ECONOMICS I ACADEMIC YEAR TUTORIAL 2 Market Equilibrium, Elasticity TA: ANDREA VENEGONI

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1 ECONOMICS I ACADEMIC YEAR TUTORIAL 2 Market Equilibrium, Elasticity TA: ANDREA VENEGONI 1.Elasticity Suppose the current price of IPADs (wireless version) in the US is $300, the average consumer has disposable income of $30,000 per year and the annual US demand for IPADs is 5 million per year. Apple s statistical studies estimate the price elasticity of demand for IPADs to be 1.3 (point formula). Now suppose that due to increasing competition from Samsung, Apple (uncharacteristically) reduces the price of IPADs to $270. a. Is the demand for IPADs elastic or inelastic? Please explain what is meant by this term, i.e. what does it mean for the demand for IPADs to be elastic or inelastic? b. Calculate the amount of IPADs sold in the US after the drop in price. Answer: a. The demand for IPADs in this market is elastic because the value of the elasticity is greater than 1 (in absolute terms, i.e. ignoring the sign). This means that a 1 percent change in the price of IPADs results in a more than 1 percent change in the quantity demanded. Because the sign is negative, the relationship is an inverse one, i.e. an increase in the price will result in a decrease in the quantity demanded and a decrease in the price will result in an increase in the quantity demanded. b. We know that the elasticity of demand is 1.3. That is, a 1 % increase/decrease in price will result in a 1.3% decrease/increase in quantity demanded. In this problem, the price of IPADs declined from $300 to $270, that is by 10%. Therefore, with an elasticity of 1.3, this means that the quantity demanded will increase by 13% (10% * 1.3). That is, the 10% fall in the price of IPADs results in a 13% increase in the quantity of IPADs demanded. Since the original amount demanded was 5 million, the new quantity demanded at the lower price will be 5 million * (1.13) = 5.65 million IPADs. Note: the information regarding the average consumer s disposable income was not necessary to solving this problem. 2. Elasticity Giovanni, the owner of Bar Castellanza notices that most of the students eating in his establishment order the fixed menu of pizza + drink + coffee for 10. He decides to increase the price of the fixed menu to 11. As a result, the quantity of fixed meals sold per week falls from 1000 to 800. a. Calculate the elasticity of demand for fixed meals using the point formula (at the original price and quantity). b. Calculate the impact of the price increase on Giovanni s revenues. Do they go up or down? c. One day a group of students from Professor Della Valle s class come in for lunch and tell him that he will make more money if he cuts the price of prix fixe meals because the increase in sales will more than make up for the reduction in price. Based on the estimate of elasticity calculated in (a) above (without doing any calculations) are they right? d. Using the point elasticity calculated in (a) above, estimate the total amount of prix fixe meals that will be demanded and total revenues per week if the price were to be reduced from 10 to 8. Answer: a. POINT FORMULA Price: Increases from 10 to 11

2 Quantity: Declines from 800 to 600 Ed = ( )/1000 = (-200)/1000 = (11-10)/10 1/10 = (-200)*10 1*1000 = -2 b. Revenues before the price increase: 1000 * 10 = Revenues after the price increase: 800 * 11 = 8800 So, the price increase results in a decline in Giovanni s revenues. c. Yes, they are right. Since demand is elastic, a decrease in price will result in an increase in revenue (because elastic demand implies that the % increase in quantity demanded will be greater than the % decline in price). d. Recall that the elasticity formula can be rewritten as: % Q Q / Q Q P E d * % P P / P P Q Substituting the values from the problem into the formula yields: Ed = -2 P = - 2 (from 10 to 8) P = 10 Q = 1000 Thus: -2 = ( Q/-$2) * 10/1000 Solving for Q yields: -2 = Q * 10/(-2 *1000) Q = -2 * -(2000/10) Q = prix fixe meals Therefore, as a result of the price cut, total prix fixe meals sold will be = 1400 per week. Revenues with the price cut will be 1400* 8 = 11,200 /week Note: Quicker way to calculate the change in quantity as a result of the change in price: A point elasticity of demand of 2 implies that a 1% change in price will result in a 2% change in quantity demanded. In this case, price declines from 10 to 8. That corresponds to an 20% decline in price ( 2/10). Therefore, quantity should increase by 20 * 2 = 40% from the original level of 1000, i.e *.40 = 400 fixed meals. Thus, with the price cuts, total fixed meals increases by 400 to ( = 1400 meals/week Total revenues increase to (1400 * 8) = 11, Demand and Supply, Price Elasticity, Price floors Jim Bean, performed an analysis for the liquor market in Australia in It displayed these demand and supply functions:

3 Liquor demand Qd = 16-3P. Liquor supply Qs = P. Where P is the price per litre and Q is millions of liquor litres sold. a. Calculate the equilibrium price P* and quantity Q* of liquor in Australia. To compute equilibrium price and quantity we have to recall the equilibrium condition of each market that is given by Qd=Qs. Knowing that we can write the following equation: 16 3P = 8 + 5P Solving for P we get: = 3P + 5P And hence, inverting the two sides: 8P = 24 From which we can easily compute that: P = 24/8 and hence P*=3 To compute now equilibrium quantity (Q*) we substitute the equilibrium price (P*) in either the demand or the supply expression. Let s choose this time the demand expression, we get: Q=16-3=13 So, knowing that under equilibrium condition Qd=Qs=Q* we can conclude that the equilibrium quantity (Q*) is equal to 8. Summarizing we have: P*=3 Q*=13 b. Plot the demand and supply equations and show the equilibrium outcome. 16 Qs 4 1, Part 2 Let s reconsider the demand and supply functions under a more correct estimation. Liquor demand Qd = 16 - P. Liquor supply Qs = P. Calculate new Price and Quantity of equilibrium and the new demand elasticity To compute equilibrium price and quantity we have to recall the equilibrium condition of each market that is given by Qd=Qs. Knowing that we can write the following equation: 16 P = 8 + 5P Solving for P we get: Qd

4 And hence, inverting the two sides: = P + 5P 6P = 24 From which we can easily compute that: P = 24/6 and hence P*=4 To compute now equilibrium quantity (Q*) we substitute the equilibrium price (P*) in either the demand or the supply expression. Let s choose this time the demand expression, we get: Q=16-4=12 So, knowing that under equilibrium condition Qd=Qs=Q* we can conclude that the equilibrium quantity (Q*) is equal to 12. Summarizing we have: P*=4 Q*=12 Jim Bean considers a raise in the price by 1 dollar from the equilibrium price. Calculate the litres of liquor that would be demanded (and sold) after the price increase. Recall that ε d = ΔQ/Q and hence, using some standard algebra, can be derived that ε ΔP/P d = ΔQ P ΔP Q Knowing that the coefficient that multiplies both in the demand and in the supply expressions the price tells us how much quantity varies after a decrease in price (in other words it is equal to ΔQ ) we ΔP can compute demand elasticity as: ε d = 1 4 = So now we know that demand elasticity is equal to -1/3, hence we can claim that demand for liquor in this market is inelastic ( ε d < 1) Knowing the demand elasticity, and exploting its formula, we can now compute the demand variation after an increase in price of 1$ as follows. Recall that: ε d = ΔQ/Q. If we want to compute ΔQ we have just to substitute the other variables ΔP/P with their values obtaining: 1 = ΔQ/8. 3 1/4 Solving now for ΔQ we have: 1 = 4ΔQ and then 1 = 4 ΔQ Going onwards: ΔQ = 1 8 = 1 2 = So finally, we can say that ΔQ = 2 and so that quantity demanded will decrease by 0.6, becoming 3 equal to b. Calculate the new level of revenues as a result of the price increase. Has it increased or decreased? Revenues are computed as price multiplied by quantity (R=P*Q) Substituting with our data we have P*=4 and Q*=12, hence: R 0 =4*12=48 If the price was to increase by 1$ we would have: (P 1 = 5, Q 1 = 11.4). R 1 = = 57

5 After a 1$ price increase, Jim Beans revenues rise by 9$. c. Are the elasticity estimation coherent with the change in revenues Yes they are! As expected, when demand is inelastic (as is in this case), a price increase generates an increase in revenues. Elasticity (10 pts.) Politician P is considering proposals to raise some tax revenues in his jurisdiction. He is considering whether to impose a new 10% tax on the price of cigarettes or on movie theatre tickets. He hires you to advise him on the issue. Specifically, he asks you estimate which tax will raise greater tax revenues. In order to evaluate the situation, you tell him that you need the following information, which his staff provides to you: Cigarettes: Total annual sales revenues: $50 million Average current price: $5/pack Estimated elasticity of demand: -.8 Movie tickets: Total annual sales revenues: $80 million Average current price: $8/ticket Estimated elasticity of demand: -1.2 Given this information, calculate the estimated amount of tax revenues raised by taxing cigarettes versus movie tickets. Which raises more tax revenues and, therefore, on which of the two goods would you advise him to impose the tax? Base your answer exclusively on the estimated tax revenues and not on other factors which may influence your choice of which good should be taxed. For simplicity, assume the tax does not cause the demand curve to shift or tilt. It only results in a movement along the curve. Answer: Your problem is to estimate what happens to total sales as a result of a 10% increase in the price of cigarettes and movie tickets, respectively. You have all the information you need to do that. You can use the formula for elasticity of demand to estimate what happens to the quantity demanded when the tax is added to the price (i.e. the price increases by 10%.) Recall: % Q E d % P Therefore, we can calculate % Q E *% P d We know that Ed = -.8 and % P = 10% So, % Q = -.8 * 10% = - 8%

6 That is, quantity decreases by 8 % from the original level of sales before the imposition of the tax. That level was 10 million packs per year ($50 million in sales/$5/pack = 10 million packs). Therefore total cigarette sales decline by.8 * 10 million = 800,000 per year. The new quantity after the imposition of the tax is therefore 10 million 800,000 = 9.2 million packs of cigarettes. Since the tax is 10%, this amounts to a tax of $0.50 per pack. Total tax revenues = Estimated packs of cigarettes sold with the tax * tax/pack Total tax revenues = 9.2 million * $0.50 = $4.6 million Therefore, total tax revenues from a 10% tax on cigarettes = $4.6 million. % Q E d % P Therefore, we can calculate % Q E *% P d We know that Ed = -1.2 and % P = 10% So, % Q = -1.2 * 10% = -12% That is, quantity decreases by 12 % from the original level of sales before the imposition of the tax. That level was 10 million movie tickets per year ($80 million in sales/$8/ticket = 10 million tickets). Therefore total movie ticket sales decline by.12 * 10 million = 1,200,000 per year. The new quantity after the imposition of the tax increase is therefore 10 million 1.2 million = 8.8 million movie tickets. Since the tax is 10%, this amounts to a tax of $0.80 per ticket. Total tax revenues = Estimated movie tickets sold with the tax * tax/ticket Total tax revenues = 8.8 million * $0.80 = $7.04 million Therefore, total tax revenues from a 10% tax on movie tickets = $7.04 million. In view of these results, you would advise politician P to impose the 10% tax on movie theatre tickets.