Government Intervention - Taxes and Subsidies (SOLUTIONS)

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1 Government Intervention - Taxes and Subsidies (SOLUTIONS) (HL Economics - Messere) 1. a) Price ($) Qd = 0 2P Qs = P Price ($) Supply Demand b) Setting Qd = Qs and solving for P: 0 2P = P 150 = 6P 25 = P Then substituting 25 for P in either (or both) equations and solving for Q: Qd = 0 2P or Qs = P Qd = 0 2(25) Qs = Qd = 50 Qs = 50 Confirming that at the equilibrium price $25, the Qd and Qs are both 50 as suggested by the graph. Page 1

2 c) Looking at the graph, we are looking at a welfare triangle that looks like: P=50 (50, 25) P = 12.5 We can confirm the y-intercepts suggested by the graph algebraically as follows: To find the y-intercept of the demand curve, find the price when the quantity is set to 0. Qd = 0 2P 0 = 0 2P 2P = 0 P = 50 T o find the y-intercept of the supply curve, find the price when the quantity is set to 0. Qs = P 0 = P 50 = 4P 12.5 = P Thus, the consumer surplus is the area represented by the following triangle: P = 50 P = 25 (50, 25) A = ½ (50) * 25 A = 625, so the consumer surplus is $625 Meanwhile, the producer surplus is the area represented by the following triangle: P = 25 (50, 25) P = 12.5 A = ½ (50) * 12.5 A = 312.5, so the producer surplus is $ Page 2

3 d) Find the quantity demanded and the quantity supplied at P = 20 by plugging 20 into both equations and finding Q Qd = 0 2P Qd = 0 2 (20) Qd = 60 Qs = P Qs = (20) Qs = 30 As quantity demanded is 60 while quantity supplied is 30, there is an excess demand of 30 units at a price of $20. e) I can easily tell how many units people will want to buy at a price of zero, as that is told to me by the fixed term in the demand function. For example, using the demand function Qd = 0 2P, I can easily see that at a price of zero, Qd = 0, as Qd = 0 2(0). While it is not so easy to find the price at which sellers will begin to bring the good to market, as that requires me to find the price when quantity is equal to zero, it is not difficult. Again using our supply function, just set Q = 0 and solve for P, as in 0 = P 50 = 4P 12.5 = P f) The demand function should get flatter, as the slope coefficient will have gotten larger. The quantity demanded has become more responsive to changes in price. For instance, looking at our demand function, if it were Qd = 0 4P, a drop in price of $1 would result in 4 more units being demanded, not 2. Similarly, the supply function would become flatter, as its slope coefficient would have also gotten larger as the quantity supplied is now more responsive to changes in price. For instance, looking at our supply function, if it were Qs = P, a price increase of $1 would bring 8 more units to market instead of just 4. Page 3

4 2. a) Price ($) Supply with $5 tax Supply Demand b) The equilibrium market price appears to have risen to around $28 (from $25) while the quantity sold has fallen to around 43 units (from 50). To find the new equilibrium point algebraically, it would be necessary to first derive the new (post-tax) supply curve. If the tax has shifted the supply curve up $5, and if the slope of the supply curve is 4, then the translation of the curve $5 higher would suggest that the x-intercept of the new curve would be 20 units further to the left. Thus, the post-tax supply curve function would be Qs = P. To find the new equilibrium point, simply set Qd = Qs and solve for P P = 0 2P 6P = 170 P = 28.3 Which implies an equilibrium quantity of: Qd = 0 2P Qd = 0 2(28.3) Qd = 43.4 However, the answers that follow are calculated according to the equilibrium point (43, 28), as my reading of the syllabus suggests that students will not be expected to derive new supply curve functions resulting from the imposition of indirect, specific taxes. c) The government has earned $5 on each of the 43 units sold, so $215. Page 4

5 The consumer surplus is the area of the following triangle: P = 50 P = 28 (43, 28) So, as A = ½ (43) * 22 A = 473 so the consumer surplus is $473. The producer surplus is the area of the following triangle at right (remember that the $5 tax comes between the price consumers pay ($28) and what producers receive ($23): P = 23 (43, 23) P = 12.5 So, as A = ½ (43) *.5 A = so the producer surplus is $ Comparing the sum of these three figures ($215 + $473 + $ = $913.75) to the sum of producer and consumer surplus before the tax was imposed ($625 + $ = $937.50) we can see that the sum from part c is greater. Thus, we can conclude that the tax has led to a decrease in overall welfare of roughly $ d) Before the tax was applied, consumer expenditures and producer revenues were both (50 * $25) $1250. After the tax was applied, consumer expenditures were (43 * $28) $1204 while producer revenue was (43 * $23) $989. The difference between the two numbers ( ) was the tax collected by the government. In this case, the tax reduced both consumer expenditure (a little bit) and producer revenue (significantly). e) Well, as the initial price was $25, the fact that the price consumers pay rose to $28 while the price received by producers fell to $23 would suggest that consumers ended up paying $3 of the $5 tax while producers ended up paying the remaining $2. The reason the tax has been borne unevenly is that the price elasticity of demand is less than the price elasticity of supply around the old equilibrium price and quantity. To calculate: PED from (60, 20) to (40, 30) is: -(40 60)/60 = 0.33 = 0.66 (30-20)/ PES from (30, 20) to (70, 30) is (70-30)/30 = 1.33 = 2.66 (30-20)/ Page 5

6 The consumers end up paying more of the tax as their demand is less sensitive to price changes than is producer supply. Whoever is less likely to change their behavior in response to a price change will end up being hit with a greater price change whenever a tax is applied. Put more simply, whoever is less likely to duck is more likely to get hit. 3. a) Price ($) Supply Supply with $5 subsidy Demand b) The subsidy has increased the equilibrium quantity from 50 to 56 while decreasing the equilibrium price from $25 to $22. c) The consumer surplus associated with the new post-subsidy equilibrium point can be calculated by finding the area of the triangle under the demand curve from Q = 0 to Q = 56 from P = $22 to P = $50: A = ½ (56) * 28 A = 784, so the consumer surplus is $784 The producer surplus associated with the same equilibrium point can be calculated by finding the area of the triangle above the supply curve from Q = 0 to Q = 56 from P = $7.5 to P = $22: A = ½ (56) * 14.5 A = 406, so the producer surplus is $408 The initial producer and consumer surplus in question 1 were $625 and $312.50, so the subsidy has clearly had a positive effect on both consumer and producer surplus, and hence overall welfare. However, the subsidy did cost the government money, to the tune of $5 per unit for each of the 56 units produced, or $280. Page 6

7 d) After the subsidy was granted, consumers spent (56 * $22) $1232, while producers would have received (56 * $27) $1512. Recall that while consumers only pay $22, the amount going to the producers is that amount plus the amount of the subsidy. The difference between these two numbers is the cost of the subsidy to government ($ = $280). Comparing these figures to the initial consumer expenditure/producer revenue of ($25 * 50) $1250, we can see that the subsidy has resulted in a slight reduction in consumer expenditure and a significant increase in producer revenue. e) Comparing the initial equilibrium price of $25 with the post-subsidy equilibrium price of $22, we can see that $3 of the $5 subsidy has been transferred to consumers, whereas producers are only gaining $2 (recall that while the price is $22, producers are receiving $22 + $5 = $27). Consumers are enjoying a greater portion of the subsidy than producers due to consumers and producers having different responses to a change in price, as measured by PED and PES. As we saw in our answer to question 2 e), the price elasticity of demand around the initial equilibrium point is only 0.66 while the price elasticity of supply is What this means is that producers are more likely to increase output in response to a price increase than consumers are likely to increase purchases in response to a price drop. So, when faced with a subsidy, which has the effect of increasing the price paid to producers even while reducing the price paid by consumers, producers are more likely to increase output than consumers are to increase purchases. This being the case, the subsidy in this instance lowers consumer prices more than it increases producer prices Supply Demand Page 7