Principles of Microeconomics + DiscoverEcon code card

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Unformatted text preview: Ch 7 Answers to Problems 1a. Consumer surplus is the triangular area between the demand curve and the price line. Its area is equal to (l/2)*(Base)*(Height). The base is 6 units and the height is 1.5 units, measured in dollars. Therefore, consumer surplus is (1/2)($l .50/unit)(6 units/wk), or $4.50 per week. b. Producer surplus is the triangular area between the supply curve and the price line. Using the same area formula, it is (1/2)($4.50/unit)(6 units/wk), or $13.50 per week. c. This $18 is the total value consumers and producers earn from trading in this market. Therefore, we can say that the maximum weekly amount that consumers and producers together would be willing to pay to trade in used DVDs is the sum of gains from trading in used DVDs—is $18 per week. .5 '9 Pzwmsa 2 a. At a price of $7.50, the quantity supplied per week = 2. The quantity demanded at this price is 18 per week, which implies a weekly shortage of 16 used DVDs. b. To find the weekly economic surplus lost as a result of the price ceiling it is best to first recognize the equation for the demand function and the equation for the supply function. Using the diagram on page 213, see that the Demand Function is P = 12 — 0.25Q (the slope is -%). Supply function is P = 6 + 0.75Q (the slope is % ). With this information, you should recognize that at a price ceiling of $7.50, only 2 DVD’s will be available for sale. The loss in economic surplus is the area of the dark-shaded triangle in the diagram, or the sum of the areas of the two triangles ABC and ACD. This is (0.5)(4)(1) + (0.5)(4)(3) = $8/wk. This price ceiling causes inefficiency, since there are possible trades that make both parties better off and nobody worse off, yet are prevented from occurring due to the legally binding price ceiling. 1,09wi 1’ when P = 7.50 g 950 : (“0.7919 => ®= 1 [30+ Buqers have a, mM Mllmg New +0 Pa‘d "‘9 P :12 awn) '2 0.51) 48 3a. When there is no charge for the tour, the surplus enjoyed by someone who takes it equals his or her reservation price for the tour. If the warden operates the tour on a first-come-flrst served basis, Faith, Penny, and Fran will be turned away. The combined consumer surplus when the four who arrive first take the tour is $20 + $14 + $30 + $15=$79. b. An offer of $15 compensation generates 3 volunteers to return another day: Fran, Jack and Jon. These people value the $15 more than the tour (or at least as much as the tour, in Jack’s case) so they are better off or at least no worse off taking the $15 and no tour. The four who go on the tour receive a total consumer surplus of $40 + $30 + $20 + $17=$107. The warden pays $45 in compensation payments to the three volunteers, which causes him a loss in economic surplus of $45, but this loss is exactly offset by the $45 gain in economic surplus that the three volunteers receive. Total economic surplus from the tour operation is now $107, which is $28 higher than before. person Reservation Price c. The compensation policy is more efficient than the first—come—first—served policy because it establishes a market for a scarce resource that would otherwise be allocated by non-market means. The limited number of tours is allocated so that the 4 spaces go to those people who place the highest value on the tour. d. YOU CAN SKIP THIS PART. Suppose the Warden auctions off the right to take the tour by announcing a high price and then lowering the price until he gets four people willing to pay that price. If he starts with a price of $50, no one wants the tour. If he lowers his price to $40 or just below, he gets one person, Penny. He will lower price all the way to $16, at which a total of four people come forward. These four (Penny, Kate, Herman and Faith) are all willing to pay at least $16 to take a tour. The warden will collect $64 from the auction. He can then give refunds to Herman and Kate, who would have gotten to go for free under the first-come-first-served scheme, so they will be just as well off as before. He can give $16 to Jack, which is $1 more than enough to compensate him for not getting to go. And he can give $15 to Jon, which is also $1 more than enough to compensate him. That leaves the warden with $1, so he too is better off than before. Faith is $1 better off than before, and Penny is $24 better off than before. All others are exactly as well off as before. 4 a. The equilibrium price is $5 and the equilibrium quantity is 3,000 units per week. The consumer surplus is the area between the demand curve and the price line—triangle ABC in the diagram— which is $4,500/wk. The producer surplus generated is the area of triangle ABD, which is $4,500/wk. Therefore, the total economic surplus is $9,000/wk. 565 ml: bf: um 15 WKWQ ($/unit) D e} S CS 2 /'\/k \ PMH’ 668:; Z 2+6? 3 P=2+Q Solve Fm 62 : (BM)(,5>/Z. (Q ‘: 2Qq®z3 34500 \A/l/vwx 62:3) P: 65 (use Dar 3 QUY'M/Ihm) Quantity 3 8 (1000s per wk) b. The tax shifts the vertical intercept of the supply curve up by $2 to $4. The new equilibrium price and quantity are $6 and 2,000 respectively. The tax revenue is $2(2,000), or $4,000/wk. Consumer surplus is now the area of the triangle A’B’C, which is $2,000/wk. Net of the $2 tax, sellers receive a price of $4 per unit. Their surplus is the area of the triangle D’ED, which is $2,000/wk. The tax revenue collected is ($2/unit)(2,000 units/wk) = $4,000/wk. Counting the revenue from the tax as part of total economic surplus because this tax revenue can be used to make people better off, the new total economic surplus is thus $2,000/wk + $2,000/wk + $4,000/wk = $8,000/wk, or $1,000/wk less than without the tax. This $1,000 is the net loss to econonimc surplus, small triangle from A’EA. Price ($/unit) new ezgui 4/“ 5 (Tax _._ new 8 P=4+Q ’ CS 42% D : 5+Tcofi ._~ P=2+Q ,: - lax Revenue 8'62 41A? : 6ZV'Zooo :4509 4 / Z ‘9 Deodwg hr [059 ,7 : r; woo (’2 2’ P = '50 (PYLUL 1‘ HQ loam) Quantity 2 8 (1000s per wk) 5. Profit is the difference between the company’s total revenue and its total cost. Producer surplus on one unit is the difference between price and the firm’s reservation price (minimum price it requires. This minimum price equals the firm’s marginal cost. Summing over all units produced, producer surplus is the difference between total revenue and the sum of marginal costs of each unit produced. This sum of marginal costs equals its variable costs (you can verify this by checking a chart of costs such as the one we produced in class for the Flag Producer). So Producer surplus is Total Revenue minus Variable costs. Therefore, the difference between Producer Surplus and profits is that profits account for fixed costs and producer surplus does not. 6a. The marginal cost curve for electric power in Charlotte would look like this: Price (cents/unit) \PD we. m a “G Units of power per day 100 300 b. The city should charge 10 cents per unit since that is the marginal cost when residents use at least 100 units/day. It should charge 10 cents per unit to all users, even those who are receiving their power from the hydroelectric facility, since if those users were to cut their consumption, they would free up hydroelectric capacity, which could then be used to serve others who are currently receiving their power from the more costly steam generator. This problem tells us that quantity demanded at 10 cents is 200 units per day. If the government charges a lower price, such as a price equal to the average of these two prices, then quantity demanded would be higher. We don’t know the exact location of the demand curve, but we can assume it is downward sloping and we know that it goes through the point (200, 10) 7. Skip 8 Skip 9. At a price of $1/gal, Islandians will consume 5 million gallons of oil per year. The true marginal cost of oil for the nation is the international price, which is $2/ga1. Therefore, the government spends $5,000,000 subsidizing oil since they have to buy 5 million gals at the international price of $2, and charge their people $1 per gals for it. If Islandians had been charged the international price of $2, they would have consumed only 4 million gal/yr. The lost surplus from consuming the larger amount of oil is the cumulative difference between the cost of the oil and the most they would have been willing to pay for it. This difference is the area of the shaded triangle in the diagram, or $500,000/yr. P ($/gal) 6 Lost 3 rplus F-‘N 4 5 6 Q (millions of gal/yr) 10a. The demand curve is as shown in the diagram. Instead of millions of gal per yr, the X axis measures the gals per year P ($/gal) Lost surplus 4 5 6 Q (gal/yr) b. With the subsidy that lowers the price of oil from $2 to $1, each family receives consumer surplus equal to the area of triangle ADE. Without the subsidy, consumer surplus equals the area of triangle ABC. The difference is the area BCED, which equals $4.50/yr. c. The government's oil subsidy is $5,000,000, which per family is =$5/yr. So the government could cut each family's taxes by $5/yr by not subsidizing oil. (1. The family's net gain would be the $5 it saves in taxes minus the $4.50 it loses in consumer surplus from its heating oil purchases, or $0.50/yr. e. The aggregate gain from the tax cut and removal of the subsidy is $500,000/yr, the same as the loss in total consumer surplus that resulted from the subsidy. ...
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