Effects of the Subsidy - Essay Example

Part I: Short Questions Exercise 2: First-Time Homebuyers Credit a. Effects of the subsidy A subsidy has a huge impact on the market as it reduces the price paid by buyers and thus increasing the quantities sold. The subsidy of $8,000 received by all first time homebuyers in US will therefore lead to a reduction in the price paid by the buyers but will lead to an increase in the price received by the producers. Subsides are pareto efficient as they cost more than they deliver benefits. For example, a market without a subsidy will reach equilibrium at the point where the demand curve intersects the pre-tax supply curve. Let’s assume that the price is P and the quantity is Q. The subsidy by the government will shift the supply curve downwards by the subsidy amount. The price paid by the buyers for the homes will fall from P to Ps, that is from $167,000 to $ 159,000 while the one to the suppliers will increase to Ps’ that is from $167,000 to $174,000. The quantity supplied will then increase from Q to Qs. In the graph below, the cost of subsidy to the government is shown. The graph clearly shows a negative balance which is the cost of the subsidy which is always greater than the benefits enjoyed by the producers and the consumers. The deadweight loss of the subsidy is the amount by which the subsidy costs exceeds the gains in the producer and consumer surpluses. The deadweight loss magnitude depends on the subsidy amount as well as the change in the production which results from the subsidy Deadweight loss = ½ (amount of the subsidy) * ∆Q b. Own price elasticity of demand = percentage change in the quantity demanded/ percentage change in price The percentage increase in sales will represent the percentage change of the quantity demanded. Therefore, own price elasticity of demand will be: 7.6% / 4% =1.9 an indication of how the demand for homes is price elastic Own price elasticity of supply = percentage change in the quantity supplied/ percentage change in price In this case, the rise in sales represents the percentage change in the quantity supplied while the rise in price is the change in price. Therefore the price elasticity of demand will be: 7.6% / 4% =1.9 an indication of how the supply for homes is price elastic c. Who gained more between the buyers and the sellers The benefits obtained from the subsidy are usually shared by the producers and the consumers in a proportion which depend on the relative slopes of supply and demand functions. However, the buyers gain more than the suppliers as the subsidy lowers prices to buyers and increases the price to the sellers. Exercise 2: Oligopoly Production function of Marton’s Meat and Kostas Kutters is given by qM = L0.6K0.4 ;qK = L0.5 K0.5 ;r= $5, capital = $10. The market demand Q=225 – 9p 2.1 Collusion Imagine that the two firms ‘collude’, they form a cartel. (a) Calculate the market output, market price and the output from each firm as well as the profit for the cartel. Explain. Output for each firm Marton’s Meat Kostas Kutters qM = L0.6K0.4 qK = L0.5 K0.5 Q= 225 -9P qK = 7.1 qM = 6.6 Market output Marton’s Meat Kostas Kutters Q=225 – 9p Q=225 – 9p Q= 225- 9(6.6) Q= 225- 9(7.1) Q= 165.6 units Q=161.1 units Market price Marton’s Meat Kostas Kutters Q=225 – 9p Q=225 – 9p 9P = 225-Q 9P = 225-Q P = (225-156.6)/9 P = (225-161.1)/9 P= 7.6 P=7.1 Total profit for the cartel P= 25-0.11 Q Total Revenue = P XQ = (25-0.11 Q) Q TR = 25Q-0.11Q2 Marginal Revenue is obtained by differentiating TR MR= 25-0.22Q MR =MC 25-0.22Q =0 Market output Q= 113.6 units Market Price for each firm P= 25-0.11 (113.6) =25-12.5 =12.5 The Profit for each firm will be 1,420 and this makes a total profit of 2,840. 2.2 Cournot equilibrium Assuming that the two firms do not collude but compete on quantities à la Cournot; (b) What are the two firms’ best response functions? Show you calculations. Q=225 – 9p P =25-0.11Q Q1= (25 -9 -2Q1)/2 X0.11 Q1= 16/2-2Q1/2.2 Q1=8 –Q1 Q for Marton’s Meat (c) Calculate the market output, market price and the output from each firm as well as the profit for the firms P= 25-0.11 Q Total Revenue = P XQ = (25-0.11 Q) Q1 TR = (25 – (0.11Q1+0.11Q2) X Q1 = 25Q1 –Q12 –Q2 XQ1 MR = 25 -2Q1-Q2 =9 Q1= 8- Q2/2 Marginal Revenue is obtained by differentiating TR MR= 25-0.22Q MR =MC 25-0.22Q =0 Market output Q= 113.6 units Cournot Equilibrium = 113.6 /2=56.8 units 2.4 Bertrand Competition with identical products Assuming the two firms compete on prices à la Bertrand with the production function and factor prices remaining the same: qM = L0.6K0.4 ;qK = L0.5 K0.5 ;the wage rate is $5 and the rental rate of capital is $10. (e) In Bertrand equilibrium, there no equilibrium in profit and there is no Bertrand equilibrium in price in this case as both firms cannot increase its profits by changing its prices either by reduction or increase in the prices. If one of the firms increases it price above the market level, then it would lose its sales to the other firm and vice versa. Competition on the basis of prices would make the two firms to continue staying in the same market. Price rigidity is a characteristic in oligopoly and rarely do prices change. The sellers or the firms are few in the market and this makes it easy for one firm to become aware of how its rival firm will behave to any likely change in price. 2.4 Bertrand Competition with differentiated products Assuming that the two firms are competing on prices à la Bertrand, and MCK = MCM = ACK = ACM =10. The two firms also sell the same products with a market demand of Q=225 – 9p (f) Bertrand equilibrium price and the market equilibrium quantity? The assumption here is that the firms usually set their prices, sell products which are differentiated, they are simultaneous and are non-cooperative. Q=225 – 9p MC1=MC2=10 MR= 25-0.22Q 25-0.22Q = 10 0.22Q=15 Q= 68.2 Units P=25-0.11 Q P= 17.5 (g) Assuming that the two firms have the same price level, the output and profit will be: Output for each firm Marton’s Meat Kostas Kutters qM = L0.6K0.4 qK = L0.5 K0.5 Q= 225 -9P qK = 7.1 qM = 6.6 Profit = 6.6 x17.5= 115.5 Profit = 7.1x17.5= 124.25 Now MM successfully lobbies in parliament to obtain the “True Hungarian” product label1, thereby differentiating its products from KK’s. As a result the demand functions facing the two firms now are: QM=145 – 6pM + 9pK and QK=100 – 9pK + 6pM (h) Bertrand equilibrium prices and the quantities QM=145 – 6pM + 9pK 9pK = -145 + 6pM + QM pK = -16.1+0.66 pM +0.11 QM……………………………….(i) QK=100 – 9pK + 6pM 9pK = 100- QK + 6pM pK= 11.1- 0.11 QK+0.67 pM………………………………….(ii) Equilibrium quantities and prices Equate equation 1 with equation 2 11.1- 0.11 QK+0.67 pM=-16.1+0.66 pM +0.11 QM 11.1- 0.11(7.1) +0.67 pM= -16.1+0.66 pM +0.11(6.6) 10.319 +0.67 pM= -15.374 +0.66 pM 5.055=-0.01 pM pM =505.5 pK= 349.0 QM =253units (i) Was it worth it for MM to obtain the “True Hungarian” product label (compare with the undifferentiated products case)? How much is the maximum amount that MM is willing ‘contribute’ to the ruling party’s re-election campaign (in order to ensure that they can keep the label)? (j) Are KK hurt by MM obtaining the “True Hungarian” label? Why or why not? Read More