# 2. The total market supply is the sum of the amount supplied by each individual firm

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1 Review The supply function: 1. The individual firm s supply is calculated in two steps: First, we figure out whether the firm produces or shuts down, is the price greater than the shutdown price? Second, if the firm produces, how much? (given by the mc(q)=p) 2. The total market supply is the sum of the amount supplied by each individual firm Useful remember: A firm that maximizes profits always produces at point where mc(q)=p, the firm makes profits if ATC(q)>p and the firm loses money if ATC(q)<p

2 Perfectly Competitive Market Topics: 1. Definition of a Perfectly Competitive Market 2.Short Run Equilibrium 3. Long Run Equilibrium

3 Perfectly Competitive Market Key definition: A perfectly competitive market satisfies the following conditions: 1. Fragmented industry consists of many small buyers and sellers 2. Buyers and Sellers are price takers : - Each buyer s purchases are small and do not effect the market price - Each seller is small and does not effect the market price -Each seller cannot effect the price of inputs 3. Firms produce identical products 4. Perfect information about prices 5. All firms have the equal access to inputs, they have the same technology, and there is free entry. Implies that firms have identical long run cost functions

4 Perfectly Competitive Market The Law of One Price: Since products are identical and there is perfect information, there is a single price at which transactions occur.

5 Short Run Equilibrium Definition: A short run equilibrium is a pair of price and quantity (Q,P) such that: 1. Each producer maximizes profits given price p 2. Markets clear Q n Q i 1 i s ( P) Q d ( P) Where Q si (P) is firm i s individual profit maximization output given price P.

6 Short Run Equilibrium Graphic depiction of a short run equilibrium

7 Short Run Equilibrium Graphic depiction of a short run equilibrium Typical firm produces Q* where MR=MC and if 100 firms make up the market then market supply must equal 100Q*

8 Short Run Equilibrium Example Suppose a market consists of 300 identical firms, all with the same cost curve: TC(q)= q 2. Consumers demand is given by Q d (P) = 60 P. What is the equilibrium price and quantity? Do firms make positive profits at the market equilibrium? Step 1: Derive individual supply curve FC=0.1 (all are sunk, NSC= 0) ; AVC(q) = 150q; MC(q)=300q Since min{avc(q)}=0, the firm always produces. The profit maximizing condition: MC(q)=MR(q), we have that 300q=p, or q s (P) = P/300. Step 2: derive the market supply curve Q s (P) = 300 q s (P) =300(P/300) = P Step 3: solve for equilibrium Q s (P)= Q d (P) or P= 60 P and P*= 30, Q* = 30 and each firm produces q* = 30/300=.1

9 Short Run Equilibrium Example Do firms make positive profits at the market equilibrium? Condition for positive profits: p* >ATC(q*) ATC (q)= TC(q)/q = 0.1/q + 150q. Since each firm produces q* = 0.1, we have that ATC(q*)=15<30= p*, Therefore P* > ATC(q*) and profits are positive The profit of each firm is: Pq-TC(q)= 30*0.1-( *0.1^2)=1.4

10 Short Run Equilibrium Example What happens when the number of firms increases from 300 to 500? The single firm s supply is unchanged: mc(q)=p and q s (P) = P/300 But now, market supply increases to Q(P)=400* (P/300) and for markets to clear we have that : 500* (P/300)= 60 P or P=22.5 and Q= 37.5 and the individual firm produces q= 37.5/500=0.075 Does each firm make earn a profit? Condition for positive profits: p* >ATC(q*); ATC (q)= 0.1/q + 150q= 0.1/ *0.075 =11.25 < 22.5 The profit of each firm Pq-TC(q)= 22.5*0.075-( *0.075^2)=1.3

11 Short Run Equilibrium Comparative Statics What happens when the number of firms increase? Market supply is increased, prices drop, and each firm produces less.

12 Long Run Equilibrium Question: What happens in the long run? The long run differs from the short run in two key ways: 1. Firms can adjust all inputs and there are no sunk costs. 2. There is entry and exit: the number of firms in the industry can change as well. A firm that suffer loses can leave the market, and a firm that anticipates gains can enter.

13 Long Run Equilibrium Since there are no sunk costs, the firm shuts down if p<minatc(q) = Ps, and the supply is given by: P = MC(Q) for P > Ps and the firm exits if P < Ps

14 Long Run Equilibrium Key definition: A long run equilibrium is a price P*, quantity Q* and number of firms n, such that: 1. Individual firms maximize profits, each firm produces q* such that: P*=mc(q*) 2. Markets clear, market demand equals market supply, Q d (P*) = Q* = Q s (P*) Where the aggregate supply Q s (P*)=nq* 3. No firm wants to exit or enter. This implies that firms must not be making profits or suffering loses: Zero profits The difference from the short run is the zero profit condition. It relies on the assumptions that firms can exit, so no losses are incurred, and there are always firms that can enter, so no profits can be gained. Why?

15 q q Long Run Equilibrium Key Property: The zero profit condition implies that in the long run each firm is producing a quantity q such that ATC(q) is at the minimum point. Why? i. If p<atc(q) firms exit and the market price will rise (why?). If p>atc(q) there are profits, firms will enter and the market price will fall (why?). Thus p=atc(q) ii. Since each firm is maximizing profits, each firm chooses a quantity q such that mc(q)=p. The only quantity level where mc(q)=p=atc(q) is the minimum of the ATC curve. /unit MC ATC \$/unit Market demand

16 Long Run Equilibrium Key Property: In the long run, the market price p and each individual firm s output q, must be such that: mc(q)=p=atc(q), \$/unit \$/unit MC ATC Market demand p q q Q* Q

17 Long Run Equilibrium Example: Suppose a certain market has the following demand function: Q d (P) = P. Firms have the cost function TC(q) = 40q - q q 3. What is the market equilibrium? We solve this in three steps: 1. Calculate the individual firm s optimal output level and then get the market price. From zero profits: ATC(q)=P and from profit maximization, mc(q)=p. Together, ATC(q)=mc(q), and we can solve for q. AC(q) = 40 q +.01q 2 and MC(q) = 40 2q +.03q 2 And we have that q* = 50 the price is P* = Calculate the market quantity. Since the price is P* = 15, from the market demand we can calculate the market quantity: Q d (P) = P, and Q d (15)= 10, Calculate the number of firms. Given the market quantity, and the individual firm s quantity produced we can calculate the number of firms: nq*=q*, and since total output Q*=10,000 and each firm produces q*=50 units, there must be n=10,000/50=200 firms.

18 Long Run Equilibrium Difference in calculating long and short run equilibrium Step 1: Individual firm s output Long Run mc(q)=atc(q)=p Step 2: Market quantity Use Price from step 1 and market demand to calculate the market quantity Step 3: Number of firms Calculate the number of firm s Short Run mc(q)=p Calculate market supply, use market clearing condition to get price and quantity Number of firms is given. Calculate individual firm s output

19 Long Run Supply Curve Definition: The Long Run Market Supply Curve maps the quantity of output supplied for each given price. The supply of firms takes place after all long run adjustments of inputs, and entry or exit of firms. The zero profit condition pins down the long run supply. P 0 p SRS LRATC=LRS Output expansion or contraction in the industry occurs along a horizontal line corresponding to the minimum level of long run average cost. D Q Q 0

20 Long Run Market Dynamics Example of industry dynamics The Super Tanker Industry Super Tankers are large ships used for transport (usually oil). A super tanker can cost around \$100 million. In the 60s and early 70s, the demand for Tankers was high, mainly driven by the high demand for oil, 500 new super Tankers were constructed. But in the 70s prices for service of Tankers collapsed, due to the oil embargo. Short run supply is inelastic, as Tankers have no alternative value. It took years for the industry to adjust. In 1978, over 20 million tons worth of tanker capacity was sold for scrap.

21 Long Run Market Dynamics In general, the long run dynamics of prices are shaped by supply side effects (such as economies of scale) and demand side effects (such as network externalities think of cell phones). For example, the revenue cycle of computer memory chips (DRAM) \$50 \$40 \$30 \$20 \$10 \$ Question: What causes such price cycles?

22 Long Run Market Dynamics We know how a single firm responds to a shift in input prices, or market price. The next goal is to understand how prices in a competitive market responds to a change in demand

23 Long Run Market Dynamics Suppose demand increases P P 1 SRS Initially market price increase, and output increases. P 0 LRATC=LRS What happens next? D 1 D 0 Q Q 0 Q 1

24 Long Run Market Dynamics Suppose demand increases P P 1 P 0 SRS 0 SRS 2 LRATC=LRS Since prices rise, p>atc, and each firm earns a profit. Leads to entry and an increase in supply. D 0 Q D 1 In the new equilibrium: - Price decreases to the original price - Output further increases. - The number of firms increase. Q 0 Q 1 Q 2

25 Long Run Market Dynamics Suppose demand decreases P SRS 2 SRS 0 Initially market price decreases, and output decreases. What happens next? LRS Since prices fall, p<atc, each firm suffers a loss. Leads to exit and a further decrease in supply. D 1 D 0 Q In the new equilibrium: - Price rise to the original price - Output further decreases. - The number of firms decreases.

26 Long Run Market Dynamics The previous analysis made two simplifying assumptions: 1. As the number of firms increases, the costs of each individual firm do not change 2. As prices change, consumers do not change their behavior

27 Long Run Market Dynamics Key definition 1. In a constant-cost Industry an increase in industry output does not affect the prices of inputs. 2. In an increasing-cost Industry an increase in industry output increases the prices of inputs. 3. In a decreasing-cost Industry an increase in industry output decreases the prices of inputs.

28 Long Run Market Dynamics Increasing-cost Industry: an increase in demand Step 1 Initial effect: prices rise. Since prices fall, p>atc, each firm makes a profit in the short run. Leads to entry. Step 2 Entry has two effects: i. Industry supply increases ii. Individual firm s costs increase In the new equilibrium: - Price rise above the original price - Output increases. - Number of firms increases - Average total costs are higher

29 Long Run Market Dynamics Decreasing-cost Industry: an increase in demand Step 1 Initial effect: prices rise. Since prices fall, p>atc, each firm makes a profit in the short run. Leads to entry. Step 2 Entry has two effects: i. Industry supply increases ii. Individual firm s costs decreases In the new equilibrium: - Price fall bellow the original price - Output increases. - Number of firms increases - Average total costs are lower

30 Long Run Supply Curve Definition: The Long Run Market Supply Curve maps the quantity of output supplied for each given price. The supply of firms takes place after all long run adjustments of inputs, and entry or exit of firms.

31 Long Run Market Dynamics 1. In a constant-cost Industry long run supply is horizontal 2. In an increasing-cost Industry long run supply increases 3. In a decreasing-cost Industry long run supply decreases

32 Long Run Market Dynamics Example of increasing cost industry: The US Ethanol market Ethanol is a liquid produced (mostly) from corn, and can be used to produce, amongst other things, bio-fuel. In 2000s there was a sharp increase in demand, increasing prices. As the industry grew, the price of corn rose sharply, increasing the production costs As a result, the number of new plants fell sharply

33 Long Run Market Dynamics Example of increasing cost industry: The computer memory market 1. Most costs are fixed (expensive plants, low production costs), leads to vertical short run supply curves 2. Economies of scale costs have decreases 30% per year 3. Demand adjust dynamically toward a long run equilibrium P 0 2 SRS 0 SRS 1 SRD 0 1 SRD 2 LRS LRD Q \$50 \$40 \$30 \$20 \$10 \$

34 Producer Surplus Difference between surplus and profit If a firm produces with better inputs it generates a surplus.

35 Producer Surplus Definitions The reservation value is the return that the owner of an input could get by deploying the input in its best alternative use outside the industry. The economic rent that is the difference between the maximum value that a firm is willing to pay for the services of the input and input s reservation value.

36 Producer Surplus Definition: Producer Surplus is the area above the market supply curve and below the market price. It is a monetary measure of the benefit that producers or other input suppliers derive from producing a good and selling it at particular price. P Market Supply Curve P* Producer Surplus

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