MICROECONOMICS EV Prof. Davide Vannoni

Exercise session 3 1.Firm in perfectly competitive market 2.Short-run and long-run competition 3.Price support (see lecture slides) 4.Import quota (see lecture slides) 5.Gasoline Tax (see lecture slides) Exercises

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 3 Exercise n. 1 Firm WWW (see exercise session 2) works in a perfectly competitive market, and bears the following costs: Q.ty FC VCTCMCAVCAFCATC ,315,334, ,527, ,89, ,726, ,46, ,85,829, ,75,131,8 FC = fixed costs VC= var costs CT= tot costs MC= marginal c. AC*=average c.* * = V, F, T

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 4 a)If the price is 40 € compute: total revenues (TR), marginal revenue (MR) and profit. PriceQ.tyTC TR (P  Q) MCMR (P)  Profit (MR –MC) Profit (TR -TC)

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 5 a)Answer the following questions: i. At which quantity profits are maximized? The quantity in correspondence of which marginal revenue is equal to marginal cost (MR = MC), therefore Q = 8. i.Which will be the profit (loss) at the above quantity? Profit = Revenues – VC – FC In correspondence of Q = 8, Profit = 320 – = 84 €

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 6 MC P= MR ATC AVC Profit

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 7 i. How much will be the producer's surplus? Producer's surplus = Revenues – VC or Surplus = Profit + FC = = 130 € i. Will the firm continue to produce in the long run? Since the profit is positive, yes!

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 8  Notice The producer's surplus can be measured - as the difference between revenues and variable costs ( P  Q - Q  AVC ), - as the sum, for all quantities up to that level, of the differences between price and marginal cost: look at the column  Profit (MR –MC) : =130 (This is shown in the two following graphs)

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 9 MC P = MR ATC AVC Producer's Surplus

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 10 MC P= MR ATC AVC Producer's surplus

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 11 a)If the price reduces up to 20 €, which will be the profit maximizing quantity in the short run? What will happen in the long run? The profit is maximized when MC= MR = P, that is in correspondence of MC = 20 €, i.e. for Q = 5. Profit = = - 30 € (loss) In the short run the firm is not making profits but reduces losses: since it cannot modify its structure (reason for which cost fixed exist), it continue to produce until (after recovering variable costs) there will be a positive margin to be used to partly recover fixed costs.

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 12 Recall the closure condition: AVC > P - in the short run, the firm will continue to produce until the producer's surplus is positive. - in the long run, all costs are variable; the firm will continue to produce only if the profit is positive. In the long run, in our example, the firm will shut down!

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 13 MC P=MR ATC AVC Loss

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 14 d)If the price reduces up to 15 €, which will be the profit (or the loss) in the case in which the firm will continue to produce? What should the firm do in the short run? For p=15 € the optimal choice will be to produce 4 units (the maximum quantity for which MC<MR). Revenues will be lower than VC, and the difference (not recovered) will be added to the fixed costs. By producing there will be a loss equal to: TR – (VC + FC) = 60 - ( ) = - 50 € The surplus will be negative: Profits + FC= = - 4 €  The firm in the short run will stop the production!

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 15 Loss Loss due to VC MC ATC P=MR AVC

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 16 Exercise n. 2 Consider a market in which there are 1000 consumers with demand p d = 8 - q d and 100 producers with the following cost function TC= q s + (1/40) q s 2. a.Find the market equilibrium. b.Compute the profits of producers and tell what will happen in a perfectly competitive market in the long run: what will be the price, the manufactured quantities, the profits?

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 17 a)To find the equilibrium we have to find the aggregate demand and supply functions. p d = 8 – q d q d = 8 – p d Q d =  q d = 8000 – 1000p d Inverse demand function: direct demand function: Aggregating for1000 individuals: The supply function coincides with the increasing portion of the MC which lies above the AVC: Marginal Cost =  C/  Q  MC = 2 + (1/20) q s Inverse supply: p s = 2 + 1/20 q s Direct supply: q s = 20p s - 40

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 18 Aggregating for 100 firms: Q s =2000 p s The market equilibrium is the price-quantity combination for which Q s = Q d  2000p = p p* = 4 Q* = 4000 q s * = 40 ; q d * = 4

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 19 a)Each producer earns a profit equal to: TR = 4 · (40) = 160 TC = · (40) + 1/40 · (40 2 ) = 130 Profits = 30 The other firms will presumably enter the market attracted from the profit opportunities. The long run equilibrium is where the Marginal Cost equals the Average Cost. MC = ATC  2 + 1/20 · q = (10 + 2·q + 1/40 · q 2 )/q 2 + 1/20 · q = 10/q /40 · q  1 /40 · q = 10/q  q 2 = 400  q = 20 Each firm will therefore produce a quantity equal to 20  MC = ATC = 3

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 20 Since the price must equal the marginal cost, p = 3. The aggregate quantity bought on the market will be: Q d = · 3 = 5000 There will be 250 firms (5000/20); the profit will be TR – TC, therefore: TR = 3 · 20 = 60 TC = · /40 · 400 = 60 Profit = TR – TC = 0

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione 3 21 P = 4 Aggregate Supply QQ PP Aggregate Demand Individual Demand Firm Supply Graphically: 2

D. Vannoni e M. Piacenza Microeconomia C, A.A Esercitazione Q P Aggregate Demand 5000 Aggregate Supply (before entry) Due to the entry of new firms, the aggregate supply will be flatter and the equilibrium price reduces from 4 to 3; the quantity will be 5000: Aggregate Supply (before entry) 2