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Exercises

Exercises. Chapters: 16 – Oligopoly 17 – Monopolistic Competition. Exercise n.1. The table reports some information about the market for good X. In this market there are two producers, firm A and firm B. We assume that the two firms have equal market shares. Compute:

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Exercises

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  1. Exercises Chapters: 16 – Oligopoly 17 – Monopolistic Competition Istituzioni di economia 2002/2003 corso C

  2. Exercise n.1 The table reports some information about the market for good X. In this market there are two producers, firm A and firm B We assume that the two firms have equal market shares. Compute: Total sales of the market and for each firm Marginal Revenue of the market Quantity for each firm Istituzioni di economia 2002/2003 corso C

  3. Istituzioni di economia 2002/2003 corso C

  4. The two firms collude in order to reach on aggregate the price-quantity pair that maximizes the aggregate profit (N.B. quantities can be only multiple of 200). Compute: The quantity produced by each firm The level of profit for each firm The price level, the aggregate quantity and the aggregate profits for the market Istituzioni di economia 2002/2003 corso C

  5. Tot. quant market =1200 Firm quantity = 600 The agreement between the firms (cartel) has the effect of making them act like a unique monopolist; they will produce on aggregate the monopoly quantity and charge the monopolistic price. Profits will be split according to the agreement (fifty-fifty) The optimal condition will be MR = MC, the firms will increase the quantity as long as the marginal revenue (of the market on aggregate) is above marginal costs (of the market on aggregate). Price = 450 € Firm Profit: TR – TC=270000 – 66000 =204000 Aggregate Profit for the market = 408000 Istituzioni di economia 2002/2003 corso C

  6. Comparison with the collusive equilibrium Qty A 600 Qty B 600 28000€ -30000€ -2000€ Firm A decides to deviate from the cartel and increases the production by 200. Provided that firm B does not change its production, how will the equilibrium change? Qty A=800 Qty B=600 Qty market = 1400 Price 400€ Profit A= (800x400)-(800X110) = 232000 € Profit B= (600x400)-(600X110) = 174000 € Aggregate Profit= (1400x400)-(1400X110) = 406000€ Istituzioni di economia 2002/2003 corso C

  7. Firm A would like to increase its profit by increasing the quantity manufactured by 200 units. How will the equilibrium change if firm B does not change its output? How will the equilibrium change in the event that firm B increases up to 1000 its output as well? Comparison with the preceding situation Qty A 800 Qty B 600 8000€ -30000€ -22000€ Qty A=1000 Qty B=600 Market Qty = 1600 Price 350€ Profit A= (1000x350)-(1000X110) = 240000 € Profit B= (600x350)-(600X110) = 144000 € Aggregate Profit= (1600x350)-(1600X110) = 384000€ Istituzioni di economia 2002/2003 corso C

  8. Comparison with the preceding situation precedente Qty A 1000 Qty B 600 -100000€ -4000€ -104000€ If firm B increases its production up to 1000: Qty A=1000 Qty B=1000 Market Qty = 2000 Price 250€ Profit A= (1000x250)-(1000X110) = 140000 € Profit B= (1000x250)-(1000X110) = 140000 € Aggregate Profit= (2000x250)-(2000X110) = 280000€ Istituzioni di economia 2002/2003 corso C

  9. Comparison with the previous situation Qty A 800 Qty B 600 18000€ -22000€ -40000€ Firm B decides, after the first increase in production by firm A, not to fulfil the cartel agreement and increases its production by 200 units Qty A=800 Qty B=800 Qty of market= 1600 Price 350€ Profit A= (800x350)-(800X110) = 192000 € Profit B= (800x350)-(800X110) = 192000 € Aggregate Profit= (1600x350)-(1600X110) = 384000€ Istituzioni di economia 2002/2003 corso C

  10. Comparison with the previous situation Qty A 800 Qty B 800 -40000€ -42000€ -2000€ Firm A reacts by increasing its production by other 200 units Qty A=1000 Qty B=800 Market Qty = 1800 Price 300€ Profit A= (1000x300)-(1000X110) = 190000 € Profit B= (800x300)-(800X110) = 192000 € Aggregate Profit= (1800x300)-(1800X110) = 342000€ Istituzioni di economia 2002/2003 corso C

  11. For a combination of 800 units for each firm, a further increase in the quantity does not give any benefit to the firms. In fact profits reduce if the quantity manufactured by one firm increases. This situation is an equilibrium one. Increasing or decreasing the production will imply a loss of profits, so firms do not have an incentive to modify the output Thus, the combination of 800 units for each firm, 1600 on aggregate, and a price of 350€ represents an equilibrium point (Nash equilibrium). Such an equilibrium is between monopoly (quantity of 600 and price of 450€) and perfect competition (P=MC with output equal to 1280 and price equal to 110€) Istituzioni di economia 2002/2003 corso C

  12. Is the initial collusive agreement likely to be stable in the long run? As we have seen in the preceding points firms have an incentive to increase the quantity above the level foreseen by the collusive agreement, since they can reach higher profits. Nevertheless, if each firm considers the possible reaction of the other firm, there are higher chances that the agreement will hold in the long run, since a reaction brings to a considerable reduction of profits. Istituzioni di economia 2002/2003 corso C

  13. Exercise n.2 pag. 301 A large part of the world supply of diamonds comes from - Russia and from South Africa. Suppose that the marginal cost of diamond extraction is 1000 € for each unit and that the demand is described by the following schedule: Istituzioni di economia 2002/2003 corso C

  14. If there are many firms selling diamonds, which will be the price and the equilibrium quantity? • If there is only one supplier on the market, which will be the price and the equilibrium quantity? • If Russia and South Africa form a cartel, what will be the price and the equilibrium quantity? If the two countries divide equally the market, what will be the production and the profit level of South Africa. What will happen to the profits if South Africa unilaterally decides to increase its quantity by 1000 units, while Russia keep respecting the collusive agreement? • Looking at the answer given to question c), explain why the collusion between the members of the cartel is not always stable. Istituzioni di economia 2002/2003 corso C

  15. Istituzioni di economia 2002/2003 corso C

  16. If there are many firms selling diamonds, which will be the price and the equilibrium quantity? If there are many firms selling diamonds, we will be in a perfect competition situation. The optimal quantity is given by the condition MC=P. The quantity will be 12.000 diamonds, quantity for which marginal cost (1.000) = price (1.000). b) If there is only one supplier on the market, which will be the price and the equilibrium quantity? This would be a monopoly situation. The optimal quantity is given by the condition MR = MC. Since there can be only multiples of 1.000, quantity is equal to 6.000 diamonds, since the marginal revenue of 2.000 is still greater than the marginal cost (1.000). In the case of only one firm 7.000 diamonds is not the optimal quantity, since in this case the marginal revenue will be equal to zero and lower than the marginal cost. Istituzioni di economia 2002/2003 corso C

  17. c) If Russia and South Africa form a cartel, what will be the price and the equilibrium quantity? If the two countries divide equally the market, what will be the production and the profit level of South Africa. What will happen to the profits if South Africa unilaterally decides to increase its quantity by 1000 units, while Russia keep respecting the collusive agreement? If Russia and South Africa form a cartel, they will behave like a monopolist and the optimal choice will be equal to the answer to question b): 6.000 units at a price of 7.000 €. If they divide equally the market shares, quantity for South Africa will be 6.000/2=3.000 and its profits will be: (TR – TC)/2 = [(QxP) – (QxMC)]/2 = [(6.000x7.000)-(6.000x1000)]/2=18.000.000 If South Africa increases production by 1000 units and Russia honours the collusive agreement, total production rises up to 7.000 units and price decreases to 6.000 €. The profit for South Africa woulb be in such a case: (TR –T C) = [(QxP) – (QxMC)]=[(4.000x6.000)-(4.000x1000)]=20.000.000 Istituzioni di economia 2002/2003 corso C

  18. d) Looking at the answer given to question c), explain why the collusion between the members of the cartel is not always stable. The cartels often are broken because firms have high incentives to cheat in order to gain more profits. This is like the situation of South Africa examined in question c): by cheating, South Africa increases its profit by 2.000.000, to the damage of Russia that encounters a reduction of its profits. Profit of Russia in the case in which South Africa unilaterally increases production: (TRRussia –T CRussia) = [(QxP) – (QxMC)]=[(3.000x6.000)-(3.000x1000)]=15.000.000 If South Africa and Russia increase their production by 1000 each with respect to the cartel agreement (monopoly production) profits decrease for both countries. In fact, quantity rises up to 8.000 and price becomes 5.000€ The profits of the two coutries becomes: (TRSouth Africa – TCSouth Africa) = [(QxP) – (QxMC)]=[(4.000x5.000)-(4.000x1000)]=16.000.000 (TRRussia –TCRussia) = [(QxP) – (QxMC)]=[(4.000x5.000)-(4.000x1000)]=16.000.000 Istituzioni di economia 2002/2003 corso C

  19. US strategies Low tariff High tariff US 25 billion US 30 billion Low tariff Mexico 25 billion Mexico 10 billion Mexico stragies US 10 billion US 20 billion High tariff Mexico 30 billion Mexico 20 billion Exercise n.5 pag.302 Consider the trade relationships between US and Mexico. Suppose that the government leaders are convinced that the results of alternative trade agreements are the following: Istituzioni di economia 2002/2003 corso C

  20. Which is the dominant strategy for US? And for Mexico? • Define a Nash equilibrium. Which is the Nash equilibrium for the trade policy? • In 1933 the US Congress signed the North American Free Trade Agreement (NAFTA), with wich US and Mexico agreed on a simultaneous reduction of trade barriers. Do the gains depicted in the table justify such an agreement? • On the base of your knowledge about the benefits of free trade (see chapters 3 and 9), do you believe that gains reported in the table correctly reflect the welfare of a country in the four possible situations? Istituzioni di economia 2002/2003 corso C

  21. Which is the dominant strategy for US? And for Mexico? From the point of view of the US If Mexico chooses low tariffs, the US should fix high tariffs, since they gain 30 instead of 25 (with a low tariff). If Mexico chooses high tariffs, the US should fix high tariffs, since they gain 20 billion instead of 10 (with a low tariff). Whatever the choice of Mexico, the US have a best strategy: the imposition of a high tariff. This is a dominant strategy for the US. From the point of view of Mexico If the US choose low tariffs, Mexico should fix high tariffs, since it gains 30 instead of 25 (with a low tariff). If the US choose high tariffs, Mexico should fix high tariffs, since it gains 20 billion instead of 10 (with a low tariff). Whatever the choice of the US, Mexico has a best strategy: the imposition of a high tariff. This is a dominant strategy for Mexico. Istituzioni di economia 2002/2003 corso C

  22. b) Define a Nash equilibrium. Which is the Nash equilibrium for the trade policy? A Nash equilibrium is a situation in which economic players interact reciprocally so that each firm selects its optimal strategy, given the strategies chosen by rivals. If an equilibrium is reached, no player has an incentive to change its choice. In this specific case, the strategic combination which corresponds to a Nash equilibrium is high tariffs for both countries with a gain of 20 each. c) In 1933 the US Congress signed the North American Free Trade Agreement (NAFTA), with wich US and Mexico agreed on a simultaneous reduction of trade barriers. Do the gains depicted in the table justify such an agreement? The NAFTA agreement represents a cooperative solution for both countries. The choice of low tariffs allows both Mexico and the US to reach a better result with respect to the Nash equilibrium: in fact they gain 25 billion each instead of 20. Istituzioni di economia 2002/2003 corso C

  23. d) On the base of your knowledge about the benefits of free trade (see chapters 3 and 9), do you believe that gains reported in the table correctly reflect the welfare of a country in the four possible situations? The low tariff-low tariff combination represents a welfare improvement with respect to the high tariff-high tariff combination. In fact tariffs are a barrier to international trade, and, as has been seen in the preceding chapters, a free international trade always bring benefits to both countries (even if not all individals within a country improve their personal positions). The results of the other two combinations low tariff- high tariff and high tariff-low tariff can be beneficial for some individuals (for example high tariff are beneficial for the producer’s surplus) but they are detrimental for the surplus of other individuals (for example consumers) and for the society as a whole. Istituzioni di economia 2002/2003 corso C

  24. Pratice Exercise: A firm in a monopolistic competition situation is characterised by the following data: • Quantity manufactured = 1000 units • Price = 150€ • Marginal Cost = 75€ • Marginal Revenue = 100€ • Total Costs = 200.000€ • Fixed Costs = 60.000€ In the short run, in order to maximize profits or minimize losses, what should the firm do? Istituzioni di economia 2002/2003 corso C

  25. In the short run, in order to maximize profits or minimize losses, what should the firm do? • Interrupt the production • Decrease the quantity and increase the price • Keep producing 1000 units but increase the price • Keep both quantity and prices at the initial levels • Increase the quantity and decrease the price Correct Answer: e) Istituzioni di economia 2002/2003 corso C

  26. A firm in a monopolistic competition market manufactures 5000 units in long run equilibrium. Price is 50€ and marginal revenue is 5€ • The marginal cost of the 5000th unit is equal to: • 5€ • 50€ • 25000€ • 250.000€ • Equal to the Total Average Cost Correct Answer: a) Istituzioni di economia 2002/2003 corso C

  27. The Total Average Cost is: • At the minimum and equal to 50€ • Above the minimum and equal to 50€ • At the minimum and equal to 5€ • Above the minimum and equal to 5€ • Nothing can be said Correct Answer: b Istituzioni di economia 2002/2003 corso C

  28. Problem n.4 pag. 316 • Scintilla is one of the large number of firms active in the toothpaste industry and is in a long run equilibrium situation. • Draw a graph that contains the demand curve for Scintilla, its marginal cost, total average cost and marginal revenue curves. Show the quantity and price that maximize its profits. • Which is the profit level for Scintilla? Why? • Show in the graph the consumer surplus and the relative deadweight loss. • If the State obliges Scintilla to manufacture the efficient quantity of toothpaste, what will happen to the firm? What will happen to customers? Istituzioni di economia 2002/2003 corso C

  29. a) Draw a graph that contains the demand curve for Scintilla, its marginal cost, total average cost and marginal revenue curves. Show the quantity and price that maximize its profits. In long run equilibrium the profit maximizing condition, for a firm in a monopolistic competitive market is: MC = MR, The equilibrium quantity is Q1 and the relative price is P1 (see the graph in the next slide) Istituzioni di economia 2002/2003 corso C

  30. Long run equilibrium Price Cost Revenue MC ATC A B P1 C Ce P2 Pe MC = Price D MC = MR Demand Marginal Revenue Q1 Q2 Qefficient Quantity Istituzioni di economia 2002/2003 corso C

  31. Which is the profit level for Scintilla? Why? The profit of Scintilla, in long run equilibrium, is zero since the total average cost is equal to the price (the average revenue). Thus TR = TC and Profit = TR-TC = 0 c) Show in the graph the consumer surplus and the relative deadweight loss. The consumer surplus is represented by the area (A+B), the deadweight loss by the area (C+D). The deadweight loss is evaluated with respect to the surplus that will be gained in the socially optimal situation, when the condition MC=Price is respected, and the equilibrium quantity and price are respectively Q2 and P2. Istituzioni di economia 2002/2003 corso C

  32. d) If the State obliges Scintilla to manufacture the efficient quantity of toothpaste, what will happen to the firm? What will happen to customers? The efficient quantity is Qe,, for which the condition MC = ATC holds (the marginal cost curve meets the average total cost curve in the minimum point of the latter). The corresponding price is Pe , which is less than the total average cost Ce If the State obliges Scintilla to manufacture the efficient quantity (i.e. the quantity which minimizes average total costs) of toothpaste, average costs would be well above the price, Scintilla would lose money and would go bankrupt. The consumers would then lose the surplus they initially had (see the answer given to the previous question). Istituzioni di economia 2002/2003 corso C

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