4/8/2016
1
Intermediate Microeconomics W3211
Lecture 17: Equilibrium with Firms Introduction
Columbia University, Spring 2016 Mark Dean: [email protected] 2
3 4 The Story So Far…. Today
• We have now thought a lot about what a single firm will • Think about what happens when firms are not on their do in a perfectly competitive market own
• We know how to maximize profits • How many firms combine to make an industry
• In the short and long run • What happens when firms and consumers interact
• This second point will take us back to the study of equilibrium
• Equilibrium will now come in two flavors • Partial Equilibrium • General Equilibrium
6 Supply From A Competitive Industry
So far we have thought about the behavior of a single firm
But typically an industry will consist of many firms
In fact, we pretty much assumed that when we started talking about perfect competition
Industry Supply How are the supply decisions of the many individual firms in a competitive industry combined to discover the market supply curve for the entire industry?
5
1 4/8/2016
7 8 Supply From A Competitive Industry Short-Run Supply
Since every firm in the industry is a price-taker, total quantity In a short-run the number of firms in the industry is, temporarily, supplied at a given price is the sum of quantities supplied at fixed. that price by the individual firms. Let n be the number of firms; i = 1, … ,n.
Si(p) is firm i’s supply function.
9 Supply From A Competitive 10 Short-Run Supply Industry
In a short-run the number of firms in the industry is, temporarily, fixed Firm 1’s Supply Firm 2’s Supply Let n be the number of firms; p p i = 1, … ,n.
Si(p) is firm i’s supply function.
The industry’s short-run supply function is
n S1(p) S2(p)
S(p) Si (p). i1
11 12 Supply From A Competitive Industry Supply From A Competitive Industry Firm 1’s Supply Firm 2’s Supply Firm 1’s Supply Firm 2’s Supply p p p p p” p’
S (p’) S (p) S (p) S (p”) S (p) S (p”) S (p) p 1 1 2 p 1 1 2 2 p” p’
S1(p’) S(p) = S1(p) + S2(p) S1(p”)+S2(p”) S(p) = S1(p) + S2(p) Industry’s Supply Industry’s Supply
2 4/8/2016
13 14 Supply From A Competitive Industry Short-Run Industry Equilibrium Firm 1’s Supply Firm 2’s Supply p p In a short-run, neither entry nor exit can occur.
Consequently, in a short-run equilibrium, some firms may earn positive economics profits, others may suffer economic losses, and still others may earn zero economic profit. S (p) S (p) p 1 2
S(p) = S1(p) + S2(p) Industry’s Supply
15 16 Short-Run Industry Equilibrium Short-Run Industry Equilibrium Firm 1 Firm 2 Firm 3 AC Short-run industry s AC MCs s supply ACs MC MC s p e s s e ps Market demand
* * * e y1 y1 y2 y2 y3 y3 Ys Y Short-run equilibrium price clears the market and is taken as given by each firm. (We will talk more about this in a minute)
17 18 Short-Run Industry Equilibrium Long-Run Industry Supply Firm 1 Firm 2 Firm 3
ACs AC In the long-run every firm now in the industry is free to exit and MCs s ACs firms now outside the industry are free to enter MCs MCs e ps (Notice: not true in all markets. There are cases in which firms are not free to enter. Examples?) > 0 < 0 = 0
* * * y1 y1 y2 y2 y3 y3 The industry’s long-run supply function must account for entry and exit as well as for the supply choices of firms that choose to be in the industry.
How is this done?
3 4/8/2016
19 20 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Positive economic profit induces entry. Mkt. Demand 2 e S (p) MC(y) AC(y) Economic profit is positive when the market price ps is higher than a firm’s minimum av. total cost; Mkt. p e > min AC(y). s Supply e Entry increases industry supply, causing ps to fall.
When does entry cease?
For simplicity, let’s assume that all firms have identical costs Y y Suppose the industry initially contains only two firms.
21 22 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y)
p2 p2 p2 p2
Y y Y y2* y Then the market-clearing price is p2. Then the market-clearing price is p2. Each firm produces y2* units of output.
23 24 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) p2 p2 p2 p2 > 0
Y y2* y Y y2* y Each firm makes a positive economic Market supply shifts outwards. profit, inducing entry by another firm.
4 4/8/2016
25 26 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) S3(p) p2 p2 p3 p3
Y y2* y Y y3* y Market supply shifts outwards. Each firm produces less. Market price falls.
27 28 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) p p p p 3 3 > 0 3 3 > 0
Y y3* y Y y3* y Each firm produces less. Each firm’s economic profit is positive. Each firm’s economic profit is reduced. Will another firm enter?
29 30 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) S4(p) S4(p) p3 p3 p3 p3
Y y3* y Y y3* y Market supply would shift outwards again. Market supply would shift outwards again. Market price would fall again.
5 4/8/2016
31 32 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) S4(p) S4(p) p4 p4 p4 p4 < 0
Y y4* y Y y4* y Each firm would produce less again. Each firm would produce less again. Each firm’s economic profit would be negative.
33 34 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Mkt. Demand The long-run number of firms in the industry is the largest MC(y) AC(y) number for which the market price is at least as large as the minimum of the AC(y). S3(p) Now we can construct the industry’s long-run supply curve S4(p) Remember, this measures how industry supply changes with p4 p4 < 0 price For example because demand changes
Y y4* y Each firm would produce less again. Each firm’s economic profit would be negative. So the fourth firm would not enter.
35 36 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Suppose that market demand is large enough to sustain only Mkt. Demand two firms in the industry. S2(p) MC(y) AC(y) S3(p)
p2’ p2’
Y y2* y
6 4/8/2016
37 38 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Suppose that market demand is large enough to sustain only Mkt. Demand two firms in the industry. S2(p) MC(y) AC(y) Then if market demand increases, the market price rises, each S3(p) firm produces more, and earns a higher economic profit.
p2’ p2’
Y y2* y
39 40 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) S3(p) p2” p2” p2” p2”
Y y2* y Y y2* y
41 42 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Mkt. Demand As market demand increases further, the market price rises 2 MC(y) AC(y) further, the two incumbent firms each produce more and earn S (p) still higher economic profits -- until a 3rd firm becomes S3(p) indifferent between entering and staying out. p2” p2”
Y y2* y Notice that a 3rd firm will not enter since it would earn negative economic profits.
7 4/8/2016
43 44 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand S2(p) MC(y) AC(y) S2(p) MC(y) AC(y) S3(p) S3(p)
p2’” p2’” p2” p2”
Y y2* y Y y2* y
45 46 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Mkt. Demand So any further increase in market demand will cause the S2(p) MC(y) AC(y) number of firms in the industry to rise to three. S3(p) p2’” p2’”
Y y2* y A third firm can now enter, causing all firms to earn zero economic profits.
47 48 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp Mkt. Demand How much further can market demand increase before a S2(p) MC(y) AC(y) fourth firm enters the industry? S3(p) p2’” p2’”
Y y2* y The only relevant part of the short-run supply curve for n = 2 firms in the industry.
8 4/8/2016
49 50 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm pp pp Mkt. Demand Mkt. Demand MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) S4(p) S4(p) p3’ p3’ p3’ p3’
Y y3* y Y y3* y A 4th firm would now earn negative economic profits if it entered the industry.
51 52 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm ppMkt. Demand ppMkt. Demand MC(y) AC(y) MC(y) AC(y) S3(p) S3(p) S4(p) S4(p) p3’ p3’ p3’ p3’
Y y3* y Y y3* y But now a 4th firm would earn zero The only relevant part of the short-run economic profit if it entered the industry. supply curve for n = 3 firms in the industry.
53 54 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm ppLong-Run Continuing in this manner builds the industry’s long-run supply Supply Curve curve, one section at-a-time from successive short-run industry MC(y) AC(y) supply curves.
Y y3* y
9 4/8/2016
55 56 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm pp As each firm gets “smaller” relative to the industry, the long- Long-Run run industry supply curve approaches a horizontal line at the Supply Curve height of min AC(y). MC(y) AC(y)
Y y3* y Notice that the bottom of each segment of the supply curve is min AC(y).
57 58 Long-Run Industry Supply Long-Run Industry Supply The Market A “Typical” Firm The Market A “Typical” Firm ppLong-Run ppLong-Run Supply Curve Supply Curve MC(y) AC(y) MC(y) AC(y)
Y y3* y Y y* y Notice that the bottom of each segment of The bottom of each segment of the supply the supply curve is min AC(y). curve is min AC(y). As firms get “smaller” the segments get shorter.
59 60 Long-Run Industry Supply Long-Run Market Equilibrium Price The Market A “Typical” Firm ppLong-Run Supply Curve If there are a large number of small firms, the long-run market MC(y) equilibrium, the market price is determined solely by the long- run minimum average production cost. AC(y) Long-run market price is
pACye min ( ). y0 Y y* y In the limit, as firms become infinitesimally small, the industry’s long-run supply curve is horizontal at min AC(y).
10 4/8/2016
62 Market Equilibrium
We now have all the tools to understand what a firm will do given prices
However, as with the case of consumers, we want to know where these prices come from
What prices will emerge from the interaction of firms and Partial Equilibrium consumers? Finding Equilibrium This is again the study of equilibrium
61
63 64 Market Equilibrium Partial Equilibrium vs General Equilibrium
It turns out that we can answer this question in two different Arguably not
ways Why? Partial Equilibrium Because what happens in one market will affect what happens in other General Equilibrium markets!
What is the difference between them? As we saw from consumer theory, the price of cantaloupes will also affect demand for bananas (and vise versa)
Partial equilibrium thinks about what happens one market at a Also, as demand for cantaloupes changes, this will affect how many time workers cantaloupe makers hire Affects the income of these workers Take a particular market (e.g. cantaloupes) Affects the demand for cantaloupes! Figures out the price that creates an equilibrium in this market In short, the economy is one massive connected system, and what happens in one part of it affects all the others, creating feedback Is this the right thing to do? This is one of the things that makes economics so bloody difficult!
65 66 Partial Equilibrium vs General Partial Equilibrium Equilibrium
General equilibrium is the way of trying to sort out this mess What is an equilibrium? Solve for equilibrium in all markets at the same time Remember from consumer theory This is, understandably, complicated. An allocation (i.e. an amount that each person gets) A set of prices We will begin with partial equilibrium Such that This may give us a good approximation of what will happen if a The allocation is feasible particular market is ‘small’ The allocation is optimal for everyone given prices And is also a lot easier
We showed that we could identify the correct prices by finding Then we will move on to general equilibrium the point at which supply equals demand
11 4/8/2016
67 68 Partial Equilibrium Market Equilibrium Market p demand We are going to do the same thing here
Find the prices such that supply of firms equals demand of consumers
Remember – Supply is the profit maximizing output of firms at each price Demand is the utility maximizing consumption of consumers at each q=D(p) price
So the price at which demand equals supply will give rise to a D(p) feasible output, and at which everyone is optimizing
69 70 Market Equilibrium Market Equilibrium Market p Market p Market supply demand supply q=S(p) q=S(p)
q=D(p)
S(p) D(p), S(p)
71 72 Market Equilibrium Market Equilibrium Market Market p Market p Market demand supply demand supply q=S(p) q=S(p) D(p*) = S(p*); the market is in equilibrium. p* p* q=D(p) q=D(p)
q* D(p), S(p) q* D(p), S(p)
12 4/8/2016
73 74 Market Equilibrium Market Equilibrium Market Market p Market p Market demand supply demand supply q=S(p) q=S(p) D(p’) < S(p’); an excess D(p’) < S(p’); an excess p’ of quantity supplied over p’ of quantity supplied over p* quantity demanded. p* quantity demanded. q=D(p) q=D(p)
D(p’) S(p’) D(p), S(p) D(p’) S(p’) D(p), S(p) Market price must fall towards p*.
75 76 Market Equilibrium Market Equilibrium Market Market p Market p Market demand supply demand supply q=S(p) q=S(p) D(p”) > S(p”); an excess D(p”) > S(p”); an excess of quantity demanded of quantity demanded p* over quantity supplied. p* over quantity supplied. p” q=D(p) p” q=D(p)
S(p”) D(p”) D(p), S(p) S(p”) D(p”) D(p), S(p) Market price must rise towards p*.
77 78 Market Equilibrium Market Equilibrium Market p Market demand supply An example of calculating a market equilibrium when the S(p) = c+dp market demand and supply curves are linear.
Dp() a bp p* Sp() c dp D(p) = a-bp
q* D(p), S(p)
13 4/8/2016
79 80 Market Equilibrium Market Equilibrium Market p Market Dp() a bp demand supply Sp() c dp S(p) = c+dp
What are the values At the equilibrium price p*, D(p*) = S(p*). p* of p* and q*?
D(p) = a-bp
q* D(p), S(p)
81 82 Market Equilibrium Market Equilibrium Dp() a bp Dp() a bp Sp() c dp Sp() c dp
At the equilibrium price p*, D(p*) = S(p*). At the equilibrium price p*, D(p*) = S(p*). That is, That is, abpcdp** abpcdp** which gives ac p* bd
83 84 Market Equilibrium Market Equilibrium Market Dp() a bp p Market demand Sp() c dp supply S(p) = c+dp * At the equilibrium price p*, D(p*) = S(p*). p That is, ac abpcdp** bd which gives ac p* D(p) = a-bp bd * ad bc D(p), S(p) ad bc q and qDpSp**() () * . b d bd
14 4/8/2016
85 86 Market Equilibrium Market Equilibrium p Market quantity supplied is fixed, independent of price. Two special cases: quantity supplied is fixed, independent of the market price, and quantity supplied is extremely sensitive to the market price.
q* q
87 88 Market Equilibrium Market Equilibrium Market p Market quantity supplied is p Market quantity supplied is fixed, independent of price. demand fixed, independent of price. S(p) = c+dp, so d=0 S(p) = c+dp, so d=0 and S(p) c. and S(p) c.
D-1(q) = (a-q)/b
q* = c q q* = c q
89 90 Market Equilibrium Market Equilibrium Market Market p Market quantity supplied is p Market quantity supplied is demand fixed, independent of price. demand fixed, independent of price. S(p) = c+dp, so d=0 S(p) = c+dp, so d=0 and S(p) c. and S(p) c. -1 p* p* = p* = D (q*); that is, (a-c)/b p* = (a-c)/b. D-1(q) = (a-q)/b D-1(q) = (a-q)/b
q* = c q q* = c q
15 4/8/2016
91 92 Market Equilibrium Market Equilibrium Market Market p Market quantity supplied is p Market quantity supplied is demand fixed, independent of price. demand fixed, independent of price. S(p) = c+dp, so d=0 S(p) = c+dp, so d=0 and S(p) c. and S(p) c. p* = p* = D-1(q*); that is, p* = p* = D-1(q*); that is, (a-c)/b p* = (a-c)/b. (a-c)/b p* = (a-c)/b. D-1(q) = (a-q)/b D-1(q) = (a-q)/b
ac q* = c q ac q* = c q ac p* p* p* bd bd b with d = 0 give * ad bc * ad bc q q qc* . bd bd
93 94 Market Equilibrium Market Equilibrium p Market quantity supplied is extremely sensitive to price. Two special cases are when quantity supplied is fixed, independent of the market price, and when quantity supplied is extremely sensitive to the market price.
q
95 96 Market Equilibrium Market Equilibrium Market p Market quantity supplied is p Market quantity supplied is extremely sensitive to price. demand extremely sensitive to price. S-1(q) = p*. S-1(q) = p*.
p* p*
D-1(q) = (a-q)/b
q q
16 4/8/2016
97 98 Market Equilibrium Market Equilibrium Market Market p Market quantity supplied is p Market quantity supplied is demand extremely sensitive to price. demand extremely sensitive to price. S-1(q) = p*. S-1(q) = p*. p* = D-1(q*) = (a-q*)/b so p* p* q* = a-bp*
D-1(q) = (a-q)/b D-1(q) = (a-q)/b
q* q q* = q a-bp*
99 Market Equilibrium
Two special cases are when quantity supplied is fixed, independent of the market price, and when quantity supplied is extremely sensitive to the market price.
Question: can you think of examples for each of these special cases? Partial Equilibrium Policy Analysis
10 0
10 Benefit-Cost Analysis 10 Policy Analysis 1 2 Price The free-market equilibrium and the gains from trade
As we discussed last lecture, we can use supply and demand generated by it. Supply graphs to do policy analysis
Using the concept of consumer and producer surplus CS
p0 PS
Demand
D S q0 Q , Q (output units)
17 4/8/2016
Benefit-Cost Analysis 10 Benefit-Cost Analysis 10 3 4 Price The gain from freely Price The gains from freely th trading the q1 unit. trading the units from Supply q1 to q0. Supply Consumer’s Consumer’s gain gains CS CS
p0 p0 PS PS Producer’s Producer’s gain gains Demand Demand
D S D S q1 q0 Q , Q q1 q0 Q , Q (output units) (output units)
Benefit-Cost Analysis 10 10 5 Policy Analysis 6 Price The gains from freely trading the units from
q1 to q0. Supply Policies that prevent trade up to this point will destroy these Consumer’s gains from trade gains For example, consider a price floor, so that prices cannot go CS below Consumers choose how much to buy at this price p0 Firms supply that amount PS Producer’s gains Demand
D S q1 q0 Q , Q (output units)
Benefit-Cost Analysis 10 10 7 Policy Analysis 8 Price An excise tax imposed at a rate of $t per traded unit destroys these gains. Policies that prevent trade up to this point will destroy these Deadweight So does a floor gains from trade CS Loss price set at pf For example, consider a price floor, so that prices cannot go pf below Consumers choose how much to buy at this price PS Firms supply that amount
For example, consider a price ceiling, so that prices cannot go above Firms decide how much to supply at this price Consumers can only buy that amount D S q1 q0 Q , Q
18 4/8/2016
Benefit-Cost Analysis 10 11 9 Policy Analysis 0 Price An excise tax imposed at a rate of $t per traded unit destroys these gains. This is (again) basically the argument behind most free market Deadweight So does a floor economics
Loss price set at pf, Moving the market away from its equilibrium destroys the gains a ceiling price set from trade In the price floor case, there are firms that want to supply at a lower CS at pc price, consumers that want to buy at a lower price, but they are not allowed In the price ceiling case there are consumers that want to buy at a p higher price, firms that want to supply at a higher price, but they are not c PS allowed Both situations lead to rationing In the first case, there are more firms that want to supply than buyers who want to buy at the price D S q1 q0 Q , Q In the second case there are more consumers who want to buy than firms that want to supply at that price
11 Policy Analysis 1
As with everything else in this course, this lesson should be taken with caution
What is it that the model is missing out?
1. Everybody is a price taker – as we will see in the next lecture, if one side gets to choose the price, things can get nasty Summary 2. No externalities
3. Ignoring general equilibrium effects
4. Ignores the fact (as you will see in the homework) that increasing trade can create winners and losers
11 2
11 Summary 3
• Today we have dealt with
1. Industry supply
2. Partial Equilibrium
19