Microeconomic Theory Basic Principles And Extensions 1st Edition Christopher M Snyder, Walter Nicholson, Robert B Stewart - Solutions

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3.11 Independent marginal utilities Two goods have independent marginal utilities if@ 2U@y@x ¼ @ 2U@x@y ¼ 0:Show that if we assume diminishing marginal utility for each good, then any utility function with independent marginal utilities will have a diminishing MRS. Provide an example to show that
3.10 Cobb–Douglas utility Example 3.3 shows that the MRS for the Cobb–Douglas function U xð Þ¼ , y xayb is given by MRS ¼ a by x# $:a. Does this result depend on whether a þ b ¼ 1? Does this sum have any relevance to the theory of choice?b. For commodity bundles for which y ¼ x, how does
3.9 Initial endowments Suppose that a person has initial amounts of the two goods that provide utility to him or her. These initial amounts are given by x and y.a. Graph these initial amounts on this person’s indifference curve map.b. If this person can trade x for y (or vice versa) with other
3.8 Find utility functions given each of the following indifference curves [defined by U (Æ) ¼ k]:a. z ¼ k1=d xa=dyb=d.b. y ¼ 0:5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 % 4 xð Þ 2 % k p % 0:5x.c. z
3.7a. A consumer is willing to trade 3 units of x for 1 unit of y when she has 6 units of x and 5 units of y. She is also willing to trade in 6 units of x for 2 units of y when she has 12 units of x and 3 units of y. She is indifferent between bundle(6, 5) and bundle (12, 3). What is the utility
3.6 Many advertising slogans seem to be asserting something about people’s preferences. How would you capture the following slogans with a mathematical utility function?a. Promise margarine is just as good as butter.b. Things go better with Coke.c. You can’t eat just one Pringle’s potato
3.5 The Phillie Phanatic (PP) always eats his ballpark franks in a special way; he uses a foot-long hot dog together with precisely half a bun, 1 ounce of mustard, and 2 ounces of pickle relish. His utility is a function only of these four items, and any extra amount of a single item without the
3.4 As we saw in Figure 3.5, one way to show convexity of indifference curves is to show that, for any two points (x1, y1) and(x2, y2) on an indifference curve that promises U ¼ k, the utility associated with the point x1 þ x2 2 ;y1 þ y2 2# $ is at least as great as k. Use this approach to
3.3 Consider the following utility functions:a. U(x, y) ¼ xy.b. U(x, y) ¼ x2 y2.c. U(x, y) ¼ ln x þ ln y.Show that each of these has a diminishing MRS but that they exhibit constant, increasing, and decreasing marginal utility, respectively. What do you conclude?
3.2 In footnote 7 we showed that for a utility function for two goods to have a strictly diminishing MRS (i.e., to be strictly quasiconcave), the following condition must hold:UxxU2 x % 2UxyUxUy þ UyyU2 y < 0 Use this condition to check the convexity of the indifference curves for each of the
3.1 Graph a typical indifference curve for the following utility functions, and determine whether they have convex indifference curves (i.e., whether the MRS declines as x increases).a. U(x, y) ¼ 3x þ y.b. U xð Þ , y ¼ ffiffiffiffiffiffiffiffi x ' y p .c. U xð Þ¼ , y ffiffiffi x p þ y.d. U
2.16 More on covariances Here are a few useful relationships related to the covariance of two random variables, xl and x2.a. Show that Cov(x1, x2) ¼ E(x1x2) – E(x1)E(x2). An important implication of this is that if Cov(x1, x2) ¼ 0, E(x1x2)¼ E(x1)E(x2). That is, the expected value of a product
2.15 More on variances The definition of the variance of a random variable can be used to show a number of additional results.a. Show that Var(x) ¼ E(x2) % [E(x)]2.b. Use Markov’s inequality (Problem 2.14d) to show that if x can take on only non-negative values, P ½ðx % lxÞ + k( - r2 xk2
2.14 More on expected value Because the expected value concept plays an important role in many economic theories, it may be useful to summarize a few more properties of this statistical measure. Throughout this problem, x is assumed to be a continuous random variable with PDF f(x).a. ( Jensen’s
2.13 Taylor approximations Taylor’s theorem shows that any function can be approximated in the vicinity of any convenient point by a series of terms involving the function and its derivatives. Here we look at some applications of the theorem for functions of one and two variables.a. Any
2.12 Proof of the envelope theorem in constrained optimization problems Because we use the envelope theorem in constrained optimization problems often in the text, proving this theorem in a simple case may help develop some intuition. Thus, suppose we wish to maximize a function of two variables
2.11 The power function Another function we will encounter often in this book is the power function:y ¼ xd, where 0 - d - 1 (at times we will also examine this function for cases where d can be negative, too, in which case we will use the form y ¼ xd/d to ensure that the derivatives have the
2.9 Concave and quasi-concave functions Show that if f(x1, x2) is a concave function then it is also a quasi-concave function. Do this by comparing Equation 2.114(defining quasi-concavity) with Equation 2.98 (defining concavity). Can you give an intuitive reason for this result? Is the converse of
2.8 Suppose that a firm has a marginal cost function given by MC(q) ¼ q þ 1.a. What is this firm’s total cost function? Explain why total costs are known only up to a constant of integration, which represents fixed costs.b. As you may know from an earlier economics course, if a firm takes price
2.7 Consider the following constrained maximization problem:maximize y ¼ x1 þ 5 lnx2 subject to k % x1 % x2 ¼ 0, where k is a constant that can be assigned any specific value.a. Show that if k ¼ 10, this problem can be solved as one involving only equality constraints.b. Show that solving this
2.6 A simple way to model the construction of an oil tanker is to start with a large rectangular sheet of steel that is x feet wide and 3x feet long. Now cut a smaller square that is t feet on a side out of each corner of the larger sheet and fold up and weld the sides of the steel sheet to make a
2.5 The height of a ball that is thrown straight up with a certain force is a function of the time (t) from which it is released given by f(t) ¼ %0.5gt2 þ 40t (where g is a constant determined by gravity).a. How does the value of t at which the height of the ball is at a maximum depend on the
2.4 The dual problem to the one described in Problem 2.3 is minimize x þ y subject to xy ¼ 0:25:
2.3 Suppose that f(x, y) ¼ xy. Find the maximum value for f if x and y are constrained to sum to 1. Solve this problem in two ways:by substitution and by using the Lagrange multiplier method.
2.2 Suppose a firm’s total revenues depend on the amount produced (q) according to the function R ¼ 70q % q2.Total costs also depend on q:C ¼ q2 þ 30q þ 100.a. What level of output should the firm produce to maximize profits (R % C)? What will profits be?b. Show that the second-order
2.1 Suppose U(x, y) ¼ 4x2 þ 3y 2.a. Calculate @U/@x, @U/@y.b. Evaluate these partial derivatives at x ¼ 1, y ¼ 2.c. Write the total differential for U.d. Calculate dy/dx for dU ¼ 0—that is, what is the implied trade-off between x and y holding U constant?e. Show U ¼ 16 when x ¼ 1, y ¼
17.11 Probabilistic voting Probabilistic voting is a way of modelling the voting pro cess that introduces continuity into individuals’ voting decisions. In this way, calculus-type derivations become possible. To take an especially simple form of this approach, suppose there are n voters and two
17.10 Public choice of unemployment benefits Suppose individuals face a probability of u that they will be unemployed next year. If they are unemployed they will receive unemployment benefits ofb, whereas if they are employed they receive w (l – t), where t is the tax used to finance unemployment
17.9 vote trading Suppose there are three individuals in society trying to rank three social states (A, B and C). For each of the methods of social choice indicated, develop an example to show how the resulting social ranking of A, B and C will be intransi tive (as in the paradox of voting) or
17.8 Taxing pollution Suppose that there are n firms each producing the same good but with differing production functions. Output for each of these firms depends only on labour input, so the functions take the form qi = fi (ii). In its production activities each firm also produces some pollution,
17.7 More on Lindahl equilibrium The analysis of public goods in this chapter exclusively used a model with only two individuals. The results are readily generalised to n persons – a generalisation pursued in this problem.a.With n persons in an economy, what is the condition for eficient
17.6 Suppose refuse removal is a pure public good;that is, once it is produced, everyone beneits from it. What would be the optimal level of this activity if it could be produced at a constant marginal cost of €120 per unit?If refuse removal were left to the private market, how much might be
17.5 Suppose there are only two individuals in society. Person A’s demand curve for refuse removal is given by qn = 100 − p;for person B, the demand curve for refuse removal is given by qb = 200 − p.a.b.c.
17.4 As an alternative to nationalisation, the Utopian government is considering an annual licence fee per well to discourage over-drilling. How large should this license fee be if it is to prompt the industry to drill the optimal number of wells?Suppose a monopoly produces a harmful externality.
17.3 Under this organisation of society, what will be the total number of ish caught?The chief of Majorca, having read an economics book, believes it is possible to increase the total number of ish caught by restricting the number of people allowed to ish on Lake x. What number should be allowed to
17.2 On the island of Majorca there are 2 lakes and 20 anglers.Each angler can fish on either lake and keep the average catch on his particular lake. On Lake x, the total number of fish caught is given by F x = 10lx − 1 2l 2 x, where lx is the number of people fishing on the lake. For Lake y, the
17.1 A firm in a perfectly competitive industry has patented a new process for making widgets. The new process lowers the firm’s average cost, meaning that this firm alone(although still a price-taker) can earn real economic profits in the long run.a.If the market price is €20 per widget and
16.8 Diagrams with three types Suppose the agent can be one of three types rather than just two as in the chapter.a.Return to the monopolist’s problem of computing the optimal nonlinear price. Represent the irst best in a schematic diagram by modifying Figure 16.4. Do the same for the second best
16.7 Doctor–patient relationship Consider the principal–agent relationship between a patient and doctor. Suppose that the patient’s utility function is given by UP (m, x), where m denotes medical care (whose quantity is determined by the doctor) and x denotes other consumption goods. The
16.6 Suppose that there are enough buyers relative to sellers that competition among them leads cars to be sold at their maximum willingness to pay.What would the market equilibrium be if sellers value good cars at €8000? At €6000?Consider the following simple model of a common values auction.
16.5 Suppose 100 cars will be offered on the used-car market.Let 50 of them be good cars, each worth €10 000 to a buyer, and let 50 be lemons, each worth only €2000.a.Compute a buyer’s maximum willingness to pay for a car if he or she cannot observe the car’s quality.b.
16.4 An individual with logarithmic utility from wealth and with a current wealth of €20 000 faces a 50 per cent chance that he or she will suffer a loss of €10 000 resulting from an accident.Insurance against loss is available at actuarially fair rates.a.Compute the outcome if the individual
16.3 Return to the nonlinear pricing problem facing the mon opoly coffee shop in Example 16.4, but now suppose the proportion of high demanders increases to 2/3 and the proportion of low demanders decreases to 1/3. What is the optimal menu in the second-best situation? How does the menu compare to
16.2 Repeat part (a) for a general contingency fee of c.Solve for the optimal linear price per gram of coffee that the coffee shop would charge in Example 16.4. How does the shop’s profit compare to when it uses nonlinear prices?Hint: Your first step should be to compute each type’s demand at a
16.1 A lawyer acts on behalf of a client. The expected reward from hiring the lawyer is l, where l is the lawyer’s effort.Effort costs the lawyer l2/2.a.What is the lawyer’s effort, his surplus, and the plaintiff ’s surplus in equilibrium when the lawyer obtains the customary 1/3 contingency
15.10 Competition on a circle Steven Salop introduced competition on a circle.18 As in the Hotelling model, demanders are located at each point, and each demands one unit of the good. A consumer’s surplus equals v (the value of consuming the good) minus the price paid for the good as well as the
15.9 Inverse elasticity rule Use the first-order condition (Equation 15.2) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 10 holds under Cournot competition(where the elasticity is associated with an individual firm’s residual demand, the demand left after all
15.8 herfindahl index of market concentration The Herfindahl index which is used to measure market concentration is defined as nH = a i=1 s 2 i , where st = qi /Q is firm i ’s market share. The higher is H, the more concentrated the industry is said to be.a.Determine the Nash equilibrium of this
15.7 Now add an entry stage after irm 1 chooses q1.In this stage, irm 2 decides whether to enter. If it enters, then it must sink cost K2, after which it is allowed to choose q2. Compute the threshold value of K2 above which irm 1 prefers to deter irm 2’s entry.Represent the Cournot, Stackelberg,
15.6 Now restore the assumption that, as in Example 15.7, deviations are detected after just one period. Next, assume that n is not given but rather is determined by the number of irms that choose to enter the market in an initial stage in which entrants must sink a one-time cost K to participate
15.5 Compute the irms’ outputs and proits.Represent the equilibrium on a best-response function diagram. Show how an increase in b would change the equilibrium. Draw a representative isoproit curve for irm 1.Recall Example 15.6, which covers tacit collusion.Suppose (as in the example) that a
15.4 Compute irm output, irm proit and market output.Is total welfare maximised in the Nash equilibrium?If not, suggest an outcome that would maximise total welfare, and compute the deadweight loss in the Nash equilibrium compared with your outcome.Consider the following Bertrand game involving two
15.3 Two firms have costs of AC1 = MC1 = 20 and AC2 = MC2 =16 respectively. Market demand is Q = 1000 − 40P.a.Suppose irms practice Bertrand competition, that is, setting prices for their identical products simultaneously. Compute the Nash equilibrium prices. (To avoid technical problems in this
15.2 Suppose instead that there are two irms in the market facing the demand and cost conditions just described for their identical products. Firms choose quantities simultaneously as in the Cournot model. Compute the outputs in the Nash equilibrium. Also compute market output, price and irm
15.1 Assume for simplicity that a monopolist has no costs of production and faces a demand curve given by Q = 150 − P.a.Calculate the proit-maximising price–quantity combination for this monopolist. Also calculate the monopolist’s proit.b.c.d.
14.9 The welfare effects of third-degree price discrimination In an important 1985 article,18 Hal Varian shows how to assess third-degree price discrimination using only properties of the indirect utility function (see Chapter 3). This problem provides a simplified version of his approach. Suppose
14.8 More on the welfare analysis of quality choice An alternative way to study the welfare properties of a monopolist’s choices is to assume the existence of a utility function for the customers of the monopoly of the form utility = U(Q, X ), where Q is quantity consumed and X is the quality
14.7 Taxation of a monopoly good The taxation of monopoly can sometimes produce results different from those that arise in the competitive case. This problem looks at some of those cases. Most of these can be analysed by using the inverse elasticity rule (Equation 14.1).a.Consider irst an ad
14.6 Use a graphical proof to show how a per-unit-of output subsidy might achieve the government’s goal.Suppose the government wants its subsidy to maximise the difference between the total value of the good to consumers and the good’s total cost. Show that, to achieve this goal, the government
14.5 If the monopolist can maintain the separation between the two markets, what level of output should be produced in each market, and what price will prevail in each market? What are total proits in this situation?How would your answer change if it costs demanders only €5 to transport goods
14.4 Suppose there is no advertising (A = 0). What output will the proit-maximising irm choose?What market price will this yield? What will be the monopoly’s proits?Now let the irm also choose its optimal level of advertising expenditure. In this situation, what output level will be chosen? What
14.3 Suppose a monopoly market has a demand function in which quantity demanded depends not only on market price (P) but also on the amount of advertising the firm does (A, measured in Euros). The specific form of this function is Q = (20 − P)(1 + 0.1A − 0.01A2).The monopolistic firm’s cost
14.2 What output level would be produced by this industry under perfect competition (where price = marginal cost)?Calculate the consumer surplus obtained by consumers in case (b). Show that this exceeds the sum of the monopolist’s proits and the consumer surplus received in case (a). What is the
14.1 A monopolist can produce at constant average and mar ginal costs of AC = MC = €10. The firm faces a market demand curve given by Q = 100 − P.a.Calculate the proit-maximising price–quantity combination for the monopolist. Also calculate the monopolist’s proits.b.c.
13.14 Intertemporal labour supply It is relatively easy to extend the single-period model of labour supply presented in Chapter 13 to many periods.Here we look at a simple example. Suppose that an indi vidual makes his or her labour supply and consumption decisions over two periods. 23 Assume that
13.13 A few results from demand theory The theory developed in this chapter treats labour supply as the mirror image of the demand for leisure. Hence, the entire body of demand theory developed in Part Two of the text becomes relevant to the study of labour supply as well.Here are three
13.12 Family labour supply A family with two adult members seeks to maximise a util ity function of the form U(c, h1, h2), where c is family consumption and h1 and h2 are hours of leisure of each family member. Choices are constrained by c = w1(24 − h1) + w2(24 − h2) + n, where w1 and w2 are
13.11 Compensating wage differentials for risk An individual receives utility from daily income (y), given by U(y) = 100y − 1 2y 2 .The only source of income is earnings. Hence y = wl, where w is the hourly wage and l is hours worked per day.The individual knows of a job that pays €5 per hour
Suppose a landowner has a ‘balanced’ woodlot with one tree of ‘each’ age from 0 to t*. What is the value of this woodlot? Hint: It is the sum of the values of all trees in the lot.If the value of the woodlot is V, show that the instantaneous interest on V (that is, r · V) is equal to the
13.10 Suppose trees are produced by applying 1 unit of labour at time 0. The value of the wood contained in a tree is given at any time t by f (t). If the market wage rate is w and the real interest rate is r, what is the PDV of this production pro cess, and how should t be chosen to maximise this
13.9 As wine ages, its value increases. One Euro of wine at year 0 is worth V (t ) = exp{2!t − 0:15t } Euros at time t. If the interest rate is 5 per cent, after how many years should a vineyard sell wine in order to maximise the PDV of this sale?
13.8 If the ishermen dictate the price of bait and the bait collectors are price-takers, determine the new equilibrium price.If the bait collectors act as a monopsonist and the ishermen acts as a price-taker, what will the equilibrium be?Assume that an individual expects to work for 40 years and
13.7 Local fishermen sell their daily catch at the local fish market at a price of €5 per kilo. The production function for village output is q = 240x − 2x 2, where x is the quantity of bait used each week. Bait is only available from the neighbouring village who charge €10 per day to collect
13.6 How many workers will the irm hire to maximise his proits, and what wage will he pay?If a minimum wage of €4 per hour is imposed what will the consequences for employment levels be?Graph your results.How does a minimum wage imposed under monopsony differ in results as compared with a minimum
13.5 Suppose the government wishes to increase the equilibrium wage to €4 per hour by offering a subsidy to employers for each person hired. How much will this subsidy have to be? What will the new equilibrium level of employment be? How much total subsidy will be paid?Suppose instead that the
13.4 and for men by CHAPTER 13 LABOUR MARKETS 405 Suppose demand for labour is given by l = −50w + 450 and supply is given by l = 100w, where l represents the number of people employed and w is the real wage rate per hour.a.What will be the equilibrium levels for w and l in this market?b.c.d.
13.3 Derive the compensated labour supply function.Show that ∂l c/∂w > 0.In South Africa the government introduces a child support grant to unemployed families of R6000 per year. This grant is reduced by R0.75 for each R1 of other income the family has.a.How much in welfare beneits does the
13.2 The person inherits an annual income of €4000. If he or she continues to devote 75 per cent of full income to leisure, how many hours will be worked?How would your answer to part (b) change if the market wage were €10 per hour instead of €5 per hour?Graph the individual’s supply of
13.1 Suppose there are 8000 hours in a year (actually there are 8760) and that an individual has a potential market wage of €5 per hour.a.What is the individual’s full income? If he or she chooses to devote 75 per cent of this income to leisure, how many hours will be worked?b.c.d.
12.13 Social welfare functions and income taxation The relationship between social welfare functions and the optimal distribution of individual tax burdens is a complex one in welfare economics. In this problem, we look at a few elements of this theory. Throughout we assume that there are m
12.12 Initial endowments, equilibrium prices and the first theorem of welfare economics In Example 12.3 we computed an efficient allocation of the available goods and then found the price ratio consistent with this allocation. That then allowed us to find initial endowments that would support this
12.11 Productive efficiency with calculus In Example 12.3 we showed how a Pareto efficiency exchange equilibrium can be described as the solution to a constrained maximum problem. In this problem we provide a similar illustration for an economy involving production. Suppose that there is only one
12.10 An example of Walras’ law Suppose there are only three goods (x1, x2, x3) in an economy and that the excess demand functions for x2 and x3 are given by ED2 = −3p2 p1+ 2p3 p1− 1, ED3 = −4p2 p1− 2p3 p1− 2.a.b.c.Show that these functions are homogeneous of degree 0 in p1, p2 and
12.9 The trade theorems The construction of the production possibility curve shown in Figures 12.2 and 12.3 can be used to illustrate three important ‘theorems’ in international trade theory.To get started, notice in Figure 12.2 that the efficiency line Ox,Oy is bowed above the main diagonal of
12.8 Returns to scale and the production possibility frontier The purpose of this problem is to examine the relationships among returns to scale, factor intensity and the shape of the production possibility frontier.Suppose there are fixed supplies of capital and labour to be allocated between the
12.7 Tax equivalence theorem Use the computer algorithm discussed in footnote 24 to show that a uniform ad valorem tax of both goods yields the same equilibrium as does a uniform tax on both inputs that collects the same revenue. Note: This tax equivalence theorem from the theory of public finance
12.6 In the country of Rotorooa there are two regions, A and B.Two goods (x and y ) are produced in both regions.Production functions for region A are given by xA = "lx, yA = "ly;here lx and ly are the quantities of labour devoted to x and y production, respectively. Total labour available in
12.5 Two backpackers have crossed paths and are travelling together for a period. Each has in his possession some slices of ham (H) and cheese (C). Shelly is a choosy eater and will eat ham and cheese only in the fixed proportions of 2 slices of cheese to 1 slice of ham. Her utility function is
12.4 Explain why the production possibility frontier of part (c) is concave.Sketch the relative price of food as a function of its output in part (c).If consumers insist on trading 4 units of food for 5 units of cloth, what is the relative price of food?Why?Explain why production is exactly the
12.3 Given this price ratio, how much x and y will A and B demand?How should labour be allocated between x and y to satisfy the demand calculated in part (b)?Consider an economy with just one technique available for the production of each good.good Labour per unit output Food 1Cloth 1Land per unit
12.2 Suppose two individuals A and B each have 10 hours of labour to devote to producing either ice cream (x) or chicken soup (y). A’s utility function is given by US = x 0.3 y 0.7, whereas B’s utility function is given by UJ = x 0.5y 0.5.The individuals do not care whether they produce x or y,
12.1 Suppose the production possibility frontier for guns (x)and butter (y) is given by x2 + 2y 2 = 900.a.b.c.d.Graph this frontier.If individuals always prefer consumption bundles in which y = 2x, how much x and y will be produced?At the point described in part (b), what will be the RPT and hence
11.9 Cobweb models One way to generate disequilibrium prices in a simple model of supply and demand is to incorporate a lag into producer’s supply response. To examine this possibility, assume that quantity demanded in period t depends on price in that period (Q Dt = a − bPt)but that quantity
11.8 The Ramsey formula for optimal taxation The development of optimal tax policy has been a major topic in public finance for centuries.17 Probably the most famous result in the theory of optimal taxation is due to the English economist Frank Ramsey, who conceptualised the problem as how to
11.7 Ad valorem taxes Given an ad valorem tax rate of t, the gap between the price consumers pay and what suppliers receive is given by PD = (1 + t)PS.a.Show that for an ad valorem tax d In PD dt b.= eS eS − eD and d In Ps dt= eD es − eD.Show that the excess burden of a small tax is DW=−0.5
11.6 What is the domestic equilibrium in the MP3 players market?Suppose MP3 players can be imported at a world price of €10 per MP3 player. If free trade were allowed, what would the new market equilibrium be? How many MP3 players would be imported?If domestic MP3 player producers succeeded in
11.5 Suppose the demand for the maintenance of swimming pools is given by Q =1100 − 50P.What will be the equilibrium in this marketplace? What will each firm’s total short-run profits be?Graph the market equilibrium and compute total short-run producer surplus in this case.Show that the total
11.4 equilibrium price of skateboards? How many irms will there be? How many entrepreneurs will be hired, and what is their remuneration?Suppose that the demand for skateboards shifts outward to Q =2428 − 50P.How would you now answer the questions posed in part (a)?The swimming pool maintenance
11.3 What is the industry’s long-run supply schedule?What is the long-run equilibrium price (P*)?The total industry output (Q*)? The output of each irm (q*)? The number of irms? The proits of each irm?The short-run total cost function associated with each irm’s long-run equilibrium output is
11.2 Assume each firm in a perfectly competitive market has an identical cost structure such that long-run average cost is minimised at an output of 20 units (qi = 20). The mini mum average cost is €10 per unit. Total market demand is given by Q =1500 − 50P.a.b.c.d.e.f.g.

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Microeconomic Theory Basic Principles And Extensions 1st Edition Christopher M Snyder, Walter Nicholson, Robert B Stewart - Solutions

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