Discussion Worksheet Chapter 5 and Chapter 6 With Answers

Discussion Section Worksheet 5: Chapter 5 and 6 Review of Concepts: • • • • • • Price Elasticity of Demand Income Elasticity of Demand Cross-price Elasticity of Demand Price Elasticity of Supply Price Ceilings and Price Floors Taxes Practice Exercises: Short Answers Price Ceilings and Price Floors 1. Consider a market where demand is described by Qd = 20−P and supply is described by Qs = 2P−4. a. For what range of prices will a price floor be binding in this market? b. If the government set a price floor at $10, would there be a shortage or surplus, and how large would the shortage/surplus be? Answer: a. Price floor binds for all prices above the equilibrium price. Let us find equilibrium price: Qd = Qs 20 − P = 2P − 4 3P = 24 P = 24/3 = $8 Price floor above $8 is binding b. Price floor at $10 is binding. Qd = 20 − P = 20 − 10 = 10 Qs = 2P – 4 = 2*10 – 4 = 20 – 4 = 16 Surplus = Qs – Qd = 16 – 10 = 6 Taxes 2. Consider the market for watches where the market demand and market supply curves are given by the equations below where P is the price per watch unit and Q is the quantity of watches measured in watch units. Market Demand: P = 500 – 10Q Market Supply: P = 100 + (10/3)Q a. Given the above information, find the equilibrium price and quantity in this market. Suppose that the government in this economy decides to impose an excise tax of $50 per watch on producers of watches. b. Given this excise tax, write an equation that represents the supply curve in this market now that producers have this new additional cost. c. Given this excise tax, find the new price consumers will pay for a watch in this market, the new price producers will receive for a watch in this market once they have met their legal obligation to the government to remit the excise tax, and the new equilibrium quantity of watches that will be sold in this market. Answers: a. To find the equilibrium price and equilibrium quantity we set the demand equation equal to the supply equation: thus, 500 – 10Q = 100 + (10/3)Q 400 = 10Q + (10/3)Q 3(400) = 30Q + 10Q 3(400) = 40Q 30 watch units = Q Equilibrium quantity is 30 watches. P = 500 – 10Q = 500 – 10(30) = $200 per watch Or, P = 100 + (10/3)(30) = $200 Equilibrium price is $200 per watch b. The new supply curve that includes the excise tax will shift to the left of the original supply curve. The y-intercept of this new supply curve will be equal to the amount of the original y-intercept from the first supply curve plus the amount of the excise tax per unit: thus, the new supply curve with the excise tax will have y-intercept of 150. The new supply curve will be parallel to the original supply curve (same slopes) and thus can be written as Pt = 150 + (10/3)Qt where Pt is the price with the excise tax and Qt is the quantity of the good with the excise tax. Price for producers = Price for consumers – Tax = Pc – Tax = 100 + (10/3)Q + 50 = 150 + (10/3)Qt c. To find the new equilibrium quantity in the market for watches with the excise tax we need to equate the demand curve to the new market supply curve: thus, 500 – 10Qt = 150 + (10/3)Qt 350 = (10/3)Qt + 10Qt 3(350) = 10Qt + 30Qt 105/4 = Qt 26.25 watches = Qt After-tax equilibrium quantity is 26.25 watches. Price for consumers = Pc = 500 – 10Qt = 500 – 10*26.25 = 500 – 262.5 = $237.50 per watch Price for producers = Price for consumers – Tax = Pc – Tax = 237.50 – 50 = $187.50 per watch Elasticity 3. The price of shirts fell from $23 to $9. The quantity supplied fell from 200 to 130 units. a. Calculate the price elasticity of supply using the midpoint method. b. Calculate the slope of the supply curve. Answer: P1 = $23 Q1 = 200 P2 = $9 a. 𝐸 = b. 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 Q2 = 130 (𝑄2 −𝑄1 )/(𝑄1 +𝑄2 )/2)×100% (𝑃2 −𝑃1 )/(𝑃1 +𝑃2 )/2)×100% = 𝑃2 −𝑃1 𝑄2 −𝑄1 = 9−23 120−200 = (130−200)/((200+130)/2)×100% (9−23)/((23+9)/2)×100% = −14 −70 = −42.42% −87.5% =0.48 =0.2 4. The average annual income rises from $20,000 to $30,000, and the quantity of apples consumed in a year by the average person falls from 30 apples to 28 apples. a. What is the income elasticity of apple consumption? b. Are apples a normal good or an inferior good? Answer: I1 = $20,000 Q1 = 30 I2 = $30,000 Q2 = 28 a. 𝐸 = (𝑄2 −𝑄1 )/(𝑄1 +𝑄2 )/2)×100% (𝐼2 −𝐼1 )/(𝐼1 +𝐼2 )/2)×100% = (28−30)/((30+28)/2)×100% (30,000−20,000)/((20,000+30,000)/2)×100% = −6.9% 40% = -0.17 b. The income elasticity of apple consumption is negative, so apples are an inferior good. 5. Suppose the cross-price elasticity of apples with respect to the price of oranges is −0.4, and the price of oranges falls by 3%. a. What will happen to the demand for apples? b. Are apples and oranges complements or substitutes? Answer: a. 𝐸 = 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑄 𝑜𝑓 𝑎𝑝𝑝𝑙𝑒𝑠 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑃 𝑜𝑓 𝑜𝑟𝑎𝑛𝑔𝑒𝑠 = −0.4 If the price oranges falls by 3%, demand for apples increases by -0.4*(-3%) = 1.2% So, there is 1.2% increase in demand b. The cross-price elasticity of apples with respect to the price of oranges is negative, so these goods are complements. 6. Suppose the demand for shirts is given by: Demand: Q = 50 – 0.5P a. What is the price elasticity of demand when the price decreases from $60 to $40 using the standard percentage change formulas? b. What is the price elasticity of demand using the midpoint method? Answers: a. When prices are $60 and $40, the quantity demanded are 20 and 30 bushels, respectively. Regular percentage change in price = (40 – 60)/60 * 100% = – 20/60 * 100% = – 1/3 * 100% = – 33.33% Regular percentage change in quantity = (30 – 20)/20 * 100% = 10/20 * 100% = 1/2 * 100% = 50% The point price elasticity of demand is: E=| % Change in Quantity / % Change in Price | = | 50% / (– 33.33%) | = 1.5 b. Mid-point method change in price = (40 – 60)/[(40 + 60)/2] * 100% = – 20/50 * 100% = – 40% Mid-point method change in quantity = (30 – 20)/[(30 + 20)/2] * 100% = 20/50 * 100% = 40% The mid-point method price elasticity of demand is: E=| % Change in Quantity / % Change in Price | = | 40% / (– 40%) | = 1 Practice Exercises: Multiple Choice Indicate the answer choice that best completes the statement or answers the question. 1. A good will have a more inelastic demand, the a. greater the availability of close substitutes. b. broader the definition of the market. c. longer the period of time. d. more it is regarded as a luxury. 2. When the price of candy bars is $1.20, the quantity demanded is 490 per day. When the price falls to $1.00, the quantity demanded increases to 500. Given this information and using the midpoint method, we know that the demand for candy bars is a. inelastic. b. elastic. c. unit elastic. d. perfectly inelastic. Figure 5-6 3. Refer to Figure 5-6. Using the midpoint method, what is the price elasticity of supply between points D and E? a. 0.53 b. 0.12 c. 0.22 d. 1.89 Indicate whether the statement is true or false. 4. If a firm is facing inelastic demand, then the firm should decrease price to increase revenue. a. True b. False 5. If the cross-price elasticity of demand for two goods is negative, then the two goods are substitutes. a. True b. False Table 5-5 Price Quantity Demanded $0 50 $2 40 $4 30 $6 20 48 10 6. Refer to Table 5-5. Using the midpoint method, what is the price elasticity of demand between $2 and $4? Indicate the answer choice that best completes the statement or answers the question. Figure 6-2 7. Refer to Figure 6-2. The price ceiling a. causes a shortage of 60 units of the good. b. makes it necessary for sellers to ration the good using a mechanism other than price. c. is not binding because it is set below the equilibrium price. d. causes a shortage of 30 units of the good. 8. Refer to Figure 6-2. The price ceiling causes quantity a. supplied to exceed quantity demanded by 60 units. b. supplied to exceed quantity demanded by 90 units. c. demanded to exceed quantity supplied by 30 units. d. demanded to exceed quantity supplied by 90 units. Figure 6-11 9. Refer to Figure 6-11. Suppose a tax of $2 per unit is imposed on this market. What will be the new equilibrium quantity in this market? a. Less than 60 units b. 60 units c. Between 60 units and 100 units d. Greater than 100 units 10. Refer to Figure 6-11. Suppose a tax of $2 per unit is imposed on this market. How much will buyers pay per unit after the tax is imposed? a. $3 b. Between $3 and $5 c. Between $5 and $7 d. $7 Answer Key 1. b 2. a 3. a 4. False 5. False 6. The price elasticity of demand is 0.43. 7. b 8. d 9. c 10. c