Answers to the Take-Home Midterm Examination

Transcription

1 Answers to the Take-Home Midterm Examination Econ 111s Spring/Summer 2009 Economics Department, Queen s University Instructor: Jean-Denis Garon Posted: June 19 Here are the main elements of the answers. Careful explanations must have been provided. Credits will be given for any answer which makes sense and which is carefully explained. 1

2 PART A : TRUE/FALSE/UNCERTAIN QUESTIONS (30 marks) Explain why each of the following statements is True, False, or Uncertain according to economic principles. Use diagrams where appropriate. No credits will be given for unsupported answers. Every question must be answered to, and each one is worth 5 marks. 1. The imposition of a quota by the government in a free and competitive market necessarily leads to a loss of economic surplus. Answer: False. In most cases it does, but not necessarily, and it depends whether the quota is binding or not. For example, if the quota is set at a quantity higher than the free-market equilibrium one, it has no effect. If it is below, it does. 2. Bob and Michael go to a full-service gas station. Each week, Bob asks for $20 of gas, and Michael asks for 20 liters of gas. Michael s demand function for gas is more elastic with respect to price than Bob s. Answer: False. Michael demands the same quantity, whatever the price, so his demand is inelastic. Bob s quantity is 20$/p where p is the price of a liter, and it depends on the price. Consequently, Bob s demand is more elastic than Michael s. Be careful: Michael s demand can be considered as perfectly inelastic. However, Bob s is not infinitely elastic, but it is downward sloping. 3. Suppose that the market for apples is competitive, and that neither demand nor supply are perfectly inelastic. If a per-unit tax is imposed on apples, the loss of consumer surplus will be greater than the loss of producer surplus. Answer: Uncertain. It depends on the relative elasticities of supply and demand. The more elastic is the demand relative to the supply, the greater is the loss in producer surplus relative to consumer surplus. 4. The income effect always leads consumers to buy more of a product whose price has fallen. Answer: False. Although the statement is true in most cases, it does not hold for Giffen goods. Just saying that the statement is true when the good is a normal one is incomplete. If goods are not normal, they can be either Giffen or Inferior. It turns out that all Giffen goods are inferior, but that not all inferior goods are Giffen. Also, inferior goods refer to changes in consumed quantities when income changes, and Giffen goods refer to what happens when prices change, which is the case here. 5. The following table shows cost of producing cars and flu vaccines in Canada and Mexico. Assume that both countries trade based on the principle of comparative advantage. We would expect Canada to import cars and to export flu vaccines. Table 1: Cost of producing cars and vaccines Cars Flu vaccines Canada $ 11$ Mexico $ 8$ Answer: False. We can see that Mexico has an absolute advantage in producing both goods. However, the opportunity cost of producing cars is lower in Canada. That is why producing a car is 2.5 times as costly as producing vaccines in Mexico, and 2 times more costly in Canada. As a result, we expect Canada to export cars and import vaccines. Note that the question is asked differently than in past years exams. The number in the table refer to costs, not to quantities, so you really have to refer to the concept of opportunity costs to get full credits. 2

3 6. Barack is a young U.S. President who has to allocate his present income I between current and future consumption, since he thinks he might not earn any money in four years. His savings yield the market interest rate r. (This means that if he saves s, he will be able to consume s(1 + r) after his Presidency). If the interest rate increases, then Barack will reduce his savings. Answer: Uncertain. He might raise or lower his savings, depending on the income and substitution effects. See the supplementary section for entire explanation. If well explained, I give credit if you wrote that it is false, and if you explain carefully that you consider that consumption is a normal good. In that case, he increases his savings. 3

4 PART B: PROBLEM SOLVING AND LONGER ANSWERS (30 marks) Read each part of the question very carefully. Answer all parts of the questions and show all steps of your calculations to get full credits. Each sub-question has to be answered to and has equal value. The domestic market demand and supply for swine flu vaccines are given by Q s = P Q d = P, where P is the price of one dose of vaccine in dollars and Q s are quantities, in number of doses. 1. Graph the supply and demand curves. Identify the P and Q intercepts for the demand curve, and only the P intercept for the supply curve. Show the equilibrium on the graph (note that a competitive equilibrium always consists of a price and quantity). Calculate the consumer and producer surpluses, and clearly identify these areas on the graph. Answer: First, you have to find the inverse supply curve. It is given by p s = q s / /3. You will see that there is a negative part, and since the price cannot be zero, you do not have to put that part on your figure. The demand curve is given by p d = 45/7 q d /7000. Setting equal these two equations, i.e. p s = p d, setting q s = q d = q gives the equilibrium quantity q = vaccines. Plugging that quantity into the inverse supply function gives p (q ) = 2. You can verify your answer by inserting the quantity into the inverse demand curve as well. Notice that the intercept of the inverse demand function (i.e. when q s = 0) equals 45/7. As a result, the consumer s surplus equals CS = (45/7 p ) q /2 = /14 = /7, or if you prefer CS = Graphically, the consumer surplus is given by area a b f of figure 1. Finding the producer s surplus is slightly more complicated, since you must not take into account the negative part of the curve. When p = 0, the inverse supply curve crosses the horizontal axis at q = The producer surplus is then P S = p ( )/ = = Graphically, it is the area e d b f in figure 1. Note, for further use, that the total surplus is At the equilibrium point found in part 1., calculate the price-elasticities of the supply and demand. Is the supply elastic or inelastic at that point? What about the demand? Answer: Because we are working at a single point, we use the point method. For the supply, we have that e S = (1/slope) P/Q,and it is the same for demand but you add a negative sign before so that we get it in absolute values. The slope of the supply curve is 1/3000, so the elasticity is /31000 = 6/31 = It is inelastic since it is smaller than one. The slope of the demand curve is 1/7000 so the elasticity is /31000 = 14/31 = Both are inelastic, but supply is more inelastic (or less elastic) than demand. 3. Suppose that an unanticipated swine flu pandemic occurs. The domestic demand function then becomes Q d = P. Plot the supply and demand curves on a new diagram, in the same way as you did in part 1. Using the concepts of consumer and producer surpluses, determine if the increase in welfare (compared 4

5 to the equilibrium of part 1) has been larger for the producer than for the consumer. Are these variations related to the price-elasticities of supply and demand? Answer: First, you must find the new equilibrium. The inverse supply curve is still the same: p s = q s / /3. The inverse demand curve is now given by p d = 55/7 q d /7000. Setting equal these two equations, i.e. p s = p d, setting q s = q d = q gives the equilibrium quantity q = vaccines. Plugging that quantity into the inverse supply function gives p (q ) = 3. Then, you must find the new consumer and producer surplus. The way to do it is the same as previously, so I do not provide a full graph. The consumer surplus is equal to (55/7 3) 34000/2 = /14 = So the consumer surplus has risen. I accept some close approximations of it. But for the future, remember that when you play with such large numbers, you can easily get far from actual answers when approximating fractions up to one decimal... Here again, the producer surplus has a trapezoid shape. The rectangular part is and the triangular one is ( ) 3/2 = = So the producer s surplus is now , and has also increased. In general, we should observe that the more elastic is demand comparatively to supply, than the larger must be the increase in consumer surplus comparatively to producer surplus. You did not have to say more than that on this point. However, if you worked the question further, you will have seen that the increase in producer surplus is larger than consumer s, and you may find that it is unintuitive. The reason is that only demand moved. (You ll see that if you play a little bit on the graph). However, if the change were, for example, the appearance of a tax, then we should have observed that the variations in surplus followed that intuition. 4. Using the midpoint method, calculate the price-elasticity of the supply function between the equilibrium point that you have found in part 1 and the new equilibrium found in part 3. What conclusions can be drawn if we compare it with price-elasticity of supply found in part 2? Answer: The price has passed from 2 to 3, and the quantity from to For the elasticity of supply, we have that ɛ S = (q 1 q 0 )/(q 1 +q 0 )/2 (p 1 p 0 )/(p 1 +p 0 )/2 = (3000/32500)/(1/2.5) = We see that it is different, since the mid-point method is just an approximation of the point method between two points, but that we can still conclude that the supply is inelastic since it is smaller than one. It is also noteworthy that both calculated elasticities are very close. 5. Let s get back to the original supply and demand functions: Q s = P Q d = P. Suppose that the government imposes sales tax of $0.50 on each dose of vaccine. Solve for the new equilibrium. What is the new producer price? What is the new consumer price? Answer: First, let us find the equilibrium. Since it is a sales tax, the new consumer price will be p + t where t = 0.5. So, to find the equilibrium, we just have to equalize supply with the following demand: Q d = (p + t), where p is the new producer price and p + t is the new consumer price. We get p = ( t)/10000 = ( )/10000 = 1.65 which stands as the new producer price. This means that for each unit sold, the producer keeps $1.65. The new consumer price is $2.15. We then observe that the consumer price increases by less than the value of the tax, and it may be attributed to the fact that demand is more elastic than supply. The new quantity which will be produced is We get it by inserting the producer price into the supply, or by inserting the consumer price into demand. It is important here to understand that because there is a tax, consumers and producer do not face the same price on the market. 5

6 6. Let Q be the equilibrium quantity found in part 1 of this question. Suppose that you are the main economic adviser to the Minister of Finance, and that he tells you that raising a sales tax of $0.50 on each dose of vaccine would generate a revenue of R = Q $0.50 to his government. Is the Minister is right or wrong on that issue? Answer: The minister is wrong on that issue. The reason is that when we impose a tax, it also changes the equilibrium quantities because of the distortion caused by the tax. When he calculates the revenue generated by the tax, he should calculate the amount of the tax times the new quantity, which is lower. 6

7 P Figure 1: Equilibrium B a S 1/7000 1/ f g b e d c D Q 7