中级微观学ch08

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范里安中级微观经济学第八版习题

1 BUDGET CONSTRAINT1.A poor person who has an income of $1000 receives $100 worth offood stamps. Draw the budget constraint if the food stamp recipient can sell these coupons on the black market for less than their face value.2.Since 1979, recipients have been given food stamps. Before 1979,however, people bought food stamps at a subsidized rate. For example, to get $1 worth of food stamps, a household paid about 15￠(the exact amount varied by household characteristics and other factors). What is the budget constraint facing an individual if that individual may buy up to $100 per month in food stamps at 15￠per each $1 coupon. 3.During his first year at school, Ximing buys eight new collegetextbooks at a cost of $50 each. Used books cost $30 each. When the bookstore announces a 20% increase in new texts and a 10% increase in used texts next year, Ximing’s father offers him $80 extra. Is Ximing better off, the same, or worse off after the price change? Why?2 PREFERENCES1. Julia consumes cans of anchovies, A, and boxes of biscuits, B. Each ofher indifference curves reflects strictly diminishing marginal rates of substitution. Where A = 2 and B = 2, her marginal rate of substitution between cans of anchovies and boxes of biscuits equals -1. Will sheprefer a bundle with three cans of anchovies and a box of biscuits to a bundle with two of each? Why?2. What assumption or assumptions rule out the following phenomenon:Geoffrey has a bundle consisting of 6 apples and 8 raspberries. He states that if he is given 1 more apple, he will ask for 3 more raspberries to keep him indifferent between his old bundle and the new bundle that he will have after he receives the 1 additional apple.3. Draw indifference curves for the following people:a) John says: “I get no satisfaction from 1 ounce of vermouth or 3 ouncesof gin, but 1 ounce of vermouth and 3 ounces of gin (a martini) really turn me on.”b) Steve says: “I will not cut my hair to please my boss unless she paysme. My price is $300 plus $1 for every 1/8 inch of hair that is cut. In other words, for every $1 above $300 that the boss pays me, I will cut 1/8 inch off my hair.”c) In Part b of this problem, what is the marginal rate of substitutionbetween dollars and hair in the region below and above $300?d) Ann says: “I enjoy beer and pretzels, but after 12 beers, any additionalbeer makes me sick.”4. Jeffrey is five years old. He likes candy and hates spinach. He isallowed 2 candy bars a day, but his mother offers him 1 additional candy bar for every 2 ounce of spinach he eats.a) On these terms, Jeffrey eats 3 ounces of spinach and 3.5 candy barseach day. Using indifference curves, illustrate his optional choice.b) Suppose that Jeffrey’s mother does not give him 2 “free” candy barseach day but still gives him 1 candy bar for every 2 ounce of spinach he eats. Would his spinach consumption be greater or smaller than in Part a? Explain your answer.4 CHOICE1. Tara has a utility function U(B, Z) = ABαZβ, Where A, α, andβareconstraints, B is burritos, and Z is pizzas. If the price of burritos, p B is $2 and the price of pizzas, p Z is $1, what is Tara’s optimal bundle?2. Assume that there are two goods in the world: apples and raspberries.Say that Geoffrey has a utility function for these goods of the following type, where r denotes the quantity of raspberries and a the quantity if apples: U = r·a.a)Draw an indifference curve that is defined by this utility function andhas a utility level of 2500.b)What is the marginal rate of substitution between the raspberries andthe apples when Geoffrey consumes 50 raspberries and 50 apples?What is the marginal rate of substitution between these two goods when Geoffrey consumes 100 raspberries and 50 apples?c)If the price of raspberries is $1 per unit and the price of apples is $1per unit and Geoffrey has $100 to spend, what bundle of raspberries and apples will he buy? Is the marginal rate of substitution equal to the ratio of the prices of these goods in the optimal bundle? If not, why not?d)If the unit prices of the raspberries and the apples are $4 and $3,respectively, what bundle of raspberries and apples will Geoffrey buy with his income of $100?3. Steve’s utility function is U = BC, where B = veggie burgers per weekand C= packs of cigarettes per week. What is his marginal rate of substitution if veggie burgers are on the vertical axis and cigarettes are on the horizontal axis? Steve’s income is $120, the price of a veggie burger is $2, and that of a pack of cigarettes is $1. How many burgers and how many packs of cigarettes does Steve consume to maximize his utility? When a new tax raises the price of a burger to $3, what is his new optimal bundle? Illustrate your answers in a graph.5 DEMAND1.Roger’s utility function is U = B1/4Z3/4, his income is Y, the price of Bis p B, and the price of Z is p Z. Derive his demand curves.2.Derive Roger’s Engel curve for B for the utility given in problem 2.7 CONSUMER’S SUPPLUS1.If the inverse demand function is p = a–bQ, what is the consumersurplus if price is a/2?2.If the supply function is Q = Apη, what is the producer surplus if priceis p*?9 EQUILIBRIUM1.In 1998, a virus killed more than half the oysters used to producepearls in the world’s busiest undersea factory. Use a diagram to indicate why the price of pearls rose 18%. How did the equilibrium quantity change?2.Increasingly, instead of advertising in newspapers, individuals andfirms use Web sites that offer free classified ads, such as , , , and portals like Yahoo and America Online.Using a supply-and-demand model, explain what will happen to the equilibrium levels of newspaper advertising as the use of the Internet grows. Will the growth of the Internet affect the supply curve, the demand curve or both? Why?3.The U.S. supply of frozen orange juice comes from Florida and Brazil.What is the effect of a freeze that damages oranges in Florida on the price of frozen orange juice in the U.S. and on the quantities of orange juice sold by Floridian and Brazilian firms?4.The supply of corn by the U.S. is Q a= a + bp, and the supply by therest of the world is Q r = c + ep. What is the world supply?5. A rent control law limits the price of an apartment. What is the likelyeffect of such a law in the short run? What is the likely effect of the law in the long run? Be sure to discuss the quantity and quality of apartments available for rent.6.The government wants to drive the price of soybeans above theequilibrium price, p1 to p2. It offers growers a payment of x to reduce their output from Q1(the equilibrium level) to Q2, which is the quantity demanded by consumers at p2. How large must x be for growers to reduce output to this level? What are the effects of this program on consumers, farmers, and total welfare? Compare this approach to (a) offering a price support of p2, (b) offering a price support and a quota set at Q1, and (c) offering a price support and a quota set at Q2.10 TECHNOLOGY1.Michelle’s business produces ceramic cups using labor, clay, and akiln. She can manufacture 25 cups a day with one worker and 35 with two workers. Does her production process illustrate diminishing returns to scale or diminishing marginal returns to scale? What is the likely explanation for why output doesn’t increase proportionatelywith the number of workers?2. Suppose that the production function is q = L 3/4K 1/4.a. What is the average product of labor ，holding capital fixed at K ?b. What is the marginal product of labor?c. Does this production function have increasing, constant, or decreasing returns to scale?3. A good recipe for a French dish called ceviche requires 16 ounces of fillet of red snapper, 3 ounces of lime juice, 1 ounce of coriander, and 8 ounces of Bermuda onion. This combination of inputs is expressed in the following production function:1243min ,,,1638z z z y z ⎧⎫=⎨⎬⎩⎭ In this production function, z 1 is fillet of red snapper, z 2 is lime juice, z 3 is coriander, and z 4 is Bermuda onion. The unit of measure for each input is the ounce, and the unit of measure for ceviche (the output) is the quantity produced by the recipe. If a restaurant has on hand 32 ounces of snapper, 9 ounces of lime juice, 5 ounces of coriander, and 48 ounces of onion, how many “units ” of ceviche can it produce?4. Construct a total product curve for a function that exhibits diminishing marginal product throughout. Then construct another total product curve for a function that exhibits initially constant and subsequently diminishing marginal product. Below the graphs of these two total products curve, derive the corresponding average and marginalfunctions. Check to see that the curves you have drawn are consistent with what you know about the relationship between the average and marginal product curves.11 PROFIT MAXIMIZATION1.You have 60 minutes to take an exam with two questions. You want tomaximize your score. Toward the end of the exam, the more time you spend on either question, the fewer extra points per minutes you get for that question. How should you allocate time between the two questions?(Hint: Think about producing an output of a score on the exam using inputs of time spent on each of the problem)2. A competitive firm’s production function is y = L + 2LK + K. What isits marginal revenue product of labor?3.A firm’s production function is y = ALαKβ. What is the firm’s marginalrevenue product of labor?1L2, 4.A competitive firm has the production of function Q= 20L–4 where Q is the number of units of output produced and L is the number of units of labor (the only input) used. The output price is $2, the wage rate is $1, and the firm faces a fixed cost of $100.a)What is the profit-maximizing quantity of labor demanded by thefirm?b)What is the firm’s profit in the short run?c)If, in the long run, the output price changes so that profits are zero,what is the quantity of labor demanded in the long run?5.A competitive firm has the production function. Q = LαKβ, where Q isthe number of units of output produced, L is the number of units of labor used, and K is the number of units of capital used. The output price p, the wage rate w, and the cost of capital r are given. Assume that α > 0, β > 0, and 0 < ( α + β ) < 1.a)What is the firm’s profit-maximizing quantity of labor if the quantityof capital is fixed at K?b)What is the firm’s profit-maximizing level of capital if both capitaland labor are variable? (Hint: Use the profit-maximizing capital-labor ratio K/L to substitute for the level of labor.)12 COST MINIMIZATION1.Assume that a firm produces 90 units of output using 9 units of inputX and 9 units of input Y. The f irm’s technological possibilities can be represented by the production function Q = 10X1/2Y1/2.a)If the price of X is $8 and the price of Y is $16, is the inputcombination of 9 units of X and 9 units of Y the most efficient way to produce 90 units of output?b)What must the ratio of input prices be for this input combination to beefficient?c)Assume that the price of X is $1 and the price of Y is $2. Derive theleast-cost way to produce 400 units of output.2.A medical center produces health services using two inputs: hospitalbeds and labor. There is a government regulation restricting the number of beds to B. Assume that the medical center is currently usingB beds and L units of labor to produce Q1 units of health services. Alsoassume that the medical center plans to expand its output to Q2 units of health services. Prepare a diagram to show how this government regulation restricting the number of hospital beds would affect the efficiency of delivering health services.3.A trucking firm’s output is measured by the number m of truck-milesmoved per day. The firm’s operating costs are as follows:i.wages of trucks, $w per hourii.cost of gasoline, $p per galloniii.fuel consumption, g= A+ Bs, where g is gallons of gasoline per truck-mile, s is the speed at which a truck is driven, and A and B are constantsa)Derive the total variable cost function of the firm if it has an unlimitednumber of trucks.b)What does the cost function look like if the firm has only one truckand that truck can be driven for a maximum of ten hours per day?4.A college student is considering whether to operate a lawn-mowingbusiness for the summer or work in a business owned by her family.Her time is worth $w1 per hour and she can work as many hours as she chooses in the family business at this rate. If she starts her own business, she will have to buy gasoline for her lawn mower at a price of $w2 per gallon. She can rent a small mower for $w3 per hour. The mower cuts a 12-inch swath of lawn and uses 1/3 gallon of gasoline per hour. With this mower, she can cut 10,000 square feet of lawn in an hour. (Use 10,000 square feet as the units of measurement for output.) Our college student can rent a large mower for $w4 per hour.This mower uses 1 gallon of gasoline per hour and cuts 3 units of lawn per hour.a)Verify that the production function for the two mowers are as follows:y = min{z1, 3z2, z3}y = 3min{z1, z2, z4}Assume that z1 is hours of labor, z2 is gallons of gasoline, and z3 and z4are the hours of the small mower and the large mower, respectively.b)Derive the cost functions.c)Show that using the small mower is a cheaper way to cut grass if 2w1 <w4 – 3w3. Why is this result independent of the price of gasoline?d)How high a price must our college student receive for cutting a unit oflawn in order to induce her to set up her own lawn-mowing firm ratherthan work in the family business?e)Assume that a firm uses two types of input in the production of acertain commodity. What is the maximum output if the marginal product of input is MP1 = 100X2 –X1 and the marginal product of input2 is MP2 = 100X1 –X2, the total amount that can be spent on inputs is$1,000, the price of input 1 is $2, and the price of 2 is $5?13 COST CURVES1.The only variable input a janitorial service firm uses to clean offices isworkers who are paid a wage, w, of $8 an hour. Each worker can clean four offices in an hour. Use math to determine the variable cost, the average variable cost, and the marginal cost of cleaning one more office. Draw a diagram to show the average cost, and marginal cost curves.2.Gail works in a flower shop, where she produces 10 floralarrangements per hour. She is paid $10 an hour for the first eight hours she works and $15 an hour for each additional hour she works. What is the firm’s cost function? What are its AC, AVC, and MC functions?Draw the AC, AVC, and MC curves.3.A firm has two plants that produce identical output. The cost functionsare C1 = 10y– 4y2 + y3and C2 = 10y– 2y2 + y3.b.At what output levels does the average cost curve of each plant reachits minimum?c. If the firm wants to produce 4 units of output, how much should it produce in each plant?4. A firm that makes widgets must build a plan that will cost $10,000. The plant will be able to produce up to 10,000 units, at which point its capacity will be reached and a new plant will be needed. The total cost function for each plant (including the fixed cost of building the plant) is C (y ) = 10,000 – x 1/2/100.a) Determine the cost function for this firm.b) Is this cost function subadditive over the range of outputs from 1 unit to 10,000 units? Is it subadditive for all levels of output?14 FIRM SUPPLY1. If a competitive firm ’s cost function is C (y ) = 100 + 10y – y 2 + 31y 3, what is the firm ’s marginal cost function? What is the firm ’s profit- maximizing condition?2. If a competitive firm ’s cost function is C (y ) = a + by + cy 2 + dy 3, where a , b , c , and d are constants, what is the firm ’s marginal cost function? What is the firm ’s profit-maximizing condition?3. Consider a firm with a total cost curve of TC = 1,000 + q 3/3 – 2q 2 + 6q . a) What is the lowest price at which this firm will want to supply a positive amount to the market in the short run?b) At the “lowest price”, how much will be supplied?c) How much will be supplied in the short run if the price is $10?4. What is the effect on firm and market equilibrium of a law requiring afirm to give its workers six months’ notice before it can shut down its plant?15 INDUSTRY SUPPLY1. Each firm in a competitive market has a cost function of C = 16 + y2.The market demand function is Q = 24–y. Determine the equilibrium price, quantity per firm, market quantity, and number of firms.2. Assume that the taxi industry in the town of New City is perfectlycompetitive. Also assume that the constant marginal cost of a taxi ride is $5 per trip and that each taxi is capable of making 20 trips a day. We will let the demand function for taxi rides each day be D(p) = 1,100 –20p.a)What is the perfectly competitive price of a taxi ride?b)How many rides will the citizens of New City make every day?c)How many taxis will operate in New City?Assume that every taxi that operates in New City has a special license. Therefore, the number of such licenses is the same as the number of taxis that you calculated in Part c of this problem. Further assume that the demand for taxi rides has increased and is now D(p) =1,200 - 20p. The cost of operating a taxi is still $5 per ride, and the number of taxis has not changed.d)Calculate the price that will equate demand with supply.e)Calculate the profit that each taxi will earn on a ride.f)Calculate the daily profit of each taxi. (Hint: Continue to assume thateach taxi can make only 20 rides a day)3. A competitive market has an unlimited number of potential suppliersproducing the same output, and each supplier has a long-run average cost function of AC= q2 –4q+ 6 and a long-run marginal cost function of MC = 3q2 – 8q + 6.a) Find the equilibrium quantity q produced by each firm in the long run.b) Find the long-run equilibrium price.4. Assume that a very large number of firms in an industry all have accessto the same production technology. The total cost function associated with this technology is TC(Q) = 40Q–24Q2 + 4Q3. If the demand function for the industry’s product is Q = 19 –P, how many firms will produce positive amounts of output at a competitive (that is, zero profit) equilibrium?5. Assume that a certain small town contains a large number ofwidget-producing firms. All the firms buy oil from the same refinery.Firm 1 is situated very close to the refinery, and the other firms are located 50 miles away. Firm 1 pays $18 per barrel for the oil, while theother firms pay $18 per barrel plus a transportation charge of $.05 cents a mile, or a total of $20.50 per barrel.To produce four widgets, a firm needs 1/10 barrel of oil, 1/2 hour of labor, and the use of one machine. The cost of labor is $10 per hour, and the necessary machine can be rented for $5 per hour. No firm has the capacity to produce more than 100 units of widgets.a)Derive the supply curve for firm1. Derive the supply curve for all theother firms.b)What is the equilibrium price?c)Does any firm earn economic rent (that is, extra economic profit) inthe industry?d)Does firm 1 affect the price of widgets in the industry? If not, whynot?e)Suppose that there is no capacity limit. What will the equilibrium pricebe?f)Will firm 1 affect the price when there is unlimited capacity?16 MONOPOLY1.Show that after a shift in the demand curve, a monopoly’s price mayremain constant but its output may rise.2.When is a monopoly unlikely to be profitable?(Hint: Discuss therelationship between market demand and average cost)3.The inverse demand curve a monopoly faces is p = 100 - Q. The firm’scost curve is C(Q) = 10 + 5Q. What is the profit-maximizing solution?4.How does your answer to Problem 3 change if C(Q) = 100 + 5Q?5.A monopoly’s production function is: y = L1/2K1/2, where L is labor andK is capital. The demand function is p = 100–y. The wage, w, is $1 per hour, and the rental cost of capital, r, is $4.a.Derive the long-run total cost curve equation as a function of y.b.What quantity maximizes this firm’s profit?c.Find the optimal input combination that produces the profit-maximizing quantity. Illustrate with a graph.6. Suppose that a monopolist faces a demand curve of P = 100 - 2Q. Herfirm has costs of C(Q) = 5Q2.a) What is the revenue function for this monopolist?b) What is the marginal revenue function?c) What is the marginal cost function?d) What is the profit-maximizing output for this monopolist?e) What is the maximum profit this firm can make?f) If this monopolist has to pay a permission free of $150 to the stategovernment in order to start the business, will her optimal level of output change? If not, why not?17 FACTOR MARKETS1.A monopsony faces a supply curve: w = 10 + x. What is its marginalexpenditure curve?18 OLIGOPOLY1.What is the duopoly Cournot equilibrium if the market demandfunction is Q = 1000–1000p, and each firm’s marginal cost is $0.28 per unit?2. Consider a duopolistic market with two firms, A and B, facing ademand curve of p = 1 –q A–q B. Assume that initially each firm has access to the same technology with constant returns to scale and that the cost of production is C A = q A/2 for firm A and C B= q B/2 for firm B.a) What is the profit function for each firm?b) Graph the reaction functions for firms.c) What is the equilibrium outputs?d) Assume that the initial output levels of the two firms are given by pointX(3/10, 4/10) and Y(1/10, 2/10). Show in a graph the process of change in the output levels of the two firms and the point at which their output levels converge.3. A duopoly faces a market demand of p= 120–Q. Firm 1 has aconstant marginal cost of MC1 = 20. Firm 2’s constant marginal cost is MC2 = 40. Calculate the output of each firm, market output, and price if there is (a) a collusive equilibrium or (b) a Cournot equilibrium.4. Assume that there are two firms in a market, firm 1 and firm 2. Thetotal demand for the identical product they make is p = 200 – 2(q1 + q2), where q1 is the output of firm 1 and q2 is the output of firm 2. The production costs of firm 1 and firm 2 are C1 = q12and C2 = q22, respectively.a) Assume that firm 2 decides to produce either 20, 40, 60, or 100 units ofoutput. Show the demand curve and the marginal revenue curve facing firm 1 in each of these situations, assuming that the output levels will remain unchanged once they are chosen.b) Define the output that represents the best (the profit-maximizing)response of firm 1 to each of the output levels chosen by firm 2.19 EXCHANGE1.Initially, Michael has 10 candy bars and 5 cookies, and Tony has 5candy bars and 10 cookies. After trading, Michael has 12 candy bars and 3 cookies. In an Edgeworth box, label the initial Allocation A and the new Allocation B. Draw some indifference curves that are consistent with this trade being optimal for both Michael and Tony. 2.In a pure exchange economy with two goods, G and H, the two tradershave Cobb-Douglas utility functions. Amos’s utility is U a =(G a)α(H a)1-α, and Elise’s is U e = (G e)β(H e) 1-β, what are their marginalrates of substitution?3. Continuing with problem 3: between them, Amos and Elise own 100 units of G and 50 units of H . Thus if Amos has G a and H a , Elise has G e =100 – G a and H e = 50 – H a . Solve for their contract curve.4. Arnold and Brigitte are marooned on a deserted island. Arnold has exactly one unit of Xylose and Brigitte has exactly one unit of Yam. Their preferences between these two items are represented by the following two equations:1/32/31/21/2A A AB B B U X Y U X Y =⋅=⋅In these equations, X A and Y A are the consumption of Xylose and Yam by Arnold. Similarly, X B and Y B are the consumption of Xylose and Yam by Brigitte.a) Is the following allocation Pareto-optimal? Explain why or why not.1211,,,2323A AB B X Y andX Y ==== b) If Arnold and Brigitte were to trade between themselves, would they be able to attain this allocation as a competitive equilibrium? What would be the equilibrium price ratio of Xylose to Yam? Would Arnold and Brigitte be able to afford this allocation at the equilibrium prices, given their endowments? If not, what kind of income transfer would be necessary?5. Two people trade two goods that they cannot produce. Suppose that one consumer ’s indifference curves are bowed away from the origin – the usual type of curves – but the other ’s are concave to the origin.In an Edgeworth box, show that a point of tangency between the two consumers’indifference curves is not a Pareto-efficient bundle.(Identify another allocation that Pareto dominates.)6.The demands for two goods depend on the prices of Good 1 and Good2, p1 and p2, Q1 = 15 – 3p1 + p2, Q2 = 6 – 2p2 + p1, but each supply curve depends on only its own price: Q1 = 2 + p1, Q2 = 1 + p2. Solve for the equilibrium: p 1, p2, Q1, and Q2.20 PRODUCTION1. Assume that you have exactly 100 hours of labor to allocate betweenproducing good X and good Y. Your output of goods X and Y depends solely on the hours of labor you spend in the following way:X=and Y=a)If you can sell your output of goods X and Y at the fixed prices P X = 10and P Y= 5, how much of goods X and Y would you produce to maximize your profits?b)Now assume further that you have the following utility function:U=If you can trade a bundle of goods X and Y that you produce in the market at fixed prices of P X = 10 and P Y = 5, what bundle would you produce and what bundle would you consume to maximize your utility?Are you a net demander and a net supplier of the two goods? Draw adiagram to depict what is happening.2. Suppose that the production possibilities frontier for cheeseburgers (C)and milk-shakers (M) is given by C + 2M = 600.a) Graph this function.b) Assuming that people prefer to eat two cheeseburgers with everymilk-shaker, how much of each product will be produced? Indicate this point in your graph.c) Assuming that this fast-food economy is operating efficiently, whatprice ratio (P C/P M) will prevail?21 WELFARE1. Suppose that society used the “opposite”of a Rawlsian welfarefunction: it tried to maximize the well-being of the best-off member of society. Write this welfare function. What allocation maximizes welfare in this society?2. Assume that Bob has a utility function of U = 8X1 + 1X2 – 3X3 and Joanhas a utility function of U = –2X1 + 7X2 + 5X3. Consider the following allocation:a)Is this allocation envy free?b)Is this allocation Pareto-optimal?c)Find a Pareto-optimal allocation, and determine whether it is envyfree.d)Do you think that the allocation in Part c of this problem is desirable?Why or why not?22 EXTERNALITIES1.Suppose that the only way to reduce pollution from paper productionis to reduce output. The government imposes a tax equal to the marginal harm from the pollution on the monopoly producer. Show that the tax may raise welfare.2.Suppose that the inverse demand curve for paper is p = 200–y, theprivate marginal cost (unregulated competitive market supply) is MC p = 80 + Q, and the marginal harm from gunk is MC g = y.a.What is the unregulated competitive equilibrium?b.What is the social optimum? What specific tax (per unit of output orgunk) results in the social optimum?c.What is the unregulated monopoly equilibrium?d.How would you optimally regulate the monopoly? What is theresulting equilibrium?3. A soot-spewing factory that produces steel windows is next to a。

(完整word版)范里安中级微观经济学

中级微观经济学1. 维克里拍卖定义：维克里拍卖的方式类似密封拍卖,但有一个重要区别：商品由报价最高的竞价人获得,但他只需要按第二高的报价支付。

换句话说，报价最高的投标人得到了拍卖商品,但是他不需要按照他自身的报价支付，而是按照报价第二高的人的报价支付。

特点：密封报、同时报价、价高者得、赢家支付次高价分析:我们分析一个只有两个投标人的特殊情形。

这两人的对商品的评价分别为1v 和2v ,他们在纸条上写下的报价分别为1b 和2b 。

投标人1的期望收益为:如果21v ＞v ,最大化胜出的概率；也就是设置11v b =。

如果21v ＜v ，最小化胜出的概率；也就是设置11v b =. 任意情况,Telling the truth is best.2. 帕累托有效率如果可以找到一种配置，在其他人的境况没有变坏的情况下，的确能使一些人的境况变得更好一些，那么，这就叫做帕累托改进；如果一种配置方法存在帕累托改进,他就称为帕累托低效率；如果一种配置方法不存在任何的帕累托改进,他就称为帕累托有效率的。

3. 价格歧视，第一、二、三级价格歧视1.价格歧视:按不同价格销售不同单位产品的做法称为价格歧视2.一、二、三级价格歧视：第一级价格歧视:是指垄断企业按不同价格出售不同产量，而且这些价格可能因人而异。

这种价格歧视有时又称为完全价格歧视。

第二级价格歧视：是指,垄断企业按不同价格出售不同产量，但是购买相同数量的每个人支付价格是相同的。

因此,价格按购买数量制定,而不是因人而异.最常见的情形是大宗购买时可以享受折扣。

第三级价格歧视：是指垄断企业的销售价格因人而异,但对于同一个人来说，每单位产品的售价是相同的。

这种价格歧视最常见.例如：对老年人打折，对学生打折等。

4.消费者剩余消费者剩余：是指购买者的支付意愿减去购买者的实际支付量。

消费者剩余衡量了购买者自己感觉到所获得的额外收益.5.显示偏好原理1.显示偏好：假定：（1)所有消费者的偏好都是严格凸性的，因此对于一个预算线来说都有且只有一个最优消费束。

中级微观经济学第八讲

规模报酬有三种可能：不变规模报酬：产出增长比例等于投入增长比例；递增规模报酬：产出增长比例大于投入增长比例；递减规模报酬：产出增长比例小于投入增长比例。
生产函数若有
y f (x1, x2 ,, xn )
f (x1, x2 ,, xn ) k y ( 1)
则 k=1、k>1 和 k<1 则分别对应上面的三种情况。
TRS (L, K ) MPL K MPK L
齐次生产函数
k 阶齐次生产函数满足
f (x1, x2 ,, xn ) k f (x1, x2 ,, xn )
两边对λ求导（以两种要素为例）
x1 f1(x1, x2 ) x2 f2 (x1, x2 ) kk1 f (x1, x2 )
令 λ= 1，可得（欧拉定理）
EL
dQ dL
/Q /L
MPL APL
B : APL MPL EL 1
MP
L
C : EL 0
AP
A : EL 1
L
常用的几个生产函数
线性生产函数
Q f (L, K) A L K
固定比例的生产函数 Q f (L, K) min (L, K)
L,K
柯布—道格拉斯生产函数
Q f (L, K ) AL K
中级微观经济学第八讲：技术与生产函数、利润最大化
2007.10.25
第18章、技术与生产函数
微观经济学中，厂商的经营目标总被认为是：通过最有效地利用所掌握的生产要素来实现最大利润；
厂商所面临的约束条件：市场约束：决定了购买投入品、出售产品的条件；技术约束：决定了利用既定的投入能够生产出产品的最大数量；预算约束：决定了生产经营的规模。
f L f K L Q K Q

北大中级微观经济学课件ch8-

1 2
x 2' x2''
x 1'
x1''
x1
Giffen Goods
In rare cases of extreme incomeinferiority, the income effect may be larger in size than the substitution effect, causing quantity demanded to fall as own-price rises. Such goods are Giffen goods.
x 2' x2''
x 1'
x1''
x1
Slutsky's Effects for Income-Inferior Goods
x2 The overall changes to demand are the sums of the substitution and income effects. (x ''',x ''')
x 2' x2''
x 1'
x1''
x1
And Now The Income Effect
x2
x 2' x2''
(x1''',x2''')
x 1'
x1''
x1
And Now The Income Effect
x2 The income effect is (x1'',x2'') → (x1''',x2'''). (x1''',x2''')

中级微观经济学(范里安)第八章斯勒茨基方程市公开课获奖课件省名师示范课获奖课件

x1
x1’’
x1
收入效应是商品1旳价格保持在p’1上不变，同步使收入从m’变到m时对商品1需求旳变动，即：
x1n x1' ( p1' , m) x1'' ( p1' , m)
假如是正常商品，则收入增长会造成需求旳增长；假如是低档商品，则收入增长会降低需求。
替代效应旳符号
假如一种商品旳价格下降，那么可归因于替代效应旳该商品旳需求旳变动一定是非负旳，即：假如p1 > p’1,则肯定有
总效应旳正负取决于收入效应。
变动率表达旳斯勒茨基方程
x1 x1s x1n
把 x1m 定义为负收入效应：
x1 x1s x1m
等式两边都除以 p1，得到：
x1 x1s x1m
p1
p1
p1
m 其中 p1 x1 ，代入上式，得：
x1 p1
x1s p1
x1m m
x1
这就是用变化率表达旳斯勒茨基恒等式。
p1x1+p2x2> p1y1+p2y2
q1y1+q2y2> q1x1+q2x2 由此，下列两不等式必成立
p1x1+p2x2≤p1y1+p2y2
q1y1+q2y2≤ q1x1+q2x2
将以上两不等式相加，重新整顿得： (q1-p1)(y1-x1) +(q2-p2)(y2-x2)≤ 0
这里， q2＝p2，于是有： (q1-p1)(y1-x1) ≤ 0
2. 假如商品1价格上升，消费者旳购置力就会下降，所以，要保持购置力不变必须增长消费者旳收入（增长消费者对商品1旳实际支出）。
所以，替代效应 x1s 就是在商品1旳价格变动到p’，

中级微观经济学范里安版本

中级微观经济学范里安版本xx年xx月xx日•导言与背景介绍•微观经济学基本概念与原理•消费者行为理论•生产者行为理论•市场结构与竞争策略•价格、产出与就业•中级微观经济学前沿问题与发展趋势目录01导言与背景介绍中级微观经济学是经济学的一个分支，主要研究个体经济行为以及市场均衡的形成，包括消费者行为、生产者行为、市场结构、价格形成等。

定义中级微观经济学是经济学的基础学科之一，对于理解整个经济系统的运行和个体经济角色的决策制定有着重要的作用。

它为政策制定者提供了理论依据，也为经济学家提供了研究工具。

重要性中级微观经济学的定义与重要性背景范里安是当代最有影响力的微观经济学家之一，他的《中级微观经济学》是经济学领域的经典著作之一，被广泛采用为大学经济学课程的主要教材。

特点该书系统地介绍了中级微观经济学的基本概念、理论和方法，内容全面、丰富，同时注重理论与实践的结合，具有很好的可读性。

范里安《中级微观经济学》的背景与特点目的学习中级微观经济学可以帮助我们深入理解经济系统的运行机制和个体经济角色的决策过程，掌握中级微观经济学的基本理论和方法，为进一步学习高级微观经济学和其他经济学分支打下坚实的基础。

要点一要点二意义通过学习中级微观经济学，我们可以更好地理解现实经济生活中的各种问题，提高自己的综合素质和决策能力，同时也可以为未来的学术研究和职业发展提供有力的支持。

学习中级微观经济学的目的与意义02微观经济学基本概念与原理需求与供给消费者在不同价格水平上愿意并能够购买的商品或服务的数量。

需求供给均衡价格价格机制生产者在不同价格水平上愿意并能够提供的商品或服务的数量。

市场供求平衡时的价格。

通过价格变动调节供求关系，以实现市场均衡。

市场均衡与价格机制均衡状态市场供给和需求达到平衡的状态。

均衡价格的形成通过价格机制，调节供给和需求的平衡。

价格对经济的调节作用通过价格信号，引导消费者和生产者的行为，实现资源的最优配置。

范里安中级微观经济学第八到十章念书笔记

一、斯勒茨基方程Topic:消费者在商品选择时如何对商品价钱的变更做出反映Highlights:1.替代效应：①商品价钱变更的两种效应：用一种商品互换另一种商品的比率发生转变；代表全数收入的购买力也会发生转变。

②如何计算替代效应：△X1s=x1(p1’,m’)-x1(p1,m)。

2.收入效应，收入效应△X1n衡量的是在使商品1的价钱维持在p1’上不变，同时使收入从m’变更至m时，商品1的需求变更，既是△X1n=x1(p1’,m)-x1(p1’,m’)。

3.替代效应老是与价钱的变更方向相反，咱们称替代效应是负的。

4.需求的总变更：①△X1= X1s+△X1n= x1(p1’,m’)-x1(p1,m)+ x1(p1’,m)-x1(p1’,m’)；②总效应可正可负；③吉芬商品一定是低档商品，但低档商品不必然是吉芬商品。

5.变更率：①价钱变更，收入维持不变时的需求变更率：△x1/△p1=(x1(p1’m)-x1(p1,m))/ △p1;②价钱变更，收入调整到恰好使原先的消费束还能支付得起时的需求变更率：△x1s/△p1=(x1(p1’,m’)-x1(p1,m))/ △p1;③价钱维持不变和收入做出调整时的需求变更率：△x1m*x1/△m=(x1(p1’,m’)-x1(p1’, m))*x1-(m’-m)。

6.需求法则：若是一种商品的需求随着收入的增加而增加，那么，这种商品的需求必然会随着价钱的上升而下降。

7.完全互补下替代效应为0，需求变更完全归因于收入效应；完全替代情况与完全互补情况相反；拟线性情况下商品1的需求变动归因于替代效应，收入效应等于0。

8.希克斯下的替代效应，不是维持购买力不变而是维持效应不变；希克斯需求曲线有时也称作补偿需求曲线。

二、购买和销售Topic：禀赋条件下的需求及其效应Highlights：1.净需求和总需求：①假设两种商品消费者的初始禀赋为（w1,w2），通过观察商品的市场价钱，将决定这两种商品的购买和销售的数量。

中级微观经济学08PPT课件

这种价格下跌是由于买方所能够掌握的有关车的信息少于卖方占有的信息（存在有隐蔽信息），从而对车的质量持有怀疑态度；
由于买方无法掌握隐蔽信息，他只能根据市场上商品的平均情况（期望值）来作出判断和决策。出于防范风险动机，买方通常采用保守的行为；
如果买方根据期望值确定意愿支付，市场上将只有次货（lemons）可供出售，好货退出市场；如果买方确定他将得到次货的话，他不再按照期望值确定意愿支付。
市场失灵是完全竞争市场的假设条件得不到满足，从而导致市场机制配置资源失去效率；
市场失灵是依靠市场机制的自发运作不能实现有效率的资源配置。它的出现有四个方面的原因：垄断；不完全信息；外部性；公共物品
40-2
市场失灵的解决方法
解决市场失灵的方法分为两个层面：确保竞争所需要的前提条件，以便使市场机制充分发挥引导资源配置的作用；如果竞争需要的前提不存在，那么就需要政府干预措施来校正市场扭曲。
政府干预常常被认为是解决市场失灵的基本手段，然而，这要求满足以下条件：政府比个人掌握更完整和准确的信息；政府的目标与社会目标相一致；政府的执行成本微不足道。
如果这些条件无法得到满足，也可能会出现政策失灵。
40-3
二、垄断市场
当厂商或要素供给者具有市场支配力时，就会产生经济效率损失；
业、工作经历、气质、推荐 ……）；实施商品保修。
40-13
道德风险
道德风险（moral hazard）指交易中的一方利用其信息优势采取行动，从而改变坏结果出现可能性的行为。例如
购买财产保险后，投保人可能比以前忽视防止事故的发生；
购买汽车保险后，投保人更愿意开快车，从而增大出事故的风险。
第八章市场失灵
主要内容

中级微观经济学-17页精选文档

第一讲微观经济学序论（讲了怎么考试什么的，没有用的！）第二讲（续）补充说明单调变换的概念：例：常见的常替代弹性效用函数形式为：证明：1、当0→ρ时，该效用函数趋近于()=21,x x u 2121ααx x 2、当-∞→ρ时，该效用函数趋近于()=21,x x u {}21,m in x x 证明：1、令1221111,ββαααβ-=+=则 u 的一个单调变换结果是：()()ρρρββ1221121,x x x x t +=()()()2122112122112221112211221121ln 1ln ln limln 1limln 1210lim lim ,ββββββββββρββρρρββρρρρρρρρx x eee ex x t x x x x x x x x x x x x =====∴+++++→→（用到罗必塔法则）()21,x x t = 2121ββx x 的一个单调变换结果是()=21,x x u 2121ααx x ，因此，当0→ρ时，原效用函数所描述的偏好趋近于效用函数()=21,x x u 2121ααx x 所描述的偏好。

如果1α与2α满足21αα+=1，那么当0→ρ时，同时有效用函数趋近于以下效用函数： 2、令1221111,ββαααβ-=+=则 u 的一个单调变换结果是：()()ρρρββ1221121,x x x x t += 当21x x π时，同理，当21x x φ时，有()21,lim x x t -∞→ρ= 2x当21x x =时，有()2121,x x x x t =≡综上所述，、当-∞→ρ时，原效用函数描述的偏好关系趋近于()=21,x x u {}21,m in x x 所描述的偏好关系。

例2 设需要满足的效用水平是=u 2,效用函数形式为21x x ，求支出函数。

解：L=p 1x 1+p 2x 2+[]5.025.01x x u -λ 则：1221x x p p = 即：*22*11x p x p = 代入支出函数表达式则有 *1x =12p e *2x =22p e 四、预算份额如果收入为,y 消费商品数量为()n x x x x ,...,,,321，价格为()n p p p ,...,2,1，则称yx p S ii i =为购买i x 的收入份额，或预算份额。

中级微观经济学考试试题答案完整版培训讲学

一．简答题1.机会成本相关答：是指为了得到某种东西而所要放弃另一些东西的最大价值。

在稀缺性的世界中选择一种东西意味着放弃其他东西。

一项选择的机会成本，也就是所放弃的物品或劳务的价值。

机会成本是指在资源有限条件下，当把一定资源用于某种产品生产时所放弃的用于其他可能得到的最大收益。

2.劣等品和低档品的逻辑推导（P78）答：低档品或劣等品（inferior goods）：指消费量随收入的上升而下降的物品。

对于正常商品，替代效应与价格呈反方向变动，收入效应也与价格成反方向变动，所以总效应与价格成反方向变动，因此正常商品的需求曲线向右下方倾斜。

对于低档品来说，替代效应与价格成反方向变动，收入效应与价格同向变动，但替代效应大于收入效应的作用，总效应与价格反方向变动，需求曲线向右下方倾斜。

吉芬商品，替代效应与价格反方向变动，收入效应与价格通向变动，收入效应极大地大于替代效应，使总效应与价格同向变动，其需求线向右上方倾斜。

二．计算题1.生产理论：已知企业的生产函数要素价格需求函数企业生产量求：市场长期均衡的产品价格和企业数量EG A: 已知生产函数为Q=KL-0.5L2—0.32K2，其中Q表示产量，K表示资本，L表示劳动，若K=10，求：（1）写出劳动的平均产量函数和边际产量函数。

（2）分别计算出当总产量、平均产量和边际产量达到极大值时，厂商雇佣的劳动量。

（3）证明当APL 达到最大值时，APL=MPL=2AN A: （1）TP=Q=10L-0.5L^2-30 把K=10带进去边际产量（MPL ）函数就是上式对L 求导。

MPL=10-L平均产量（APL ）函数就是总产量除以投入的劳动。

APL=TP/L=10-0.5L-30/L（2）当TP 最大时，MPL=0。

令MPL=10-L=0 ，解得L=10，所以当劳动投入量L=10时，劳动的总产量TP 达到极大值。

当APL 最大时，是APL 与MPL 相交的时候。

中级微观经济学第八次作业及解答最终版

中级微观经济学第八次作业及解答1.请判断下列说法的正误，并简要说明理由（1）已知某种商品是X,Y,Z三种生产要素结合的产物，当它们同时增加1个单位时，该种商品的产量增加3个单位。

这表明生产要素的边际实物产量为3。

错。

当说明某种生产要素的边际产量时,要保持其他生产要素不变。

（2）若某种商品是X,Y,Z三种生产要素的产物，在保持X和Y不变的前提下，增加1单位Z使产量增加了2个单位，那么这2单位产量是这1单位Z生产出来的。

错。

只能说明Z的边际产量是2单位,但是事实上,这2单位产出是由三种要素共同生产出来的。

（3）假若厂商使用先进的机器设备以代替劳动，劳动的需求曲线将向右方移动。

错。

向左移动。

因为机器代替劳动,厂商对劳动的需求会减少,所以劳动的需求曲线将向左移动。

（4）为消除外部性影响，政府所制订的排污费和排污许可证制度的经济效果是无差异的。

错。

排污费制度的结果是选择减污的边际成本等于边际外部成本；许可证制度的均衡水平是所有厂商减污的边际成本都相等，且等于许可证的价格。

只有当许可证的价格恰好等于边际外部成本时，二者的经济效果才一样。

（5）当存在外部不经济时，厂商的私人成本高于社会成本。

错。

在存在外部不经济时，边际社会成本等于边际私人成本加上边际外部成本，即MSC=MPC+MEC。

（6）一种物品有竞争性，但无排他性，通常我们称之为公共资源。

对。

这是公共资源的定义。

（7）一个产品具有非排他性，是指排除他人使用是不可能的，或者排除他人使用的成本过于昂贵。

对。

这是非排他性的定义。

2. 英文教材Nicholson: Chapter 21, Problem 21.5 Page 599。

Assume the quantity of envelopes licked per hour by Sticky Gums, Inc., is Q , where L is the number of laborers hired per hour by the firm. Assume further that theenvelope-licking business is perfectly competitive with a market price of $.01 perenvelope.a. How much labor would be hired at a competitive wage of $10? $5? $2? Use your results to sketch a demand curve for labor.b. Assume that Sticky Gums hires its labor at an hourly wage of $10. What quantity of envelopes will be licked when the price of a licked envelope is $.10, $.05, $.02? Use your results to sketch a supply curve for licked envelopes.解(a) MP=5000*L -1/2, MRP=VMP=P*MP=50*L -1/2.由VMP=w ，得 50*L -1/2=10,5,2, 得L=25,100,625。

中级微观经济学完整版

中级微观经济学完整版一、名词辨析1.规范分析与实证分析；实证分析（positive analysis）方法实证分析不涉及价值判断，只讲经济运行的内在规律，也就是回答“是什么”的问题；实证分析方法的一个基本特征它提出的问题是可以测试真伪的，如果一个命题站得住脚，它必须符合逻辑并能接受经验数据的检验。

规范分析（normative analysis）方法规范分析以价值判断为基础，以某种标准为分析处理经济问题的出发点，回答经济现象“应当是什么”以及“应当如何解决”的问题，其命题无法证明真伪。

2.无差异曲线与等产量线；无差异曲线是指这样一条曲线，尽管它上面的每一点所代表的商品组合是不同的，但消费者从中得到的满足程度却是相同的。

等产量线表示曲线上每一点的产量都相等，是由生产出同一产量的不同投入品组合所形成的曲线。

3.希克斯补偿与斯卢茨基补偿;希克斯补偿是指当商品价格发生变化后，要维持原有效用水平所需补偿的货币数量。

斯卢茨基补偿是指当商品价格发生变化后，要维持原有消费水平所需补偿的货币数量。

4.边际替代率与边际技术替代率；边际替代率是指，消费者在增加额外一单位商品X之后，若要保持满足水平不变而必须放弃的商品Y的数量。

边际替代率就等于无差异曲线在该点的斜率的绝对值。

边际技术替代率是指，当只有一种投入品可变时，要增加产量，企业必须投入更多的另一种投入品；当两种投入品都可变时，企业往往会考虑用一种投入品来替代另一种投入品。

等产量线斜率的绝对值就是两种投入品的边际技术替代率。

5.边际产出与边际收益产出边际产出（marginal putout），就是指在其他生产资源的投入量不变的条件下,由于增加某种生产资源一个单位的投入,相应增加的产出量。

当产出以产量表示时,即为边际产量;当产出以产值表示时,即为边际产值。

边际收益产出是指，额外单位劳动给企业带来的额外收益是劳动的边际产品与产品的边际收益的乘积。

6.显性成本与隐性成本；显性成本：是指厂商在生产要素市场上购买或租用所需要的生产要素的实际支出；隐性成本：是指厂商本身所拥有的且被用于该企业生产过程的那些生产要素的总价格。