1 Experiment 3 Suppose that sellers pay a tax of 15. If a seller with cost 5 sells to a buyer with value 45 at a price of 25, the seller earns a profit of and the buyer earns a profit of. Suppose you are a seller with cost 13 who must pay a sales tax of 15. What is the lowest price you can sell at and not lose money? Suppose you are a buyer with value 30 and must pay a sales tax of 15. What is the highest price you can pay and still make a profit? Are buyers better off when the sellers pay the tax than when buyers pay the tax?
2 Sales Taxes You are a seller and have to pay 15 in taxes. The good costs you 8. What is the least you would possibly accept? General principle: a sales tax imposed on the seller shifts the supply up (vertically). Similarly, if the tax is imposed on the buyer, demand shifts down by the amount of the tax.
3 Buyer s Price Tax Seller s Price Demand Supply Supply with Tax
4 It doesn t matter if the buyer pays the tax or the seller pays the tax. The price the buyer pays, the price the seller gets, and the quantity are the same Demand if Seller Pays Tax Demand if Buyer Pays Tax Demand Supply Supply with Tax Demand with Tax
5 The Incidence of the Tax Who pays the tax? Who is most affected? Buyer s Tax Seller s Tax Demand Supply Supply with Tax Dark Red: Excess Burden or Dead Weight Loss
6 Only one quantity makes the price from demand minus the price from supply equal the tax. Price to Buyer S Tax Price to Seller D Q with Tax
7 A Major use of elasticities for this class: Suppose price and quantity are in balance at a price p and a quantity q. Suppose a 10% tax is imposed. What happens to the buyer s price paid and the seller s price received? Let x be the percent that the buyer s price rises. Then the seller s price falls by 10%-x. Moreover, η x = η% p = % q = ε% p = ε(10% x). d s ε Thus, x = 10%. ε + η That is, the elasticities give the relative incidence of a per unit tax increase. When demand is very inelastic (η is small), x is close to 1, and most of the tax is passed to consumers. In contrast, when demand is very elastic, (η is very large), x is near zero, and most of the tax is paid by firms. For example, in for automotive gasoline sold in California, η is about 0.25, and ε around 2. Thus, a 10% tax will increase prices by 2/2.25 x 10%, or 8.9%. ηε The quantity change is % Q = ηx = 10%. ε + η
8 tax increase (in percent)=%dpd- %Dps = %DQ/h + %DQ/e, solves for %DQ. Then, compute %Dpd, %Dps S %Dpd Tax %Dps D %DQ
9 Summary: Who pays the sales tax doesn t affect the buyer s price and seller s price. Buyer s price goes up by x = ε ε (amount of + η tax). Seller s price goes down by η (amount of ε + η tax). The quantity falls by ηε (amount of ε + η tax). The excess burden or dead weight loss is the value of the trades rendered unprofitable by the sales tax. The size of the excess burden is approximately 1 ηε (amount of tax) 2. 2 ε + η
10 1. Draw and label a market with a perfectly elastic supply and a perfectly inelastic demand. P Q
11 2. (Short answer) Suppose that, at a price of $10, there are twice as many apples demanded as supplied. How does the price adjustment eliminate the shortage? At $10, some consumers fail to obtain apples. Sellers can raise prices and still make sales. Increasing prices reduce quantity demanded and increase quantity supplied, eliminating the shortage. 3. (Short answer) Is electricity a normal good? Why or why not? Yes, for richer consumers will buy more electricity. Thus electricity demand rises as income rises, the definition of a normal good.
12 4. (Short answer) Red shirts and blue shirts are substitutes in production. (i) If the demand for red shirts falls, but the demand for blue shirts is unchanged, what will happen to the prices of red shirts and blue shirts? Both prices fall. The price of red shirts falls because of the demand decrease, and the price of blue shirts falls because sellers substitute to the more profitable blue shirts, increasing supply. (ii) Illustrate your answer with supply and demand diagrams: Red Shirts Blue Shirts P P Q Q
13 5. (Short answer) Provide two examples of by-products of the production of goods. What does the increase in price of a by-product do to the other good's supply? Why? Gold and silver, beef and hides, lumber and wood chips (for paper), oil and natural gas. An increase in the price of the byproduct makes the first good more profitable, increasing the supply.
14 6. Suppose the elasticity of demand for shirts is 2. A 10% tax is imposed, which reduces supply in the following way: for any given quantity on the old supply curve, the required price to obtain the same quantity on the new supply curve is 10% higher. (i) Using one diagram, illustrate the supply shift, and find the maximum that the equilibrium quantity can fall. P S 10% Price buyer pays rises by no more than 10%. Thus, -%DQ =h %DP 20% D Q %DQ
15 (ii) Now assume that the supply elasticity is 3. Using a second diagram, estimate the percentage change in the equilibrium price and quantity. 10%=%Dpd- %Dps = -%DQ/h +- %DQ/e =-%DQ(1/2 + 1/3) =-%DQ(5/6). Thus, %DQ=-12%, %Dpd=6%, %Dps=-4% S %Dpd 10% %Dps D %DQ
16 7. (No diagrams are necessary for the answer to this question) Tylenol is a substitute (in demand) for aspirin. (i) What does the introduction of Tylenol do to the supply and demand for aspirin? Tylenol, a substitute in demand for aspirin, will reduce demand for aspirin without affecting supply. (ii) What happens to the price of aspirin when Tylenol is introduced? The price of aspirin should fall due to the demand reduction. (iii) A bottle of poisoned Tylenol causes the company to withdraw Tylenol from the market. What happens to the price and quantity of aspirin traded? The price and quantity traded should increase, and return to their pre-tylenol level.
17 8. Consider the sales tax imposed in experiment 3. Using a supply and demand diagram (you may draw this with smooth curves), show how the tax on suppliers reduces quantity, raises the price paid by consumers by an amount less than the tax, and lowers the price paid to suppliers. On the same diagram, illustrate the dead weight loss, and outline the area corresponding to the total tax revenue collected. S with Tax Portion of tax Buyer Pays; Portion Seller Pays Tax Revenue DWL S D DQ
18 9. Consider experiment 2, where the fishers sometimes caught one, two or three fish. (i) Explain how an increase in the number of fish caught can reduce the total earnings of fishers. An increase in the number of fish reduces price, so revenue, which is price times quantity, can fall. (ii) How does the elasticity of demand affect the earnings of fishers when the number of fish caught increases? Revenue falls when the quantity increases if demand is inelastic. (iii) Fishers paid 10 to run their boats. If prices fall to 1, these fishers lose money. How many would you expect them to exit the industry? What should happen to prices? Enough should exit so that prices increases to the level that makes fishing profitable. Since some are exiting, the price should equal average cost.
19 10. Using supply and demand diagrams, show that the effect of a 15 per unit sales tax on buyers and sellers is the same when the buyer pays the tax as when the seller pays the tax. How does this claim accord with your experimental findings? Did it matter who paid the tax? Only one quantity makes the price from demand minus the price from supply equal the tax. Price to Buyer S Tax Price to Seller D Q with Tax
20 11. (i) Why does demand give marginal value of the good? Consumers are willing to pay up to their value for the good. Thus, the marginal consumer values the good at the price. (ii) What is consumer surplus? Illustrate with a demand diagram. Consumer surplus is the net gains from trade earned by consumers.
21 12. If a and b are complementary goods (in consumption) and the price of a increases, we will observe a. an increase in the price and the quantity traded of b. b. a decrease in the price and the quantity traded of b. c. an increase in the price but a decrease in the quantity traded of b. d. a decrease in price but an increase in the quantity traded of b. b. Demand complements (think consumed together ) mean that as the price of a increases, the demand for b falls. Thus both price and quantity of b should fall. 13. If a and b are substitutes in production and the price of a falls, the supply of b will a. increase, and thus the price of b will increase. b. increase, and thus the price of b will decrease. c. decrease, and thus the price of b will decrease. d. decrease, and thus the price of b will increase. b. With substitutes in production, an decrease in the price of a makes producing a less profitable, so sellers produce more b, shifting supply of b out. Thus price of b falls and quantity rises.
22 14. An increase in income will a. increase the demand for turnips if turnips are inferior goods. b. increase the demand for turnips if turnips are normal goods. c. increase the supply of turnips. d. decrease the supply of turnips. b. An increase in income increases demand for normal goods. 15. If the production of good a is a by-product of the production of good b, then an increase in the price of a will cause a. an increase in the supply of a. b. a decrease in the supply of a. c. an increase in the supply of b. d. a decrease in the supply of b. c. An increase in the price of a increases the value of producing a and b, thus shifting out the supply of b.
23 16. Silver and gold are complements in supply and substitutes in demand. A new kind of film is developed that has the direct effect of reducing the demand for silver, affecting the gold market only through substitution. The price of gold and the quantity of gold traded. a. increases, decreases b. is indeterminate, decreases c. decreases, is indeterminate d. decreases, increases b. The shift in the demand for silver decreases the price of silver. As a demand substitute, this reduces the demand for gold (decreasing both price and quantity of gold). As a supply complement, the decrease in the price of silver decreases the supply of gold (increasing price and decreasing quantity of gold). Thus, the quantity falls, but the price could go up or down.
24 17. Suppose a decrease in the price of peanuts due to an increase in supply occurs, and both the price and quantity traded increase for chicken. Which of the following would explain this observation? a. chicken and peanuts are substitutes in supply. b. chicken and peanuts are complements in demand. c. chicken and peanuts are substitutes in demand. d. chicken and peanuts are complements in supply. b. Price and quantity both increasing requires an increase in demand. Thus, chicken and peanuts would have to be demand complements. 18. The demand for a good is inelastic if a. an increase in price results in an increase in total revenue. b. a decrease in price results in a decrease in total revenue. c. an increase in price results in a decrease in total revenue. d. the good is a luxury. a. Think perfectly inelastic, or vertical. An increase in price increases total revenue.
25 19. A demand curve that has a price elasticity of a. 0 will be vertical. b. 0 will be horizontal. c. 1 will be vertical. d. 1 will be horizontal. a. Zero elasticity no change in quantity with a change in price is vertical. 20. A 10 percent increase in the quantity of good a demanded results from a 20 percent decline in its price. The price elasticity of demand for good a is a b c. 2 d d. % Q η = % P = 10% 20%
26 21. If the price elasticity of demand is 3, a 15% increase in price will cause a a. 45% decrease in quantity demanded. b. 5% decrease in quantity demanded. c. 15% decrease in quantity demanded. d. It cannot be determined without knowing the supply elasticity. a. % Q 3 =η = % P % Q = 15%
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