CURVE
Because each firm’s supply curve coincides with its marginal cost curve (over the range of prices for which the firm is willing to
produce positive output), the market supply curve tells us the marginal cost of producing the last unit supplied in the market.
The process of obtaining the market supply curve by summing the individual firm supply curves is subject to one important
qualification: This approach is valid only if the prices that firms pay for their inputs are constant as the market output varies. The
assumption that input prices are constant may be valid in many markets. For example, if the industry’s demand for the services of
unskilled labor is but a small fraction of the overall demand for unskilled labor throughout the economy, then changes in industry
output would have a negligible effect on the wage rate for unskilled workers.
However, in some markets the prices of certain inputs might vary as market output changes. For example, suppose that an industry
employs a kind of skilled labor that no other industry employs. As the quantity supplied increases in response to a higher price, the
industry’s demand for skilled labor would rise, possibly leading to a higher wage rate. If so, each producer’s marginal cost curve would
shift upward. The higher marginal cost would mean that a producer in this industry would supply less output at any market price than
it would have if the wage rate of skilled labor had not increased. This implies that the market supply for this product would be less
responsive to a change in the price of this product than it would be if the wage rate for skilled workers were constant.
SHORT-RUN PERFECTLY COMPETITIVE EQUILIBRIUM
We can now explore how market price is determined in a competitive market. A short-run perfectly competitive equilibrium occurs
when the quantity demanded by consumers equals the total quantity supplied by all the firms in the market—that is, at a point where
the market demand curve and the market supply curve intersect. Figure 3(b) shows the market demand curve D and the short-run
market supply curve SS in an industry that consists of 100 identical producers. The equilibrium price is P*, where quantity supplied is
equal to quantity demanded. Figure 3(a) shows that a typical firm will produce output Q*, at which its marginal cost equals the market
price P*. Since there are 100 firms, each supplying Q* units of output, market supply (which equals market demand at the price P*)
must equal 100Q*.
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Week 9: Perfectly Competitive Markets
Figure 3: Short-Run Equilibrium The short-run equilibrium price is P*, the price at which market supply equals market demand. Panel (a) shows that a
typical firm produces Q*, where short-run marginal cost equals price. Panel (b) shows that total quantity supplied and demanded at P* is equal to
100Q*.
Problem -- Short-Run Market Equilibrium
A market consists of 300 identical firms, and the market demand curve is given by D(P) = 60 - P. Each firm has a short-run total cost
curve STC = 0.1 + 150Q2, and all fixed costs are sunk. The corresponding short-run marginal cost curve is SMC = 300Q, and the
corresponding average variable cost curve is AVC = 150Q. The minimum level of AVC is 0; thus, a firm will continue to produce as
long as price is positive. What is the short-run equilibrium price in this market?
Solution
Each firm’s profit-maximizing quantity is given by equating marginal cost and price: 300Q = P. Thus the supply curve s(P) of an
individual firm is s(P) = P/300. Since the 300 firms in this market are all identical, short-run market supply equals 300s(P). The short-run
equilibrium occurs where market supply equals market demand, or 300(P/300) = 60 - P. Solving for P, we find that the equilibrium price
is P = $30 per unit.
COMPARATIVE STATICS ANALYSIS OF THE SHORT-RUN EQUILIBRIUM
The competitive equilibrium shown in Figure 3(b) should look familiar.
Figure 4: Comparative Statics Analysis: Increase in the Number of Firms An increase in the number of firms shifts the short-run supply curve rightward,
from SS0 to SS1. The quantity supplied at any price goes up. The rightward shift drives the equilibrium price down and the equilibrium quantity up.
Figure 4 shows one example of a comparative statics analysis: what happens when the number of firms in the market goes up. Adding
more firms moves the short-run market supply curve rightward, from SS0 to SS1, which means that at any given market price, such as
$10 per unit, the quantity supplied goes up. Thus, as a result of the increase in the number of firms, the price falls and the equilibrium
quantity rises.
Figure 5 shows another comparative statics analysis: what happens when the market demand increases from D to D’. As a result of the
increase in market demand, the equilibrium price and quantity both go up.
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Week 9: Perfectly Competitive Markets
Figure 5: The Impact of a Shift in Demand on Price Depends on the Price Elasticity of Supply In panel (a), supply is relatively elastic, and a shift in
demand has a modest impact on price. In panel (b), supply is relatively inelastic, and the identical shift in demand has a more dramatic impact on the
equilibrium price.
HOW THE MARKET PRICE IS DETERMINED: LONG-RUN EQUILIBRIUM
In the short run, firms operate within a given plant size, and the number of firms in the industry does not change. As a result, at the
short-run perfectly competitive equilibrium, firms might earn positive or negative economic profits. By contrast, in the long run,
established firms can adjust their plant sizes and can even leave the industry altogether. In addition, new firms can enter the industry.
In the long run, these forces drive a firm’s economic profits to zero.
FREE ENTRY AND LONG-RUN PERFECTLY COMPETITIVE EQUILIBRIUM
In our analysis of short-run perfectly competitive equilibrium, we assumed that the number of firms in the industry was fixed. But in
the long run, new firms can enter the industry. A firm will enter the industry if, given the market price, it can earn positive economic
profits and thereby create wealth for its owners.
A long-run perfectly competitive equilibrium occurs at a price at which supply equals demand and firms have no incentive to enter or
exit the industry. More specifically, a long-run perfectly competitive equilibrium is characterized by a market price P*, a number of
identical firms n*, and a quantity of output Q* per firm that satisfies three conditions:
Each firm maximizes its long-run profit with respect to output and plant size. Given the price P*, each active firm chooses a level of
output that maximizes its profit and selects a plant size that minimizes the cost of producing that output. This condition implies that a
firm’s long-run marginal cost equals the market price, or P* = MC(Q*).
Each firm’s economic profit is zero. Given the price P*, a prospective entrant cannot earn positive economic profit by entering this
industry. Moreover, an active firm cannot earn negative economic profit by participating in this industry. This condition implies that a
firm’s long-run average cost equals the market price, or P* = AC(Q*).
Market demand equals market supply. At the price P*, market demand equals market supply, given the number of firms n* and
individual firm supply decisions Q*. This implies that D(P*) = n*Q*, or equivalently, n* = D(P*)/Q*.
Figure 6 shows these conditions graphically. Because the equilibrium price simultaneously equals long-run marginal cost and long-run
average cost, each firm produces at the bottom of its long-run average cost curve. If the minimum of the average cost occurs at a single
level of output such as Q* in Figure 6, the firm produces at minimum efficient scale. The condition that supply equals demand then
implies that the equilibrium number of firms equals market demand divided by minimum efficient scale output.
Figure 6: Long-Run Equilibrium in a Perfectly Competitive Market The long-run equilibrium price P* equals the minimum level of long-run average
cost ($15 per unit). Each firm produces a quantity Q* equal to its minimum efficient scale (50,000 units). The equilibrium quantity demanded is 10
million units. The equilibrium number of firms is this amount divided by the output per firm of 50,000 (n* = D(P*) / Q* = 10,000,000 / 50,000 = 200).
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Week 9: Perfectly Competitive Markets
Problem: Calculating a Long-Run Equilibrium
In this market, all firms and potential entrants are identical. Each has a long-run average cost curve AC(Q) = 40 - Q + 0.01Q2 and a
corresponding long-run marginal cost curve MC(Q) = 40 - 2Q + 0.03Q2 where Q is thousands of units per year. The market demand
curve is D(P) = 25,000 - 1,000P, where D(P) is also measured in thousands of units. Find the long-run equilibrium quantity per firm,
price, and number of firms.
Solution
Let asterisks denote equilibrium values. The long-run competitive equilibrium satisfies the following three equations.
𝑃 ∗= 𝑀𝐶 (𝑄 ∗) = 40 − 2𝑄 ∗ +0.03 𝑄 ∗2 (𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛)
𝑃 ∗ = 𝐴𝐶 (𝑄 ∗) = 40 − 𝑄 ∗ +0.01 𝑄 ∗2 (𝑧𝑒𝑟𝑜 𝑝𝑟𝑜𝑓𝑖𝑡)
𝑛∗=
𝐷(𝑃 ∗)
25000 − 1000𝑃 ∗
=
(𝑠𝑢𝑝𝑝𝑙𝑦 𝑒𝑞𝑢𝑎𝑙𝑠 𝑑𝑒𝑚𝑎𝑛𝑑)
𝑄∗
𝑄∗
By combining the first two equations, we can solve for the quantity per firm, Q*: 40 - 2Q* + 0.03(Q*)2 = 40 - Q* + 0.01 (Q*)2, or Q* = 50.
Thus, each firm in equilibrium produces 50,000 units per year. By substituting Q* = 50 back into the average cost function, we can solve
for the equilibrium price, P*: P* = 40 - 50 + 0.01(50)2 = 15. The equilibrium price of $15 per unit corresponds to each firm’s minimum
level of average cost. By substituting P* into the demand function, we can find the equilibrium market demand: 25,000 - 1,000(15) =
10,000, or 10 million units per year. The equilibrium number of firms is equilibrium market demand divided by minimum efficient
scale: 10,000,000/ 50,000 = 200 firms.
LONG-RUN MARKET SUPPLY CURVE
In our analysis of the short-run competitive equilibrium, we depicted the equilibrium price by the intersection of the market demand
curve and the short-run market supply curve. In this section, we will see that the long-run equilibrium can be depicted in a similar way:
by the intersection of the market demand curve and the long-run market supply curve. (In this section we will make the same
assumption that we made when obtaining the short-run market supply curve—namely, that changes in industry output do not affect
input prices.
In the next section, we will see how to obtain the long-run market supply curve when this assumption doesn’t hold.) The long-run
market supply curve tells us the total quantity of output that will be supplied in the market at various prices, assuming that all longrun adjustments take place (such as adjustments in plant size and new firms entering the market). However, we cannot obtain the longrun market supply curve in the same way we obtained the short-run curve, by horizontally summing the individual firm supply
curves. The reason is that, in the long-run as opposed to the short run, market supply can vary as firms enter or exit the market; thus,
there is no fixed set of individual firm supply curves that we can sum together.
Figure 7: Long-Run Market Supply Curve: Initially, the industry is in long-run equilibrium at a price of $15 per unit. Each of the 200 identical firms in
the market produces its minimum efficient scale output of 50,000 units per year, as indicated by point A in panel (a); thus, total market supply is 10
million units per year, at the intersection of the initial demand curve D0 and the long-run supply curve LS in panel (b). If demand then shifts rightward
from D0 to D1, the short-run equilibrium price is $23, where the short-run supply curve SS0 intersects D1. In the short run, each firm is at point B in panel
(a), supplying 52,000 units per year and earning a positive economic profit equal to the area of the shaded region. The opportunity to earn a profit
induces new entry, which shifts the short-run supply curve rightward, until it reaches SS1. At this new long-run equilibrium, the industry now has 360
firms, each firm is again supplying 50,000 units per year, and the equilibrium price is again $15 per unit. Thus, the long-run supply curve LS is a
horizontal line at $15—in the long run, all market supply occurs at this price.
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Week 9: Perfectly Competitive Markets
Figure 7 shows how to construct a long-run market supply curve. Initially, the market is in long-run equilibrium at a price of $15. At
this price, each of the 200 identical firms produces at its minimum efficient scale of 50,000 units per year, so market supply is 10 million
units per year (the quantity demanded is also 10 million units per year, of course, because the market is in equilibrium). Point A in
Figure 7(a) represents the position of a typical firm at this long-run equilibrium.
Now suppose that market demand shifts from D0 to D1, as shown in Figure 7(b). Also suppose that this demand shift is expected to
persist, so the market will reach a new long-run equilibrium.
In the short run, with 200 firms in the market, equilibrium occurs at a price of $23, with each firm maximizing profit by producing
52,000 units per year and with total market supply and demand at 200 x 52,000 = 10.4 million units per year. For the individual firm,
this situation is represented by point B in Figure 7(a); for the market, it is represented by the intersection of the short-run supply curve
SS0 and the new demand curve D1 in Figure 7(b).
At a price of $23, each of the 200 firms in the market earns a positive economic profit equal to the area of the shaded rectangle in Figure
10(a). The availability of an economic profit attracts new firms into the market, shifting the short-run supply curve rightward. Entry of
new firms continues until the short-run supply curve has shifted to SS1 and the price has fallen back to $15 per unit, as represented by
the intersection of SS1 and D1 in Figure 7(b). At this point, 160 new firms have entered the industry, and each firm (new and old)
maximizes its profit by producing at its minimum efficient scale of 50,000 units per year. Once price falls to $15, there is no incentive for
additional entry or exit because each firm earns zero economic profit. Moreover, the market clears because market demand at $15
equals the total market supply of 360 x 50,000 = 18 million units per year.
This analysis shows that, in a perfectly competitive market that is initially in long-run equilibrium at a price P, additional market
demand will be satisfied in the long run by the entry of new firms. Although the equilibrium price may increase in the short run, in the
long run this process of new entry will drive the equilibrium price back down to its original level. Thus, the long-run market supply
curve will be a horizontal line corresponding to the long-run equilibrium price P. In Figure 7(b), LS is the long-run market supply curve
corresponding to the long-run equilibrium price of $15.
CONSTANT-COST, INCREASING-COST, AND DECREASING-COST INDUSTRIES
Constant-Cost Industry When constructing the long-run supply curve in the previous section, we assumed that the expansion of
industry output that occurs as a result of new entry does not affect the prices of inputs (e.g., labor, raw materials, capital) used by firms
in the industry. As a result, when new firms enter the industry, the cost curves of incumbent producers do not shift. This assumption
holds when an industry’s demand for an input is a small part of the total demand for that input. In this case, increases or decreases in
the industry’s use of that input would not affect its market price.
Increasing-Cost Industry When an expansion of industry output increases the price of an input, we have an increasing-cost industry.
An industry is likely to be increasing cost if firms use industry-specific inputs—scarce inputs that only firms in that industry use.
Decreasing-Cost Industry In some situations, an increase in industry output can lead to a decrease in the price of an input. We then
have a decreasing-cost industry. To illustrate, suppose an industry relies heavily on a special kind of computer chip as an input. The
industry may be able to acquire computer chips more inexpensively as the industry’s demand for chips rises, perhaps because
manufacturers of computer chips can employ cost-reducing techniques of production at higher volumes. In a decreasing-cost industry,
each firm’s average and marginal cost curves may fall, not because the firms produce with economies of scale, but because input prices
fall when the industry produces more.
ECONOMIC RENT AND PRODUCER SURPLUS
In the preceding sections, we studied how price-taking firms adjust their production decisions in light of the market price. We also
explored how the market price is determined. We now explore how firms and input owners (e.g., providers of labor services or owners
of land or capital) profit from their activities in perfectly competitive markets. We will introduce two concepts to describe the
profitability of firms and input owners in perfectly competitive markets: economic rent and producer surplus.
ECONOMIC RENT
In the theory we have developed so far, we have assumed that all firms that operate in a perfectly competitive market have access to
identical resources. This was reflected in our assumption that all active firms and potential entrants had the same long-run cost curves.
But in many industries some firms gain access to extraordinarily productive resources, while others do not.
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Week 9: Perfectly Competitive Markets
Economic rent measures the economic surplus that is attributable to an extraordinarily productive input whose supply is limited.
Specifically, economic rent is equal to the difference between the maximum amount a firm is willing to pay for the services of the input
and the input’s reservation value. The input’s reservation value, in turn, is the return that the input owner could get by deploying the
input in its best alternative use outside the industry. Putting the pieces of this definition together, we thus have: economic rent =A - B,
where
A = maximum amount firm is willing to pay for services of input
B = return that input owner gets by deploying the input in its best alternative use outside the industry
To illustrate this definition, suppose that the maximum amount that a firm would be willing to pay to hire an extraordinary worker the A term in our definition of economic rent—is equal to $105,000
Suppose further that the worker’s best available employment opportunity outside the industry is to work for an annual salary of
$70,000. This is the B term in our definition. The economic rent attributable to the extraordinary worker is thus $105,000 - $70,000 =
$35,000 per year.
PRODUCER SURPLUS
Producer surplus is the difference between the amount that a firm actually receives from selling a good in the marketplace and the
minimum amount the firm must receive in order to be willing to supply the good in the marketplace. Just as consumer surplus
provides a measure of the net benefit enjoyed by price-taking consumers, producer surplus provides a measure of the net benefit
enjoyed by price-taking firms from supplying a product at a given market price.
Producer Surplus for an Individual Firm
Figure 11 shows the producer surplus for a firm that faces a marginal cost curve MC and an average nonsunk cost curve ANSC. For
this firm, the supply curve is a vertical spike 0E up to the shutdown price of $2 per unit. Above this price, it is the solid portion of MC.
When the market price is $3.50 per unit, the firm supplies 125 units. The firm’s producer surplus when the market price is $3.50 is the
area between the supply curve and the market price, or the area of region FBCE. This area is the sum of two parts: rectangle FACE and
triangle ABC. Rectangle FACE is the difference between total revenue and the total non-sunk cost of the first 100 units supplied. It thus
represents the producer surplus of these 100 units. Triangle ABC is the difference between the additional revenue and the additional
cost if the firm expands output from 100 units to 125 units. It thus represents the producer surplus of the last 25 units supplied. For
each additional unit of output in this range, the firm’s profit goes up by the difference between the price and the marginal cost MC of
that additional unit, and so area ABC is the additional profit due to increasing output from 100 to 125 units. As before, the overall
producer surplus at a market price of $3.50 (area FBCE) equals the difference between the firm’s total revenue and its total non-sunk
cost when it supplies 125 units. In the short run, when some of the firm’s fixed costs might be sunk, a firm’s producer surplus and its
economic profit are not equal, but differ by the extent of the firm’s sunk costs—in particular, economic profit equals total revenue
minus total costs, while producer surplus equals total revenue minus total non-sunk cost. However, in the long run, when all costs are
nonsunk (i.e., avoidable), producer surplus and economic profit are the same. Notice that in both cases the difference in producer
surplus at one market price and producer surplus at another price is equal to the difference in the firm’s economic profits at these two
prices (because fixed costs do not change). Thus, for example, in Figure 11, area P1P2GH is the increase in economic profit as well as
the increase in producer surplus that the firm enjoys when the price increases from P1 to P2.
Figure 11: Producer Surplus for a Price-Taking Firm The producer surplus at price $3.50 is equal to the area between the price and the supply curve,
area FBCE. This area is equal to the difference between the firm's total revenue and its total nonsunk cost when it produces 125 units of output. The
change in producer surplus when the market price moves from P1 to P2 is equal to the area of P1P2GH. This is the change in the firm's economic profit
that results when the market price increases from P1 to P2.
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Week 9: Perfectly Competitive Markets
Producer Surplus for the Entire Market:
In the short run, the number of producers in the industry is fixed, and the market supply curve is the horizontal sum of the supply
curves of the individual producers. Because of this, the area between the short-run market supply curve and the market price is the
sum of the producer surpluses of the individual firms in the market. Figure 12 illustrates this for a market that consists of 1,000
identical firms, each with a supply curve ss. The market supply curve SS in Figure 12(b) is the horizontal sum of these individual
supply curves. The area between this supply curve and the price—the producer surplus for the entire market—equals total market
revenue minus the total non-sunk costs of all firms in the industry. For example, when the price is $10 per unit, each individual firm in
Figure 12 produces 200 units per year and has a producer surplus equal to area ABCD, which in this case equals $350.34 Total market
supply at $10 is equal to 200,000 units per year, and the area between the market supply curve and price, area EFGH, is equal to
$350,000. This is the combined producer surplus of 1,000 individual firms, each with a producer surplus of $350 ($350,000 = $350 *
1,000). The market-level producer surplus of $350,000 is thus the difference between the total revenue of all 1,000 firms and their total
non-sunk costs.
Figure 12: Market-Level Producer Surplus: Number of Firms in the Industry Is Fixed Panel (a): A typical firm has a supply curve ss. At a price of $10, a
firm supplies 200 units, and its producer surplus is area ABCD. This area equals $350. Panel (b): With 1,000 firms in the industry, the market supply
curve is SS. At a price of $10, market supply is 200,000 units, and the market-level producer surplus is area EFGH. This area equals $350,000.
Problem -- Calculating Producer Surplus
Suppose that the market supply curve for milk is given by Q = 60P, where Q is the quantity of milk sold per month (measured in
thousands of gallons) when the price is P dollars per gallon
Problem (a) What is the producer surplus in this market when the price of milk is $2.50 per gallon? (b) By how much does producer
surplus increase when the price of milk increases from $2.50 to $4.00 per gallon
Solution
(a) When the price is $2.50 per gallon, 150,000 gallons of milk are sold per month [Q = 60(2.50) = 150]. The producer surplus is
triangle A, the area between the supply curve and the market price. This area equals (1/2)(2.50
0) (150,000) 187,500. Producer surplus in this market is thus $187,500 per month.
(b) If the price increases from $2.50 to $4.00, the quantity supplied will increase to 240,000 gallons per month. Producer surplus
will increase by area B ($225,000) plus area C ($67,500). Producer surplus in this market thus increases by $292,500 per month.
Problems:
1.
Dave’s Fresh Catfish is a northern Mississippi farm that operates in the perfectly competitive catfish farming industry. Dave’s
short-run total cost curve is 𝑆𝑇𝐶(𝑄) = 400 + 2𝑄 + 0.5𝑄2, where 𝑄 is the number of catfish harvest per month. The
corresponding short-run marginal cost curve is 𝑆𝑀𝐶(𝑄) = 2 + 𝑄. All of the fixed costs are sunk.
(a) What is the equation for the average variable cost (𝐴𝑉𝐶)?
(b) What is the minimum level of average variable costs?
(c) What is Dave’s short-run supply curve?
(a) 𝑇𝑉𝐶 = 2𝑄 + 0.5𝑄2 so 𝐴𝑉𝐶 = 𝑇𝑉𝐶/𝑄 = 2 + 0.5𝑄.
(b) The minimum level of 𝐴𝑉𝐶 occurs at the 𝑄 where 𝑆𝑀𝐶 = 𝐴𝑉𝐶, or 2 + 𝑄 = 2 + 0.5𝑄, or 𝑄 = 0. The minimum level of AVC is
thus 2.
(c) Since all fixed costs are sunk, the firm will not produce if the price is below the minimum level of 𝐴𝑉𝐶., or 2. For prices above
2, the quantity supplied is found by equation price to marginal cost, or 2 + 𝑄 = 𝑃, which implies 𝑄 = 𝑃 − 2. Thus, the
firm’s short-run supply curve is
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Week 9: Perfectly Competitive Markets
𝑠(𝑃) = 0, 𝑖𝑓 𝑃 < 2
.
𝑠(𝑃) = 𝑃 – 2 𝑖𝑓 𝑃  2
2. Newsprint (the paper used for newspapers) is produced in a perfectly competitive market. Each identical firm has a total variable
cost TVC(Q) = 40Q + 0.5Q2, with an associated marginal cost curve SMC(Q) = 40 + Q. A firm’s fixed cost is entirely nonsunk and equal to
50.
a) Calculate the price below which the firm will not produce any output in the short run.
b) Assume that there are 12 identical firms in this industry. Currently, the market demand for newsprint is D(P) = 360 − 2P, where D(P)
is the quantity consumed in the market when the price is P. What is the short-run equilibrium price?
a)
The firm will not produce any output when the price falls below the point where SMC = ANSC, i.e. the minimum of the ANSC
curve. Therefore
50 / Q  40  0.5Q  40  Q
This implies Q = 10. The corresponding price, below which the firms will not produce, is equal to MC(10) = ANSC(10) = 50.
P  40  Q . This means that each firm’s supply curve is
Q  P  40 if P > 50 and zero if P < 50. Therefore market supply equals 12( P  40) and in equilibrium this must equal market
demand, 360  2 P . Therefore the equilibrium price is P = 60. At this price, each firm produces 20 units of output. The firm’s profit is
PQ  V (Q)  F and this equals 30. Substituting Q = 20 and P = 60, we get total fixed costs, F = 170. Since non-sunk fixed costs are 50,
b)
Each firm will produce according to the relation, P = MC, or
sunk fixed costs must total up to 120.
3.
The oil drilling industry consists of 60 producers, all of whom have an identical short-run total cost curve, STC(Q) = 64 + 2Q2,
where Q is the monthly output of a firm and $64 is the monthly fixed cost. The corresponding short-run marginal cost curve is
SMC(Q) = 4Q. Assume that $32 of the firm’s monthly $64 fixed cost can be avoided if the firm produces zero output in a
month. The market demand curve for oil drilling services is D(P) = 400 − 5P, where D(P) is monthly demand at price P. Find
the market supply curve in this market, and determine the short-run equilibrium price.
The firm’s ANSC curve is given by 32/Q + 2Q. To find the shut-down price, we find the minimum level of ANSC. This occurs at the
quantity at which ANSC equals MC, or
32/Q + 2Q = 4Q. Solving for Q yields Q = 4, and substituting this into the expression for ANSC tells us that the minimum level of ANSC
is equal to 32/4 + 2(4) = $8. At prices below $8, a firm’s supply is 0. At prices above $8, a firm produces a quantity at which
P = SMC: P = 4Q, or Q = P/4. Thus, the short-run supply curve for a firm is:
0

s( P )   P
 4
if P  8.
if P  8
Since there are 60 identical producers, each with this supply curve, the short-run market supply curve S(P) is 60 times s(P), or:
0
S(P)  
15 P
if P  8.
if P  8
To find the equilibrium price, we equate market supply to market demand and solve for P: 15P = 400 – 5P, or P = 20.
4.
A perfectly competitive industry consists of two types of firms: 100 firms of type A and 30 firms of type B. Each type A firm
has a short-run supply curve sA(P) = 2P. Each type B firm has a short-run supply curve sB(P) = 10P. The market demand curve
is D(P) = 5000 − 500P. What is the short-run equilibrium price in this market? At this price, how much does each type A firm
produce, and how much does each type B firm produce?
Total industry supply is the sum of the supply curves of the individual firms. Since we have 100 type A firms, total supply from type A
firms is 100sA(P) = 200P, and since we have 30 type B firms, total supply from type B firms is 30sB(P) = 300P. The short-run industry
supply curve is thus S(P) = 200P + 300P = 500P. The short-run market equilibrium occurs at the price at which quantity supplied equals
quantity demanded, or 5000 – 500P = 500P, or P = 5. At this price, a type A firm supplies 10 units, while a type B firm supplies 50 units.
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Week 9: Perfectly Competitive Markets
5.
A market contains a group of identical price taking firms. Each firm has a marginal cost curve SMC(Q) = 2Q, where Q is the
annual output of each firm. A study reveals that each firm will produce if the price exceeds $20 per unit and will shut down if
the price is less than $20 per unit. The market demand curve for the industry is D(P) = 240 − P/2, where P is the market price.
At the equilibrium market price, each firm produces 20 units. What is the equilibrium market price, and how many firms are
in this industry?
To determine the quantity supplied for a given price, set
P  SMC .
P  2Q
Thus the supply curve for each firm is
Q  12 P
s( P)  12 P . If each firm is producing 20 units, then
20  12 P
P  40
So the market price is 40. Substituting into demand reveals
D( P)  240  12 (40)
D( P)  220
If each firm is producing 20 units, the market will have
220
20
 11 firms.
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