Answers to Review Questions 1. The principle of increasing opportunity cost, also known as the low-hanging-fruit principle, says that the least costly options should be exploited first, with more costly tions taken up only after the least costly ones have been exhausted. At low prices, only those with low opportunity costs of producing the product would find it worthwhile to offer it for sale. As prices rise, others with higher opportunity cost could profitably enter the market 2. To build, or even rent, a new factory often takes years, certainly many months. By contrast, add itional production workers can be hired in days, or at most weeks. Se the factory is far more likely to be a fixed factor over the next two months 3. Not enough seeds for the plants needed to feed 6 billion people would fit in a single flower pot, let alone develop into healthy plants with only a minuscule amount of soil available per seed 4. An exception to the price = marginal cost rule occurs when market price is so low that total revenue is less than variable cost when price equals marg inal cost. So FALSE 5. To calculate producer surplus, we need to know the reservation price of sellers at every level of output. The vertical interpretation of the supply curve tells us marginal cost at every level of output, and marginal cost is the reservation price of sellers Answers to problems 1. If the price of a fossil is less than $6, Zoe should devote all her time to photography because when the price is, say, $5 per fossil, an hour spent looking for fossils will give her 5(5 )=$25, or $2 less than she'd earn doing photography. If the price of fossils is 6, Zoe should spend one hour searching, will supply 5 fossils, and will get $30 revenue, which is $3 more than she'd earn from photography. However,an add itional hour would yield only 4 add itional fossils or $24 additional revenue, so she should not spend any further time looking for fossils. If the price of fossils rises to $7 however, the additional hour gathering fossils would yield an add itional $28, so gathering fossils during that hour would then be the best choice, and Zoe would therefore supply 9 fossils per day. Using this reasoning, we can derive a price-quantity supplied relationship for fossils as follows Price of fossils(S) Number of fossils supplied per day
Answers to Review Questions 1. The principle of increasing opportunity cost, also known as the low-hanging-fruit principle, says that the least costly options should be exploited first, with more costly options taken up only after the least costly ones have been exhausted. At low prices, only those with low opportunity costs of producing the product would find it worthwhile to offer it for sale. As prices rise, others with higher opportunity cost could profitably enter the market. 2. To build, or even rent, a new factory often takes years, certainly many months. By contrast, additional production workers can be hired in days, or at most weeks. So the factory is far more likely to be a fixed factor over the next two months. 3. Not enough seeds for the plants needed to feed 6 billion people would fit in a single flower pot, let alone develop into healthy plants with only a minuscule amount of soil available per seed. 4. An exception to the price = marginal cost rule occurs when market price is so low that total revenue is less than variable cost when price equals marginal cost. So FALSE. 5. To calculate producer surplus, we need to know the reservation price of sellers at every level of output. The vertical interpretation of the supply curve tells us marginal cost at every level of output, and marginal cost is the reservation price of sellers. Answers to Problems 1. If the price of a fossil is less than $6, Zoe should devote all her time to photography because when the price is, say, $5 per fossil, an hour spent looking for fossils will give her 5($5) = $25, or $2 less than she’d earn doing photography. If the price of fossils is 6, Zoe should spend one hour searching, will supply 5 fossils, and will get $30 revenue, which is $3 more than she’d earn from photography. However, an additional hour would yield only 4 additional fossils or $24 additional revenue, so she should not spend any further time looking for fossils. If the price of fossils rises to $7, however, the additional hour gathering fossils would yield an additional $28, so gathering fossils during that hour would then be the best choice, and Zoe would therefore supply 9 fossils per day. Using this reasoning, we can derive a price -quantity supplied relationship for fossils as follows: Price of fossils ($) Number of fossils supplied per day 0-5 0 6 5
7.8 9 14-26 14 27+ If we plot these points, we get Zoe's daily supply curve for fossils Price(Sfos sil) 14 Number of fossils 5912115 2. The marg inal cost of each of the first 6 air cond itioners produced each day is less than $120, but the marginal cost of the 7th air cond itioner is $140. So the company should produce 6 air conditioners per day Air Conditio Total Cost(S/day) 31 405 6 510 800 3a. As indicated by the entries in the last column of the table below, the profit-maximizing quantity of bats for Paducah is 20/day, which yields daily profit of $35 b. Same quantity as in part a, but now profit is $65, or $30 more than before
7, 8 9 9-13 12 14-26 14 27+ 15 If we plot these points, we get Zoe’s daily supply curve for fossils: Number of fossils Price ($/fossil) 6 7 5 9 9 12 14 15 27 14 2. The marginal cost of each of the first 6 air conditioners produced each day is less than $120, but the marginal cost of the 7th air conditioner is $140. So the company should produce 6 air conditioners per day. Air Conditioners/day Total Cost ($/day) 1 100 2 150 3 220 4 310 5 405 6 510 7 650 8 800 3a. As indicated by the entries in the last column of the table below, the profit-maximizing quantity of bats for Paducah is 20/day, which yields daily profit of $35. b. Same quantity as in part a, but now profit is $65, or $30 more than before
Total Revenue Total labor cost Total cost Profit 0 0 0 60 -60 15 75 25 90 10 15 20 200 105 165 35 25 250 165 225 0 350 330 390 40 4. A tax of $10 per day would decrease Paducah's profit by $10 per day at every level of output. But the company would still maximize its profit by producing 20 bats per day. a tax that is independent of output does not change marginal cost, and hence does not change the profit- maximizing level of output But a tax of $2 per bat has exactly the ther $2 Increase in marginal cost of making each bat. as we see in the last column of the table below the company's profit-maximizing level of output now falls to 15 bats per day. At that level it earns exactly 0 profit, but at any other level of output it would sustain a Total Revenue Total labor cost Total cost Profit (S/day) 0 0 0 60 60 85 10 110 -10 15 150 200 105 205 300 240 35 350 330 460 -110 5. Producer surplus is the area of the shaded triangle, $18, 000/day
Q (bats/day) Total Revenue ($/day) Total labor cost ($/day) Total cost ($/day) Profit ($/day) 0 0 0 60 -60 5 50 15 75 -25 10 100 30 90 10 15 150 60 120 30 20 200 105 165 35 25 250 165 225 25 30 300 240 300 0 35 350 330 390 -40 4. A tax of $10 per day would decrease Paducah’s profit by $10 per day at every level of output. But the company would still maximize its profit by producing 20 bats per day. A tax that is independent of output does not change marginal cost, and hence does not change the profit-maximizing level of output. But a tax of $2 per bat has exactly the same effect as any other $2 increase in the marginal cost of making each bat. As we see in the last column of the table below, the company’s profit-maximizing level of output now falls to 15 bats per day. At that level it earns exactly 0 profit, but at any other level of output it would sustain a loss. Q (bats/day) Total Revenue ($/day) Total labor cost ($/day) Total cost ($/day) Profit ($/day) 0 0 0 60 -60 5 50 15 85 -35 10 100 30 110 -10 15 150 60 150 0 20 200 105 205 -5 25 250 165 275 -25 30 300 240 360 -60 35 350 330 460 -110 5. Producer surplus is the area of the shaded triangle, $18,000/day
Price (S per slice) Supply Demand Quantity 24(1000s of slices per day) 6. The market supply curve(right) is the horizontal summation of the supply curves of the individual market participants (left and center P=2Q1 6 4 Q Horizontal summation means holding price fixed and add ing the corresponding quantities. If you want to derive the market supply curve algebraically, solve eacl individual supply curve for quantity and add. Pay careful attention to the region for which the supply curves don't overlap(here, the region P2 we add Q1+Q2 to getQ= P/2+(P-2), which reduces to Q=(3P/2)-2. Rewriting this, we have P=(4/3)+(2/ 3)Q for P>2. Expressed algebraically, the market supply curve is thus P= 2Q for P2
6 12 24 Quantity (1000s of slices per day) Price ($ per slice) 3 Supply Demand 6. The market supply curve (right) is the horizontal summation of the supply curves of the individual market participants (left and center). 6 3 P=2Q1 4 P=2+Q2 1 4 2 6 6 4 2 2 4 1 2 2 4 7 P Q P Q P Q 1 2 S Horizontal summation means holding price fixed and adding the corresponding quantities. If you want to derive the market supply curve algebraically, solve each individual supply curve for quantity and add. Pay careful attention to the region for which the supply curves don't overlap (here, the region P2 we add Q1+Q2 to get Q = P/2+(P-2), which reduces to Q = (3P/2)-2. Rewriting this, we have P = (4/3)+(2/3)Q for P>2. Expressed algebraically, the market supply curve is thus P = 2Q for P2
7. This firm will sell 570 slices per day, the quant ity for which P= MC. Its profit will be(P-ATCXQ =($2.50/slice-$1.40/slice)x(570 slices/day)=$627/day AT 2.50 8. This firm will sell 360 slices per day, the quantity for which P= MC. Its prof it will be(P-ATCXQ=($0.80/slice-$1.03/slice)x(360 slices/day)=-$82.80/day S/slice AVC 9. Because price is less than the minimum value of AVC, this producer will shut down in the short run. He will thus experience a loss equal to his fixed cost. Fixed cost is the difference between total cost and total variable cost. For Q=260 slices/day, we know both ATC and AVC, so for that output level we can calculate TC =(260 slices/day ) ($1. 18/slice)=$306.80/day and vc =(260 slices/day )(0.68/slice) $176.80/day. So fixed cost $306. 80/day -$176.80/day =$130/day. This producer's profit is thus -$130.day
7. This firm will sell 570 slices per day, the quantity for which P = MC. Its profit will be (P-ATC)xQ = ($2.50/slice - $1.40/slice)x(570 slices/day) = $627/day. AVC ATC $/slice slices/day 1.40 2.50 MC 570 8. This firm will sell 360 slices per day, the quantity for which P = MC. Its profit will be (P-ATC)xQ = ($0.80/slice - $1.03/slice)x(360 slices/day) = -$82.80/day. AVC ATC $/slice slices/day 1.03 MC 360 0.80 9. Because price is less than the minimum value of AVC, this producer will shut down in the short run. He will thus experience a loss equal to his fixed cost. Fixed cost is the difference between total cost and total variable cost. For Q = 260 slices/day, we know both ATC and AVC, so for that output level we can calculate TC = (260 slices/day)($1.18/slice) = $306.80/day and VC = (260 slices/day)($0.68/slice) = $176.80/day. So fixed cost = $306.80/day - $176.80/day = $130/day. This producer’s profit is thus -$130.day
ATC 1.18 slices/day 10. This producer will sell 435 slices per day, the quantity for which P= MC. His total revenue will therefore be PxQ =($1. 18/slice)x(435 slices/day)=$513.30/day His variable cost is AVCxQ=($0.77/slice )(435 slices/day)=$334.95/day. To this we add his fixed cost of $130/day to obtain tC=$464.95/day( calculated using the method shown in problem 9). So this producer's profit is $5 1330/day -$464.95/day =$48.35/dav MC ATC AVC 1.18 0.77
AVC ATC $/slice slices/day 1.18 MC 260 0.50 0.68 10. This producer will sell 435 slices per day, the quantity for which P = MC. His total revenue will therefore be PxQ = ($1.18/slice)x(435 slices/day) = $513.30/day. His variable cost is AVCxQ = ($0.77/slice)(435 slices/day) = $334.95/day. To this we add his fixed cost of $130/day to obtain TC = $464.95/day (calculated using the method shown in problem 9). So this producer’s profit is $513.30/day - $464.95/day = $48.35/day. AVC ATC $/slice slices/day 1.18 MC 260 0.50 0.68 435 0.77