生產過程 ¡ 生產技術是投入與產出的數量關係。 ¡ 一個勞動密集的技術是大部份依賴 人力資本而非資本。 ¡ 一個資本密集的技術是大部份依賴 資本而非人力資本。
生產函數 ¡ 生產函數或總生產函數是產出和 投入的一個數學關係式。 ¡ 它顯示總產出是投入的一個函數。
生產四要素： 土地、資本、勞動、企業能力
生產函數 Q=f(K, L, t) Q：產出的數量 K：資本 L：勞動 t：技術
生產函數 Q = f(K, L)*A(t) Q: 產出的數量 K：資本 L：勞動 A(t)：技術進步因子
特性 • 生產函數乃各生產要素之增函數 L , K Q
短期與長期的決策 • 短期的條件： 廠商某一規模或生產要素是固定 2. 廠商既無法加入也無法退出產業 1.
短期與長期的決定 ¡ 長期是指生產無固定投入要素的一 段時間。廠商能增加或減少運作的 規模，同時新廠商能加入，且既存 廠商能退出產業。
短期: (short run) • f(L, K, t)=f(L) • 資本與生產技術固定，生產 函數只是勞動的函數
生產函數與規模報酬遞增(increasing return to scale): • 所有投入要素增加n倍，則產出會大於n倍 Q=f( L, K), >
生產函數與規模報酬 • 規模報酬遞減(decreasing return to scale): 所有投入要素增加n倍，則產出會g少於n倍 Q=f( L, K), >
生產函數與規模報酬 • 規模報酬固定(constant return to scale): 所有投入要素增加n倍，則產出亦會增加n倍 Q=f( L, K)
生產函數與規模報酬遞增(increasing return to scale): • 所有投入要素增加n倍，則產出會大於n倍 Q=f( L, K), >
生產函數與規模報酬 • 規模報酬遞減(decreasing return to scale): 所有投入要素增加n倍，則產出會g少於n倍 Q=f( L, K), >
生產函數與規模報酬 • 規模報酬固定(constant return to scale): 所有投入要素增加n倍，則產出亦會增 加n倍 Q=f( L, K)
生產函數與規模報酬遞增(increasing return to scale): • 所有投入要素增加n倍，則產出會大於n倍 Q=f( L, K), >
生產函數與規模報酬 • 規模報酬遞減(decreasing return to scale): 所有投入要素增加n倍，則產出會g少於n倍 Q=f( L, K), >
生產函數與規模報酬 • 規模報酬固定(constant return to scale): 所有投入要素增加n倍，則產出亦會增 加n倍 Q=f( L, K)
三明治的生產函數 (1) 勞動量) (2) 總產出 (3) 勞動邊際 產出 (4) 勞動平 均產出 0 0 - - 1 10 10 10. 0 2 25 15 12. 5 3 35 10 11. 7 4 40 5 10. 0 5 42 2 8. 4 6 42 0 7. 0
邊際產出和平均產出 總產出變量 邊際勞動產出= 勞動使用量 • 平均產出是每單位可變生產要素的平均產量。 總產出 勞動平均產出= ¡ 邊際產出是其他條件不變下，多增加一單位 總勞動量 投入的使用，產生額外產出的數量。
三明治的生產函數 (1) 勞動量) (2) 總產出 (3) 勞動邊際 產出 (4) 勞動平 均產出 0 0 - - 1 10 10 10. 0 2 25 15 12. 5 3 35 10 11. 7 4 40 5 10. 0 5 42 2 8. 4 6 42 0 7. 0
邊際產出和平均產出 總產出變量 邊際勞動產出= 勞動使用量 • 平均產出是每單位可變生產要素的平均產量。 總產出 勞動平均產出= ¡ 邊際產出是其他條件不變下，多增加一單位 總勞動量 投入的使用，產生額外產出的數量。
三明治的生產函數 (1) 勞動量) (2) 總產出 (3) 勞動邊際 產出 (4) 勞動平 均產出 0 0 - - 1 10 10 10. 0 2 25 15 12. 5 3 35 10 11. 7 4 40 5 10. 0 5 42 2 8. 4 6 42 0 7. 0
邊際報酬遞減法則 • 邊際報酬遞減法則是指： 資本固定下，可變生產投入增加，總 產量增加到某一程度之後，可變投 入的邊際產量會遞減。
三明治的生產函數 (1) 勞動量) (2) 總產出 (3) 勞動邊際 產出 (4) 勞動平 均產出 0 0 - - 1 10 10 10. 0 2 25 15 12. 5 3 35 10 11. 7 4 40 5 10. 0 5 42 2 8. 4 6 42 0 7. 0
總，平均，及邊際產出 ¡ 邊際產出是總產出的斜率。 • 在A點，總產出的斜率最高， 因此，邊際產出最高。 • 在C點, 總產出達最大，總產 出函數的斜率=0，邊際產 出與橫軸相交。
總產出與邊際產出之關係 (1)L 1之前: TP呈遞增率上升，且 M PL上升, MPL>0 (2)L 1 至L 3之間: TP呈遞減率上升，但 MPL下降，但MPL>0 (3)L 3之後: TP呈遞增率，MPL下降，但 MPL<0 (4)A點: TPL之反曲點，MPL最大 (5)C點: TPL最大，MPL為零
總，平均，與邊際產出 ¡ 當一條由原點出發的 線與總產出相切時， 平均產出達最大，同 時等於邊際產出。 • 之後，平均產出會低於 B點的左與右方。
平均產出與邊際產出之關係 (1)L 1之前: MPL>APL，且MPL及APL 均上升 (2)L 1至L 2之間: MPL>APL，且MPL下 降，APL上升 (3)L 2至L 3之間: MPL<APL，且MPL及 APL均下降 (4)A點: MPL最大 (5)C點: MPL=0 (6)B點: APL最大，且APL=MPL
總，平均，與邊際產出 ¡ 當一條由原點出發的 線與總產出相切時， 平均產出達最大，同 時等於邊際產出。 • 之後，平均產出會低於 B點的左與右方。
生產合理區 • 何種區域中才算具有經濟效率的 合理區? • 將生產區分為三個階段
生產合理區 第一階段: 0至L 2之間 • > ，即 成遞增階段 • L增加， 一直增加，會不斷 僱用L，而不會在此階段生產， 為不合理生產階段
生產合理區 第二階段: L 2至L 3之間 • = 至 =0之間 合理生產階段
生產合理區 第三階段: L之後 • <0，表示L增加， 會下降，故會減少L僱用量， 不合理生產階段
總，平均，與邊際產出 ¡ 當一條由原點出發的 線與總產出相切時， 平均產出達最大，同 時等於邊際產出。 • 之後，平均產出會低於 B點的左與右方。
生產合理區 生產階段 MP狀況 AP與MP比 較 生產 合理 性 第一階段 先遞增後遞減，正 遞增，正 MP>AP 不合理 第二階段 遞減，正 MP<AP 合理 第三階段 遞減，負 遞減，正 MP<AP 不合理
Cobb-Douglas生產函數 Q=AK L A: 、 為固定常數 Q: 產出的數量 K: 資本 L: 勞動 A=1時，表示無技術進步因子 A>1時，表示技術進步因子存在
Cobb-Douglas生產函數 • (1) + >1 規模報酬遞增 產量(Q)增加比率大於要素(L，K)投入比例 • (2) + <1 規模報酬遞減 產量(Q)增加比率小於要素(L，K)投入比例 • (3) + =1 規模報酬固定 產量(Q)增加比率等於要素(L，K)投入比例
兩個生產投入的生產函數 ¡ 在很多的生產過程中，生產投入是一起 作，被視 為是互補品。 ¡ 例如，增加資本的使用可以使勞動生產力增加。 Inputs Required to Produce 100 Diapers Using Alternative Technologies TECHNOLOGY UNITS OF CAPITAL (K) UNITS OF LABOR (L) A 2 10 B 3 6 C 4 4 D 6 3 • 在技術既定下, 最 小成本的選擇決 定於投入要素的 價格。
兩個生產投入的生產函數 Cost-Minimizing Choice Among Alternative Technologies (100 Diapers) (1) TECHNOLOG Y (2) UNITS OF CAPITAL (K) (3) UNITS OF LABOR (4) COST WHEN PL = $1 PK = $1 (5) COST WHEN PL = $1 PK = $1 A 2 10 $12 $52 B 3 6 9 33 C 4 4 8 24 D 6 3 9 21 E 10 2 12 20
生產函數與對生產要素需求之特性 比較 生產函數的特性 1. 2. 3. 對生產要素需求的特 性 產量是要素量的增 1. 是一種引申需求 函數 (間接需求) 要素間有互補性 2. 是一種聯合需求 (有互補性) 要素間有替代性 3. 是一種競爭需求 (有替代性)
等產量曲線 ¡ 在技術不變下，產量相同所必須 使用二種要素(L，K)的組合軌跡
等產量曲線
等產量曲線(Isoguant) 1. 2. 3. 4. 5. 斜率為負 凸向原點 任兩條等產量曲線不可相交 任一點必有一條等產量曲線通過 愈往右上角的等產量曲線其產量 會越大
邊際技術替代率(Marginal Rate of Technology Substitution) ¡ 等產量曲線的斜率 MRTS= ¡ 為維持相同的產量，在放棄一單位的勞動後，所必須 多使用資本的數量。 Marginal Product of labor 勞動的邊際產量 Marginal Product of capital 資本的邊際產量
邊際技術替代率(Marginal Rate of Technology Substitution)
等成本線(Isocost line) ¡ 在要素價格不變下，生產者以一定 之成本，所能購買兩種要素L、K的 各種不同組合的軌跡。
等成本線的斜率 ¡ 等成本線的斜率 為兩要素的相對價格之比
成本最小均衡條件(Cost-minimizing equilibrium condition) Slope of isoguant= =slope of isocost= 等產量曲線與等成本線相切時，達到最小成本組合。
成本最小均衡條件(Cost-minimizing equilibrium condition)
成本最小均衡條件(Cost-minimizing equilibrium condition) K G A H L 1. G點： > 應多使用L，少用K，最後達均衡。 2. H點： < 應多使用K，少用L，最後達‘均衡。
PROBLEM 1 • Two former Berkeley students worded in an investment bank at a salary of $60, 000 each for 2 years after they graduated. Together they saved $50, 000. After 2 years, they decided to quit their job and start a business designing Web sites. They used the $50, 000 to buy computer equipment, desks, and chairs. For the next 2 years they took in $40, 000 in revenue each year, paid themselves $10, 000 annually each, and rented an office for $18, 000 per year. Prior to the investment, their $50, 000 was in bonds earning interest at a rate of 10 percent. Are they now earning economic profits? Explain your answer.
Problem 1 Answer • They are nit earning economics profits; they are not considering opportunity cost of capital is 10 percent of $50, 000 annually. Because simple revenue minus cost yields an accounting profit of only $2, 000 , adding $5, 000 in opportunity cost means the firm is suffering losses of at least $3, 000. In addition they are not considering the opportunity cost of their own labor.
Problem 2 • The following table gives total output or total product as a function of labor units used: Labor 0 1 2 3 4 5 Total Output 0 5 9 12 14 15
Problem 2 a. Define diminishing returns. b. Does the table indicate a situation of diminishing returns? Explain your answer.
Problem 2 Answer a. The marginal product decrease as a single variable factor increases, holding all other factors constant. b. The table does exhibit diminishing returns because the marginal product of labor falls as labor increase: L TP 0 1 2 3 4 5 0 5 9 12 14 15 MP ─ 5 4 3 2 1
PROBLEM 3 • A female student who lives on the fourth floor of Bates Hall is assigned to a new room on the seventh floor during her junior year. She has 11 heavy boxes of books and “stuff” to move. Discuss the alternative combinations of capital and labor that might be used to make the move. How would your answer differ if the move were to a new dorm 3 miles across campus, and to a new college 400 miles away?
PROBLEM 3 Answer • Clearly the labor-intensive way would be to carry the boxes down the hall and up the stairs one at a time. She could get a friend or two to help. If the dorm has an elevator and she can borrow a hand truck, the job would be a piece of cake. She would be using capital to raise her productivity. To go three miles across campus, a car (capital) or a truck (more capital) would be nice, although she could carry them one at a time across campus as well. In the developing world, where capital is scarce, people carry a lot of stuff. To get the boxes to a new campus, she would probably mail them or send them UPS. In this case, they would go in a big truck or in an airplane (a whole lot of capital).
PROBLEM 4 • During the early phases of industrialization, the number of persons engaged in agriculture usually drops sharply, even as agricultural output is growing. Given what you know about productivity technology and production functions, can you explain this seeming inconsistency?
PROBLEM 4 Answer • The addition of capital (tractors, combines, etc. ) and the application of technology (nitrous fertilizers) raise the productivity of labor, just as the new grill discussed in the chapter raised the productivity of workers. Capital us also a substitute input for labor.
Problem 5 • Since the end of World War , manufacturing firms in the United States and in Europe have been moving farther and farther outside of central cities. At the same time, firms in finance, insurance, and other parts of the service sector have been locating near the downtown areas in tall buildings. One major reason seems to be that manufacturing firms find it difficult to substitute capital for land, while service-sector firms that use office space do not.
Problem 5 a. What kinds of buildings represent substitution of capital for land? b. Why do you think that manufacturing firms might it difficult to substitute capital for land? c. Why is it relatively easier for a law firm or an insurance company to substitute capital for land? d. Why is the demand for land likely to be very high near the center of a city? e. One of the reasons for substituting capital for land near the center of a city is that land is more expensive near the center. What is true about the relative supply of land near the center of a city? (Hint: What is the formula for the area of circle? )
Problem 5 Answer a. Tall buildings—skyscrapers. b. Product usually has to move along an assembly line and out into a warehouses. An assembly line usually takes a lot of space on a single floor. (Can you imagine a vertical assembly line? ) c. Offices can be “stacked up. ”People can move by stairs or elevators easily. d. Accessibility! e. The area of land increases with the square of distance from the center: When a city grows from a radius of 1 mile to a radius of 5 miles, the new area is 25 times as large as the original (Area=)
Problem 6 • A firm can use three different production technologies, with capital and labor requirements at each level of output as follows: Technology 1 Technology 2 Technology 3 Diary Output K L K L 100 3 7 4 5 5 4 150 3 10 4 7 5 5 200 4 11 5 8 6 6 250 5 13 6 10 7 8
Problem 6 a. Suppose the firm is operating in a high-wage country, where capital cost is $100 per unit per day and labor cost is $80 per worker per day. For each level of output, which technology is the cheapest? b. Now suppose the firm is operating in a low-wage country, where capital cost is $100 per unit per day but labor cost is only $40 per unit per day. For each level of output, which technology is the cheapest? c. Suppose the firm moves from a high-wage to a low-wage country but that its level of output remains constant at 200 units per day. How will its total employment change?
Problem 6 Answer a. The first step is to calculate the cost for each level of output using each of the three technologies. With capital costing $100 per day, and labor costing $80 per day, the results are as follows: Technology 1 Technology 2 Technology 3 Diary Output 100 860 800 820 150 1100 960 900 200 1280 1140 1080 250 1540 1400 1340 From the table, we can see that for output of 100 , Technology 2 is the cheapest. For output levels of 150, 200, or 250, Technology 3 is cheapest.
Problem 6 a. Suppose the firm is operating in a high-wage country, where capital cost is $100 per unit per day and labor cost is $80 per worker per day. For each level of output, which technology is the cheapest? b. Now suppose the firm is operating in a low-wage country, where capital cost is $100 per unit per day but labor cost is only $40 per unit per day. For each level of output, which technology is the cheapest? c. Suppose the firm moves from a high-wage to a low-wage country but that its level of output remains constant at 200 units per day. How will its total employment change?
Problem 6 Answer b. In a low-wage country, where capital costs $100 per day and labor costs only$ 40 per day, the cost figures are as follows: Diary Output Technology 1 Technology 2 Technology 3 100 580 600 660 150 700 680 700 200 840 820 840 250 1020 1000 1020 From the table, we can see that for output of 100, Technology 1 is now cheapest. For output levels of 150, 200, or 250, Technology 2 is now cheapest. c. If the firm moves from a high-wage country and continues to produce 200 units per day, it will change from technology 3 (with six workers)to technology 2 (with eight workers). Employment increases by two workers.
Problem 6 a. Suppose the firm is operating in a high-wage country, where capital cost is $100 per unit per day and labor cost is $80 per worker per day. For each level of output, which technology is the cheapest? b. Now suppose the firm is operating in a low-wage country, where capital cost is $100 per unit per day but labor cost is only $40 per unit per day. For each level of output, which technology is the cheapest? c. Suppose the firm moves from a high-wage to a low-wage country but that its level of output remains constant at 200 units per day. How will its total employment change?
Problem 6 Answer b. In a low-wage country, where capital costs $100 per day and labor costs only$ 40 per day, the cost figures are as follows: Diary Output Technology 1 Technology 2 Technology 3 100 580 600 660 150 700 680 700 200 840 820 840 250 1020 1000 1020 From the table, we can see that for output of 100, Technology 1 is now cheapest. For output levels of 150, 200, or 250, Technology 2 is now cheapest. c. If the firm moves from a high-wage country and continues to produce 200 units per day, it will change from technology 3 (with six workers)to technology 2 (with eight workers). Employment increases by two workers.
1)Jerry sells cherry sno-cones along the boardwalk in New Jersey. During the summer this is a perfectly competitive business, and Jerry faces a perfectly elastic demand curve. If he wants to try to increase revenues he should a)raise the price of his sno-cones to make more per sales. b)lower the price of his sno-cones to try to sell more. c)keep the price the same but produce more to increase sales. d)do nothing; there is nothing he can do to increase revenue.
Piece per bushel Figure 6. 2 5 Bushels of corn Q 2)Refer to Figure 6. 2. This corn producer produces 100 bushels of corn and sells each bushel at $5. The cost of producing each unit bushel is $2. This corn producer's total revenue is a)$20. b)$200. c)$300. d)$500.
3)Refer to Figure 6. 2. This corn producer earns a total revenue of $900. Each bushel of corn is sold for $5. This corn producer must be selling ______ bushels of corn. a)180 b)450 c)900 d)4, 500
5)The Wax Works sells 400 candles at a price of $10 per candle. The Wax Works' total costs for producing 400 candles are $500. The Wax Works' normal profits are a)$100. b)$3, 500. c)$4, 500. d)indeterminate from this information.
SCENARIO 1: You are the owner and only employee of a company that writes computer software that is used by gamblers to collect sports data. Last year you earned a total revenue of $90, 000. Your costs for equipment, rent, and supplies were $60, 000. To start this business you quit a job at another computer software firm that paid $40, 000 a year. 6)Refer to Scenario 1. During the year your economic costs were a)$40, 000. b)$60, 000. c)$100, 000. d)$130, 000.
7)Refer to Scenario 1. A yearly normal profit for your computer software firm would be a)$20, 000. b)$40, 000. c)$60, 000. d)$100, 000. 8)Refer to Scenario 1. Your profit last year was a)$10, 000. b)$30, 000. c)$50, 000. d)$60, 000.
9)Refer to Scenario 1. Your economic profit last year was a)-$40, 000. b)-$10, 000. c)$10, 000. d)$30, 000. SCENARIO 2: You are the owner and only employee of a company that sets odds for sporting events. Last year you earned a total revenue of $100, 000. Your costs for rent and supplies were $50, 000. To start this business you quit a job as a blackjack dealer that paid $20, 000 a year. 10)Refer to Scenario 2. During the year your economic costs were a)$70, 000. b)$60, 000. c)$50, 000. d)$20, 000.
11)Refer to Scenario 2. A yearly normal profit for your company is a)$20, 000. b)$40, 000. c)$60, 000. d)$100, 000. 12)Refer to Scenario 2. Your profit last year was a)$10, 000. b)$30, 000. c)$50, 000. d)$60, 000.
13)Refer to Scenario 2. Your economic profit last year was a)-$40, 000. b)-$10, 000. c)$10, 000. d)$30, 000. 14)There are 100 dog kennels in Atlanta. An economist studying the pricing behavior of dog kennels tells you that she is limiting her analysis to a time period that does not allow for any new dog kennels to enter the industry or for any established dog kennels to leave the industry. The time period this economist referred to is a)the market period. b)the industry run. c)the long run. d)the short run.
Technology A B C D Unit of Capital 4 6 8 12 Number of Employees 18 12 Table 6. 1 8 6 15)Refer to Table 6. 1. Which technology is the most labor intensive? a)A b)B c)C d)D
22)Refer to Table 6. 2. If the hourly price of labor is $10 and the hourly price of capital is $1, which production technology should be selected? a)A b)B c)C d)D 23)When Burger Barn hires one worker, 20 customers can be served in an hour. When Burger Barn hires two workers, 50 customers can be served in an hour. The marginal product of the second worker is ______ customers served per hour. a)15 b)30 c)40 d)67. 5
24)At the Pampered Pet Salon the marginal products of the first, second, and third workers are 20, 16, and 10 dogs washed, respectively. The total product (number of dogs washed) of the three worker is a)15. 33. b)30. c)46. d)138. 25)At the Larson Bakery the marginal products of the first, second, and third workers are 20, 17, and 11 customers served, respectively. The total product (number of customers served) of the three workers is a)11. b)40. c)46. d)48.
26)If diminishing marginal returns have already set in for The Picture Perfect Framing Store and the marginal product of the fifth picture framer is 20, then the marginal product of the sixth picture framer must be a)negative. b)zero. c)less than 20. d)greater than 20. 27)If labor is a variable input in production, the law of diminishing marginal returns implies that in the short run a)labor's marginal product is constant. b)labor's marginal product decreases after a certain point. c)total product is negative. d)total product is negative after a certain point has been reached.
28)If the marginal product of labor is less than the average product of labor, then the a)marginal product must be increasing. b)average product must be decreasing. c)marginal product must be decreasing. d)Both b and c 29)The law of diminishing returns a)implies that as we add more workers our output decreases. b)applies only in the short run. c)is true only when all inputs are variable. d)All of the above
30)Suppose output varies, ceteris paribus, with labor input in the following manner: L 0 1 2 3 4 5 After how many units of labor do diminishing returns set in? a)A b)B c)C d)D
31)When total product is maximized, a)both marginal product and average product are zero. b)marginal product is positive but average product is zero. c)marginal product is zero but average product is positive. d)both marginal product and average product are zero. 0 32)After the point where total product is maximized, a)marginal product is negative, but average product is still positive. b)both marginal and average products are negative. c)marginal product is positive, but average product is negative. d)both average product and marginal product are positive.
33)If marginal product is greater than average product, then a)average product must be decreasing. b)marginal product must be decreasing. c)marginal product must be increasing. d)marginal product could either be increasing or decreasing. 34)If we assume that labor is the only variable input, the slope of the total product curve in the short run a)has no economic significance. b)measures the average product of labor. c)measures the marginal product of labor. d)measures both the marginal and average product depending where on the total product curve we are.
35)You own a business that answers telephone calls for physicians after their offices close. You have an incentive to substitute capital for labor if a)price of capital increases. b)price of labor decreases. c)price of labor increases. d)marginal product of labor increases. 36)Firms have an incentive to substitute labor for capital as the a)price of capital increases. b)price of labor decreases. c)price of labor increases. d)marginal product of labor decreases.
37)The specific technology chosen by a profit-maximizing clothing manufacturer depends on a)input prices. b)output prices. c)demand for the output. d)supply of the output. 38)Assume that the price of labor and capital have remained the same, but that the average educational level of workers has increased and therefore the productivity of labor has increased. This would lead a firm to a)use a more capital-intensive production technology. b)use a more labor-intensive technology. c)not change its production technology, but to produce fewer units of output. d)use only labor to produce the product.
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