Q1) TRUE or FALSE: a) If consumer 1 has the demand function x 1 = 1000 2p and consumer 2 has the demand function x 2 = 500 p, then the aggregate demand function for and economy with just these two consumers would be x = 1500 3p True: In order to find the aggregate demand function, we need to sum individual demands (uantities) for any price, that is, x(p) = x 1 (p) + x 2 (p) = 1000 2p + 500 p = 1500 3p b) If the supply curve is horizontal, then an upward shift in the demand function will lead to a higher price and uantity in euilibrium. False: If supply is horizontal, then for any uantity demanded firms will put the same price. Thus, a positive shift in demand will result in higher uantity, but the price will stay the same. c) The supply curve slopes up and to the right. If the demand curve shifts upward and the supply curve does not shift, then the euilibrium price and uantity must necessarily increase. True: If supply is strictly increasing in the price then the new demand curve will intersect supply curve in a point with higher price and uantity
Q2) If Kamile is willing to pay $35000 in cash for a convertible BMW, her consumer surplus from getting one free is: a) $0 b) -$35000 c) $35000 d) Insufficient data Consumer surplus is the difference between what consumer is willing to pay for a commodity and its market price (in this situation, what consumer really paid for the commodity). Since Kamile got the car for free, the price she paid for it is 0. Then, her consumer surplus is $35000 - $0 = $35000 Answer: c) Q3) The demand function for fresh strawberries is = 200 5p and the supply function is = 60 + 2p. What is the euilibrium price? a) 10 b) 20 c) 40 d) 50 e) None of the above In euilibrium, supply and demand uantities are eual: S = D, solving 200 5p = 60 + 2p yields p = 20 Answer: b) Q4) The (inverse) demand function for eggs is given by p = 200 4 where is the number of cases of eggs. The (inverse) supply function is p = 2 + 2. In the past, eggs were not taxed, but now a tax of $18 per case has been introduced. What is the effect of the tax on the uantity of eggs supplied? a) Quantity drops by 2 cases b) Quantity drops by 3 cases c) Quantity drops by 6 cases d) Quantity drops by 4 cases e) None of the above Solve for the euilibrium before the tax was introduced: 200 4 = 2 + 2 implies = 33; p = 68 After the tax was introduced, demand did not change (tax doesn t influence individual preferences), but supply function shifted to p = 2 + 2 + tax, because cost per unit increased by tax uantity, thus p = MC also increased by tax uantity. Thus, the new euilibrium will be 200 4 = 2 + 2 + 18, and euilibrium uantity is 30. Then, uantity dropped by 33 30 = 3 cases.
Answer: b) Q5) The (inverse) demand function for cases of whiskey is p = 300 5 and the (inverse) supply function is p = 6 + 2. Originally there was no tax on whiskey. But now government began to tax suppliers of whiskey $14 for every case they sold. How much did the price paid by consumers rise when the new euilibrium was reached? a) $15 b) $12 c) $10 d) $6 e) None of the above As in previous example, old euilibrium is 300 5 = 6 + 2, = 42, p = 90 New euilibrium is 300 5 = 6 + 2 + 14, = 40, p = 100. Then price rises by 100 90 = 10 dollars Answer: c) Q6) The (inverse) demand function for cigars is p = 240 2 where is the number of boxes of cigars. The (inverse) supply function is p = 2 + 2. Cigars are taxed at $4 per box. Who pays the larger share of the tax? Before the tax: euilibrium is defined by 240 2 = 2 + 2, 1 = 59,5; p 1 = 121 (point A); After the tax: euilibrium is defined by 240 2 = 2 + 2 + 4, 2 = 58,5; p 2 = 123 (point B). Tax shifts the supply curve, decreasing both consumer surplus (area between demand curve and price) and producer surplus (area between price and supply curve).
Before the tax: CS = 1 D p 1 d = 1 240 2 p 0 1 d = (240 2 59,5 121 ) 0 0 59,5 59,5 59,5 = 59,5 59,5 = 3540,25 PS = 1 p 1 S d = 1 121 2 2 d = (119 2 0 0 3540,25 = 119 ) 0 59,5 = 119 59,5 59,5 59,5 = After the tax: CS = 2 D p 2 d = 2 240 2 123 d = (240 2 58,5 123 ) 0 0 0 58,5 58,5 58,5 = 58,5 58,5 = 3422,25 PS = 2 p 2 S d = 2 123 6 2 d = (117 2 0 0 3422,25 = 117 ) 0 58,5 = 117 58,5 58,5 58,5 = As we see, decrease in consumer surplus and producer surplus is the same, that is, both consumers and producers pay the same share of the tax. Note: consumer and producer surpluses are eual, because absolute values of slopes of demand and supply functions are same. In this case, CS and PS are represented by euivalent triangles with areas i 2. Q7) In a certain country, the demand function for bread is = 480 6p and the supply function is = 120 + 3p where p is the price in tilas and is the loaves of bread. The government made it illegal to sell bread for a price above 30 tilas per bread. To avoid shortages, he agreed to pay bakers enough of a subsidy for each loaf of bread so as to make supply eual demand. How much would the subsidy per loaf have to be? If there wouldn t be the government intervention, the price would satisfy 480 6p = 120 + 3p, p = 40, which is greater than the maximum legal price. In order to maintain prices at level 30, the uantity of bread should satisfy demand function: = 480 6p = 480 180 = 300. Then, after the subsidy is performed, the supply function is p = /3 40 s, and s = /3 40 p = 100 70 = 30. Q8) The demand function for butter is = 600 5p and the supply function is = 120 + 3p, where is the number of units sold per year and p is the price per unit, expressed in dollars. The government decides to support the price of butter at a price floor of $86 per unit by buying butter and destroying it. How many units of butter must the government destroy per year? At price $86, uantity demanded is D = 600 5p = 600 430 = 170; the uantity supplied is S = 120 + 3p = 120 + 258 = 378. The difference is the amount that the government should buy and destroy: 378 170 = 208. Q9) The demand function for rental apartments is = 960 7p and the supply function is = 160 + 3p. The government makes it illegal to charge a rent higher than 35. How much excess demand will there be? At price 35, uantity demanded is 960 7p = 960 245 = 715; uantity supplied is 160 + 3p = 160 + 105 = 265. Then, excess demand is 715 265 = 450.
Q10) The demand function for potatoes is = 200 p and the supply function is = 50 + 0.5p. The government sets the price of potatoes at 150 and agrees to purchase and destroy any excess supply of potatoes at that price. How much money does it cost the government to buy this corn? At price 150, uantity supplied is S = 50 + 0.5p = 125 and the uantity demanded is p D = 200 p = 50. In order to maintain euilibrium, the government has to buy the excess supply eual to 125 50 = 75 at price p = 150, and it will cost 75 150 = 11250. Q11) Suppose that all firms in a given industry have the same supply curve given by S i (p) = 2p when p is greater than or eual to $2 and S i (p) = 0 when p is less than $2. Suppose that market demand is given by D(p) = 14 p. If firms continue to enter the industry as long as they can do so profitably, what will be the long-run euilibrium price and the long-run euilibrium number of firms? For p < 2, whatever the number of firms n would there be, the total supply is n S i (p) = 0, and this cannot be an euilibrium, because D(p) = 14 p > 12, and there is excess demand. For price p 2, euilibrium is characterized by euation n S i (p) = D(p), or n (2p) = 14 p and p = 14 2. The euation 2n+1 7 is the constraint for the number of firms: the firms will 2n+1 continue to enter the industry until 2n + 1 = 7 (after this point, the price drops under 2 and supply becomes 0). Thus, n = 3 and p = 2. Q12) A company can rent one of two copying machines. The first costs $34 a month to rent and costs an adiitional 2 cents per copy to use. The second costs $107 a month to rent and and additional 1 cent per copy to use. How many copies would the company need to make per month in order for it to be worthwhile to rent the second machine? Cost function of the first machine is c 1 () = 34 + 0.02; of second machine is c 2 () = 107 + 0.01. In order for the second machine to be more profitable, it is necessary to c 2 () be less than c 1 (): 107 + 0.01x 34 + 0.02x, or x 7300. Q13) Tosun has uasilinear preferences and loves to eat simit. His inverse demand function for simits is p(x) = 29 2x, where x is the number of simits he consumes per week. What will be the change in his consumer surplus if the price of simit rises from 1 TL to 3 TL?
Tosun s consumer surplus is the area between his demand function and the price. At the old price, the uantity he consumed was = (29 p)/2 = 14 and his surplus was (29 1)(14 0)/2 = 196 (area A + B + C); at new price, uantity is = (29 p)/2 = 13 and surplus is (29 3)(13 0)/2 = 169 (area A). Change in his surplus is 169 196 = -27. Q14) Suppose the demand for a good is D(p) = 100 p, where p is the price in TL. The supply function is S(p) = p. What will be the effect on consumers surplus if government imposes a price ceiling of 40 per unit of the good? Without the price ceiling, the euilibrium would be 100 p = p, p = 50, = 50. With the government intervention, the uantity supplied will be (p) = p = 40. Then, the consumer surplus without intervention is (50 50)/2 = 1250 (area A + D), and the consumer surplus with price ceiling is (40 40)/2 + 20 40 = 1600 (area A + B). In total, consumer surplus increased by 1600 1250 = 350. Q15) Suppose that King Canuta, demands that each of his subjects give him 1 coconut for every coconut that they consume. The king then sells all of the coconuts that he collects in the market at the going market price. The supply of coconuts is given by S(p S ) = 100p S, where p S is the price received by suppliers. The demand for coconuts by the king s subjects is given by D(p d ) = 4500 100p d, where p d is the price paid by the consumers. In euilibrium, how much will be the price received by the suppliers? The price will be determined by euation D(p) + D(p) = S(p) + D(p) uantity that uantity that people have uantity sold uantity sold by the king (which is people want to give to the king (eual by fellow eual to uantity he received, that to consume to uantity consumed) suppliers is, uantity consumed) 9000 200p = 100p + 4500 100p, or p = 22,5; = 2250. Q16) TRUE or FALSE. Explain. a) If the demand curve is linear, then the elasticity of demand is the same at all prices.
False: elasticity of demand is calculated as dq/q P = a dp/p dp Q depends on P, which means it is not same at all prices. P a bp if demand is linear, and b) If the demand function is = 3m/p, where m is income and p is price, then the absolute value of the price elasticity of demand decreases as price increases. False: elasticity is dq/q P = 3m dp/p dp Q p 2 p 3mp 1 = 1 is constant for all prices. c) If the demand curve for beans is price inelastic at all prices higher than the current price, we would expect that when bad weather reduces the size of the bean crop, total revenue of bean producers will fall. False: total revenue is just P Q, an increasing function in both P and Q. When size of bean crop (Q) drops, its price (P) rises (by the law of demand). Thus, there are two effects on total revenue: fall in Q decreases, and rise in P increases total revenue. When the demand curve is inelastic, the price effect is higher and total revenue rises: drevenue dp = d(q P) dp dq P + Q = Q P dq + 1 > 0 because 1 < P < 0 (demand is dp dp Q dp Q inelastic). Thus, as P increases, Revenue also rises. d) The demand function for potatoes has the euation = 1000 10p. If the price of potatoes goes from 10 to 20, the absolute value of the elasticity of demand increases. dq/q dp/p True: for the given function, elasticity of demand is P = 10. dp Q 1000 10p Atp 1 = 10, E d = -1/9. Atp 2 = 20, E d = -1/4, which is greater in absolute value than -1/9. e) If the price elasticity of demand for a good is -1, then doubling the price of that good will leave total expenditures on that good unchanged. True: Expenditure on some good is uantity of that good multiplied by the price: Exp = P Q. Then, dexp = d(q P) dq P + Q = Q P dq + 1 = 0 because P = 1. Thus, expenditure on this dp dp dp dp Q dp Q good doesn t depend on the price, and if the price doubles, expenditure will remain the same. Q17) The transit authority is thinking about raising the fare on its buses. Suppose demand is currently inelastic. This will lead to: a) a reduction in total revenues b) an increase in total revenues c) no change in total revenues d) not enough information is given to answer this uestion The uestion is the same as Q16, c). The fare on the bus is the same as price of the service. As we have showed, when price is inelastic, increase in price leads to increase in the total revenue (despite the negative effect of decrease in uantity sold on the total revenue). p
Q18) Macit s demand for spaghetti is given by X = 100 2p, where X is the servings of spaghetti and p is the price per serving. Macit s demand elasticity when p = $2 is: a) 20 b) -20 c) 2/3 d) none of the above E d /Q P = 2 dp/p dp Q p = 1. 100 2p 24 Q19) In a perfectly competitive market, the economic incidence of a tax depends on: a) whether the tax is levied on producers or consumers b) the demand elasticity c) the supply elasticity d) both b) and c) Answer: d) Incidence of a tax doesn t depend on a): suppose that before the tax the inverse demand function is P = P d (Q), and inverse supply is P = P S (Q). If a tax is levied on suppliers, then they add the tax uantity to the price they charge, and supply becomes P = P s (Q) + tax. If the tax is levied on consumers, then they have to pay price and tax when they buy a good, that is, price they pay increases by tax uantity and the new demand becomes P + tax = P d (Q). In both cases, the new euilibrium is determined by euation P S (Q) + tax = P d (Q), and euilibrium price and uantity are the same in both cases. The elasticity of demand and supply are percentage changes of uantity, caused by percentage change of price. These values determine the share of tax burden payed by consumers and producers as shown on figure below. Inelastic supply, elastic demand: the burden is on producers Similar elasticities: burden shared