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rice effects include income effects, they need not be symmetric. That is, @xi/@pj does not necessarily equal @xj/@pi. PROBLEMS • Focusing only on the substitution effects from price changes eliminates this ambiguity because substitution effects are symmetric; that is, @xc j =@pi. Now two goods are deﬁned as net (or Hic...
elative price of the more expensive good =@t > 0 [i.e., (p2 þ (where we use compensated demand functions to eliminate pesky income effects). Borcherding and Silberberg show this result will probably hold using the following steps. t)/(p3 + t) decreases as t increases]. This will increase the relative demand for the exp...
ed in such situations. We seek to understand the steps they take to mitigate risk, including buying insurance, acquiring more information, and preserving options. Chapter 8 looks at decisions made in strategic situations in which a person’s well-being depends not just on his or her own actions but also on the actions o...
xiÞ ¼ ð ! xi 1,000,000 1,000,000, if xi ) if xi > 1,000,000: The von Neumann–Morgenstern Theorem Among many contributions relevant to Part 3 of our text, in their book The Theory of Games and Economic Behavior, John von Neumann and Oscar Morgenstern developed a mathematical foundation for Bernoulli’s solution to the S...
ch is a 50–50 chance of winning or losing $h, and gamble B, which is a 50–50 chance of winning or losing $2h. The utility of current wealth is U(W0), which is also the expected value of current wealth because it is certain. The expected utility if he or she participates in gamble A is given by EU(A): EU A ð Þ ¼ 1 2 U W...
tant absolute risk aversion is facing a 50–50 chance of winning or losing $1,000. How much ( f ) would he or she pay to avoid the risk? To ﬁnd this value, we set the utility of W0 % f equal to the expected utility from the gamble: f % ½% exp W0 % A ð A W0 þ ð W0 % A ð Because the factor AW0) is contained in all the ter...
o cheaply monitor customer behavior. We will discuss the adverse selection and moral hazard problems in more detail in Chapter 18, and discuss ways the insurance company can combat these problems, which besides the above strategies include offering only partial insurance and requiring the payment of deductibles and cop...
fuel, then this $5,000 could be viewed as the option price. Model of real options Let x embody all the uncertainty in the economic environment. In the case of the ﬂexible-fuel car, x might reﬂect the price of fossil fuels relative to biofuels or the stringency of government regulation of fossil fuels. In terms of the ...
the difference between the expected payoffs in Equations 7.53 and 7.54, which equals 1/4. This is the maximum premium the person would pay for the ﬂexible-fuel car over a single-fuel car. Scaling payoffs to more realistic levels by multiplying by, say, $10,000, the price premium (and the option value) of the ﬂexible-f...
c of a pure public good (see Chapter 19). That is, the information is both nonrival, in that others may use it at zero cost, and nonexclusive, in that no individual can prevent others from using the information. The classic example of these properties is a new scientiﬁc discovery. When some prehistoric people invented ...
o the U1 indifference curve where Wg ¼ Wb—a point on the ‘‘certainty line’’ where wealth (W,) is independent of which state of the world occurs. At W, the slope of the indifference curve [p /(1 p)] is precisely equal to the price ratio pg /pb. If the market for contingent wealth claims were not fair, utility maximizati...
ertainty to be approached in a familiar choice-theoretic framework. PROBLEMS 7.1 George is seen to place an even-money $100,000 bet on the Bulls to win the NBA Finals. If George has a logarithmic utilityof-wealth function and if his current wealth is $1,000,000, what must he believe is the minimum probability that the ...
e polar cases R c. A rise in the price of contingent claims in ‘‘bad’’ times (pb) will induce substitution and income effects into the demands for Wg and Wb. If the individual has a ﬁxed budget to devote to these two goods, how will choices among them be affected? Why might Wg rise or fall depending on the degree of ri...
alth, we have exp A exp ½% 1 W0ð A ð 1 AW0ð rf Þ þ þ exp rf Þ’ k r ð % Ak rf ÞÞ’ r % ð : rf Þ’ ¼ ½% þ That is, the marginal utility function can be separated into a random part and a nonrandom part (both initial wealth and ½% (iii) the risk-free rate are nonrandom). Hence the optimality condition from Equation ii can b...
return is referred to as the beta coefﬁcient for the asset. Estimated beta coefﬁcients for ﬁnancial assets are reported in many publications. Studies of the CAPM This version of the CAPM carries strong implications about the determinants of any asset’s expected rate of return. Because of this simplicity, the model has ...
in player 1’s position for a moment. We do not know what player 2 will do yet because we have not solved out the game, so let’s investigate each possibility. Suppose player 2 chose to ﬁnk. By ﬁnking ourselves we would earn one year of freedom versus none if we remained silent, so ﬁnking is better for us. Suppose playe...
lent, so we underline u2 ¼ 3 in the lower left box. Now that the best-response payoffs have been underlined, we look for boxes in which every player’s payoff is underlined. These boxes correspond to Nash equilibria. (There may be additional Nash equilibria involving mixed strategies, deﬁned later in the chapter.) In Fi...
iliar in certain settings. Students are familiar with the setting of class exams. Class time is usually too limited for the professor to examine students on every topic taught in class, but it may be sufﬁcient to test students on a subset of topics to induce them to study all the material. If students knew which topics...
: A New Proof,’’ International Journal of Game Theory 2 (1973): 235–50. Games in which there are ties between payoffs may have an even or inﬁnite number of Nash equilibria. Example 8.1, the Prisoners’ Dilemma Redux, has several payoff ties. The game has four pure-strategy Nash equilibria and an inﬁnite number of differ...
cal axis. These best responses are simply lines and thus are easy to graph in this example. (To be consistent with the axis labels, the inverse of Equation 8.15 is actually what is graphed.) The two best responses intersect at the Nash equilibrium E1. The graphical method is useful for showing how the Nash equilibrium ...
uilibria. The third outcome is a Nash equilibrium because the strategies are rational along the equilibrium path. However, following the wife’s choosing ballet—an event that is off the equilibrium path—the husband’s strategy is irrational. The concept of subgame-perfect equilibrium in the next section will rule out irr...
at nothing that happens in 1 affects what happens subsequently because players both ﬁnk in period T regardperiod T 1 were the last, and the Nash equilibrium of this subgame is less. It is as though period T again for both to ﬁnk. Working backward in this way, we see that players will ﬁnk each period; that is, players w...
e subsequent section then 10Nobel Prize–winning economist Gary Becker introduced a related point, the maximal punishment principle for crime. The principle says that even minor crimes should receive draconian punishments, which can deter crime with minimal expenditure on policing. The punishments are costless to societ...
for q1H and q1L from Equation 8.27 into Equation 8.29 and then substituting the resulting expression for q1 into Equation 8.30 yields q2 ¼ 30 þ q2 4 , (8:31) 40. Substituting q’2 ¼ 40 back into Equation 8.27 implies q’1H ¼ implying that q’2 ¼ 30: q’1L ¼ Figure 8.16 depicts the Bayesian–Nash equilibrium graphically. He...
he player moving there are formed using Bayes’ rule (based on prior beliefs and other players’ strategies). 286 Part 3: Uncertainty and Strategy The requirement that players play rationally at each information set is similar to the requirement from subgame-perfect equilibrium that play on every subgame form a Nash equi...
p Þ ! w, Þ ¼ (8:41) as from playing NJ, which equals 0. Setting Equation 8.41 equal to 0, substituting for Pr(H\|E) from Equation 8.40, and then solving for e gives w e’ ¼ p ð w ½ ! 1 ! Pr Þ Pr H ð H ð Þ Þ+ : (8:42) QUERY: To complete our analysis: In this equilibrium, type H of player 1 cannot prefer to deviate from E....
ce. If players are sufﬁciently patient in an inﬁnitely repeated game, then a folk theorem holds implying that essentially any payoffs are possible in the repeated game. • In games of private information, one player knows more about his or her ‘‘type’’ than another. Players maximize their expected payoffs given knowledg...
child. Prove that, ! 2 ! ! 1 þ U1ð , but the parent maximizes U2ð L Þ in a subgame-perfect equilibrium, the child will opt for the value of r that maximizes ! 1 þ ! 2 even though he has no altruistic intentions. Hint: Apply backward induction to the parent’s problem ﬁrst, which will give a ﬁrst-order condition that imp...
ies si and s–i. As Equation 2.176 showed, expected values are linear functions of the underlying probabilities. Linear functions are, of course, continuous. E8.4 Games with continuous actions Nash’s existence theorem applies to ﬁnite games—that is, games with a ﬁnite number of players and actions per player. Nash’s the...
eas when l 50, production of ﬂyswatters amounts to only 25 million. 40, Equation 9.7 shows that q ¼ ¼ l 40 (9:11) ¼ ¼ Average product. To ﬁnd the average productivity of labor in ﬂyswatter production, we divide q by l, still holding k 10: APl ¼ q l ¼ 60,000l $ 1,000l2: (9:12) 306 Part 4: Production and Supply Again, th...
k, l ð 600k2l2 k3l3: MPl ¼ MPk ¼ fl ¼ fk ¼ @q @l ¼ @q @k ¼ 1,200k2l 3k3l2, $ 1,200kl2 3k2l3: $ (9:22) (9:23) Notice that each of these depends on the values of both inputs. Simple factoring shows that these marginal productivities will be positive for values of k and l for which kl < 400. Because and fll ¼ 1,200k2 6k3l...
urns to scale can be separated from issues involving the shape of an isoquant. In these cases, changes in the returns to scale will just change the labels on the isoquants rather than their shapes. In the next section, we will look at how shapes of isoquants can be described. ¼ The n-input case The deﬁnition of returns...
ell. The mathematical form of the ﬁxed-proportions production function is given by q , a, b > 0, Þ where the operator ‘‘min’’ means that q is given by the smaller of the two values in parentheses. For example, suppose that ak < bl; then q ak, and we would say that capital is the binding constraint in this production pr...
he Leontief production function generalizes the ﬁxed-proportions case. For more details see the discussion of Leontief production functions in the Extensions to this chapter. Chapter 9: Production Functions 321 FIGURE 9.5 Technical Progress Technical progress shifts the q0 isoquant toward the origin. The new q0 isoquan...
e production function and its related isoquant map. Technical improveimproved, more ments may arise from the use of productive inputs or from better methods of economic organization. Chapter 9: Production Functions 325 PROBLEMS 9.1 Power Goat Lawn Company uses two sizes of mowers to cut lawns. The smaller mowers have a...
(see Chapter 11) is sophisticated and illuminating. Shephard, R. W. Theory of Cost and Production Functions. Princeton, NJ: Princeton University Press, 1978. Extended analysis of the dual relationship between production and cost functions. Silberberg, E., and W. Suen. The Structure of Economics: A Mathematical Analysi...
entials. For a summary, see Borjas (1994). References Atkeson, Andrew, and Patrick J. Kehoe. ‘‘Models of Energy Use: Putty-Putty versus Putty-Clay.’’ American Economic Review (September 1999): 1028–43. Bairam, Erkin. ‘‘Elasticity of Substitution, Technical Progress and Returns to Scale in Branches of Soviet Industry: A...
, q0). The ﬁrm will of course earn some revenue R from this output choice, but we will ignore revenue for now. We will focus solely on the question of how the ﬁrm can produce q0 at minimal cost. 336 Part 4: Production and Supply Cost-Minimizing Input Choices Mathematically, this is a constrained minimization problem. B...
he ratio of the two inputs. If the ratio of input costs does not change, the ﬁrms will use the same input ratio no matter how much it produces—that is, the expansion path will be a straight line through the origin. b ¼ 0.5, w As a numerical example, suppose a 3, and that the ﬁrm wishes ¼ to produce q0 ¼ 40. The ﬁrst-or...
ecause they are pulled upward by increasingly higher marginal costs. Consequently, we have shown that the AC curve also has a Ushape and that it reaches a low point at q), where AC and MC intersect.5 In empirical studies of cost functions, there is considerable interest in this point of minimum average cost. It reﬂects...
ain constant at that level. With ﬂuctuating input prices, the ﬁrm can adapt its input mix to take advantage of such ﬂuctuations by using a lot of, say, labor when its price is low and economizing on that input when its price is high. ¼ 4. Average and marginal costs. Some, but not all, of these properties of total cost ...
here there are variable returns to scale. Even in these more complex cases, however, technical improvements will cause total costs to decrease. EXAMPLE 10.3 Shifting the Cobb–Douglas Cost Function In Example 10.2 we computed the Cobb–Douglas cost function as C v, w, q ð Þ ¼ q1= a ð ÞBva= b ð þ a þ Þw b= b a ð b Þ, þ (1...
rious cases cannot be compared directly because different values for s scale output differently, we can, as an example, look at the consequence of a increase in w to 27 in the lowsubstitutability case. With w 53.3. In this case, the 27, the ﬁrm will choose k cost savings from substitution can be calculated by comparing...
d. In (a), the underlying production function exhibits constant returns to scale: In the long run, although not in the short run, total costs are proportional to output. In (b), the long-run total cost curve has a cubic shape, as do the short-run curves. Diminishing returns set in more sharply for the short-run curves,...
nal cost of the 150th page of the ﬁnished book? Of the 300th page? Of the 450th page? 10.3 Suppose that a ﬁrm’s ﬁxed proportion production function is given by q min 5k, 10l ð : Þ ¼ a. Calculate the ﬁrm’s long-run total, average, and marginal cost functions. b. Suppose that k is ﬁxed at 10 in the short run. Calculate t...
any two inputs. The CES permits s to take any value, but it requires that the elasticity of substitution be the same between any two inputs. Because empirical economists would prefer to let the data show what the actual substitution possibilities among inputs are, they have tried to ﬁnd more ﬂexible functional forms. O...
the decisions and receives all the proﬁts and losses from the ﬁrm’s operations. The combination of these elements—production technology, entrepreneur, and inputs used (labor l, capital k, and others)—together constitutes what we will call the ‘‘ﬁrm.’’ The entrepreneur acts in his or her own self-interest, typically le...
at is, MR q& ð Þ ¼ MC q& ð : Þ (11:6) 2Notice that this is an unconstrained maximization problem; the constraints in the problem are implicit in the revenue and cost functions. Speciﬁcally, the demand curve facing the ﬁrm determines the revenue function, and the ﬁrm’s production function (together with input prices) de...
demand curve is negatively sloped, the marginal revenue curve will fall below the demand (‘‘average revenue’’) curve. For output levels beyond q1, MR is negative. At q1, total revenues (p1 Æ q1) are a maximum; beyond this point, additional increases in q cause total revenues to decrease because of the concomitant decr...
output level; and (4) the rental rate of capital, v, is irrelevant to short-run supply decisions because it is only a component of ﬁxed costs. Numerical example. We can pursue once more the numerical example from Example 10.5, where a 80. For these speciﬁc parameters, the supply function is 0.5, v 3, w b ¼ ¼ ¼ ¼ p1 $ ¼...
general, it is this long-run approach that will prove more useful for our subsequent study of the welfare impacts of price changes. Because the proﬁt function is nondecreasing in output prices, we know that if P2 > P1 then P ð P2, . . . P P1, . . . ð Þ , Þ + and it would be natural to measure the welfare gain to the ﬁ...
otice that diminishing marginal productivity for each input is not sufﬁcient to ensure increasing marginal costs. Expanding output usually requires the ﬁrm to use more capital and more labor. Thus, we must also ensure that increases in capital input do not raise the marginal productivity of labor (and thereby reduce ma...
ever, the ambiguity stemming from Giffen’s paradox in the theory of consumption demand does not occur here. We start with a reminder that we have two concepts of demand for any input (say, labor): (1) the conditional demand for labor, denoted by lc(v, w, q); and (2) the unconditional demand for labor, which is denoted ...
ts at its plant in Gulch, Nevada, for sale throughout the world. The cost function for total widget production (q) is given by total cost 0.25q2. ¼ 2PA) and Lapland (where the Widgets are demanded only in Australia (where the demand curve is given by qA ¼ demand curve is given by qL ¼ qL. If Universal Widget can contro...
put effects from Chapter 11. Note: The notion that the elasticity of the derived demand for an input depends on the price elasticity of demand for the output being produced was ﬁrst suggested by Alfred Marshall. The proof given here follows that in D. Hamermesh, Labor Demand (Princeton, NJ: Princeton University Press, ...
teresting. If the alternative theories merely compared ﬁrms to perfectly competitive markets, markets would always end up ‘‘winning’’ in the comparison. Instead, ﬁrms are compared to negotiated sales, a more subtle comparison without an obvious ‘‘winner.’’ We will explore the subtle comparisons offered by the two diffe...
problem, referring to the colorful image of a bandit holding up a citizen at gunpoint. Nothing illegal is happening here; hold up is just a feature of bargaining. hG ¼ The efﬁcient outcome is for investments to be set at x&F and x&G and for parties not to undertake any haggling actions: hF ¼ 0. Haggling does not genera...
‘‘horizontal sum’’ of each individual’s demand curve. At each price the quantity demanded in the market is the sum of the amounts each individual demands. For example, at p$x the demand in the market is x$1 þ x$2 ¼ X$. px px px px* x1 x1 x1* x2 x2* x2 X* X X (a) Individual 1 (b) Individual 2 (c) Market demand the point...
iods: (1) very short run, (2) short run, and (3) long run. Although it is not possible to give these terms an exact chronological deﬁnition, the essential distinction being made concerns the nature of the supply response that is assumed to be possible. In the very short run, there is no supply response: The quantity su...
w value for eS, P implies that it takes relatively large changes in price to induce ﬁrms to change their output levels because marginal costs increase rapidly. Notice that, as for all elasticity notions, computation of eS, P requires that input prices and technology be held constant. To make sense as a market response,...
ﬁrst a shift inward in the short-run supply curve for a good. As in Example 12.2, such a shift might have resulted from an increase in the prices of inputs used by ﬁrms to produce the good. Whatever the cause of the shift, it is important to recognize that the effect of the shift on the equilibrium level of P and Q wi...
As we predicted earlier, the 10 percent increase in real income made car prices increase by nearly 14 percent. In the process, quantity sold increased by approximately 1.77 million automobiles. A shift in supply. An exogenous shift in automobile supply as a result, say, of changing auto workers’ wages would also affect...
3P, & (12:43) where QD is the quantity demanded per month and P is the price per frame. To determine the long-run equilibrium in this market, we must ﬁnd the low point of the typical ﬁrm’s average cost curve. Because AC C q ð Þ q ¼ ¼ q2 & 20q þ 100 8,000 q þ (12:44) 9These equilibrium conditions also point out what se...
ponse to proﬁt opportunities. All these supply responses are summarized in the following elasticity concept Long-run elasticity of supply. The long-run elasticity of supply (eLS,P) records the proportionate change in long-run industry output in response to a proportionate change in product price. Mathematically, eLS, P...
g MC AC yields ¼ 2q2 8q & ¼ 4,950 q , (12:56) (12:57) which has a solution of q signiﬁcantly reduced the optimal size for frame shops. With q AC 15. Therefore, this particular change in the total cost function has 15, Equations 12.56 show 535, and with this new long-run equilibrium price we have MC ¼ ¼ ¼ ¼ QD ¼ These 8...
mpliﬁed proof. Given the demand curve (D) and the long-run supply curve (S), the sum of consumer and producer surplus is given by distance AB for the ﬁrst unit produced. Total surplus continues to increase as additional output is produced—up to the competitive equilibrium level, Q$. This level of production will be ach...
ket outcomes are generated by Q(P1Þ ¼ min ½ QD(P1), QS(P1)], (12:65) suppliers will be content with this outcome, but demanders will not because they will be forced to accept a situation of excess demand. They have an incentive to signal their dissatisfaction to suppliers through increasing price offers. Such offers ma...
nt of view of the buyers and sellers, it makes little difference whether t represents a per-unit tax or a per-unit transaction fee because the analysis of the fee’s effect on the market will be the same. That is, the fee will be shared between buyers and sellers depending on the speciﬁc elasticities involved. Trading v...
rease in rents between parts (a) and (b). Show that this value is identical to the change in long-run producer surplus as measured along the stilt supply curve. 2,428 Q ¼ & 50P. 12.6 The handmade snuffbox industry is composed of 100 identical ﬁrms, each having short-run total costs given by and short-run marginal costs...
Analysis, 3rd ed. New York: W. W. Norton, 1992, chap. 13. Terse but instructive coverage of many of the topics in this chapter. The importance of entry is stressed, although the precise nature of the long-run supply curve is a bit obscure. DEMAND AGGREGATION AND ESTIMATION EXTENSIONS In Chapters 4–6 we showed that the...
ed and consumers will demand the quantity that is supplied. We also assume that there are no transaction or transportation charges and that both individuals and ﬁrms have perfect knowledge of prevailing market prices. The law of one price Because we assume zero transaction cost and perfect information, each good obeys ...
ility frontier The efﬁciency locus in Figure 13.2 shows the maximum output of y that can be produced for any preassigned output of x. We can use this information to construct a production possibility frontier, which shows the alternative outputs of x and y that can be produced with the ﬁxed capital and labor inputs. In...
e substitution shows that the production possibility frontier is given by lx þ ly ¼ 100, x2 y2 þ ¼ 100 for x, y 0: ( (13:4) (13:5) In this case, the frontier is a quarter-circle and is concave. The RPT can now be computed directly from the equation for the production possibility frontier (written in implicit form as f ...
olute pricing into the model, let’s consider all prices in terms of the wage rate, w. Because total labor supply is 100, it follows that total labor income is 100w. However, because of the diminishing returns assumed for production, each ﬁrm also earns proﬁts. For ﬁrm x, say, 50p . Therefore, the the total cost functio...
ns utility from the vector of goods he or she consumes ui(xi) where i 1. . . m. Individuals also possess initial endowments of the goods given by xi. Individuals are free to exchange their initial endowments with other individuals or to keep some or all the endowment for themselves. In their trading individuals are ass...
the forces of supply and demand can establish equilibrium prices in the general equilibrium model of exchange we have developed, it is natural to ask what are the welfare consequences of this ﬁnding. Adam Smith14 hypothesized that market forces provide an ‘‘invisible hand’’ that leads each market participant to ‘‘prom...
XAMPLE 13.3 A Two-Person Exchange Economy To illustrate these various principles, consider a simple two-person, economy. Suppose that total quantities of the goods are ﬁxed at x y utility takes the Cobb–Douglas form: ¼ two-good exchange 1,000. Person A’s ¼ UAð and person B’s preferences are given by: xA, yAÞ ¼ A y1=3 x...
re are r ﬁrms involved in production. Each of these ﬁrms is bound by a production function that describes the physical constraints on the ways the 17J. Rawls, A Theory of Justice (Cambridge, MA: Harvard University Press, 1971). 18A detailed study of labor supply theory is presented in Chapter 16. Chapter 13: General Eq...
supplied to the market is consumed as leisure). Households are assumed to maximize utility. Their incomes are determined by the amounts of inputs they ‘‘sell’’ in the market and by the net result of any taxes they pay or transfers they receive. Finally, a full general equilibrium model must specify how the government ...
nd then used that model to make a few statements about welfare. Some highlights of this chapter are listed here. • Preferences and production technologies provide the building blocks on which all general equilibrium models are based. One particularly simple version of such a model uses individual preferences for two go...
qualization theorem: Use Figure 13.4 to show how the international price ratio, p, determines the point in the Edgeworth box at which domestic production will take place. Show how this determines the factor price ratio, w/v. If production functions are the same throughout the world, what will this imply about relative ...
of their reduction) focuses on impacts on real wages, such general equilibrium models are especially appropriate for the task. Two unusual features tend to characterize such models. First, because the models often have an explicit focus on domestic versus foreign production of speciﬁc goods, it is necessary to introdu...
utput decision will, in fact, determine the good’s price. In this sense, monopoly markets and markets characterized by perfect competition are polar-opposite cases Monopoly. A monopoly is a single supplier to a market. This ﬁrm may choose to produce at any point on the market demand curve. At times it is more convenien...
input costs. Therefore, market price moves proportionally to marginal cost: Increases in marginal cost will prompt the monopoly to increase its price proportionally, and decreases in marginal cost will cause the monopoly to reduce its price proportionally. Even if elasticity is not constant along the demand curve, it ...
s market were competitive, output would be Qc—that is, production would occur where price is equal to long-run average and marginal cost. Under a simple single-price monopoly, output would be Qm because this is the level of production for which marginal revenue is equal to marginal cost. The restriction in output from ...
f providing this ﬂow to consumers. The monopoly would, of course, choose an output level that restricted the ﬂow of services to maximize proﬁts, but—assuming constant returns to scale in production—there is no reason that durability per se would be affected by market structure. This result is sometimes referred to as S...
pursue such a policy. The monopoly then sets a price in each market according to the inverse elasticity rule. Assuming that marginal cost is the same in all markets, the result is a pricing policy in which 1 ei Pi 1 ! þ Pj 1 ! þ ¼ " 1 ej " (14:32) or þ þ where Pi and Pj are the prices charged in markets i and j, which...
e maximal entry fee that might be charged without causing this person to leave the 6q. If the market. Consequently, the two-part tariff in this case would be T(q) monopolist opted for this pricing scheme, its proﬁts would be AC R 30 18 and q2 ¼ T ð 72 (14:41) q2Þ 36 ¼ " ¼ " þ ¼ C p q1Þ þ 6 ’ þ T q2Þ " ð 6 30 ’ " q1 þ ð...
vation could not be obtained by the innovating ﬁrm. Schumpeter stresses the point that the monopolization of a market may make it less costly for a ﬁrm to plan its activities. Being the only source of supply for a product eliminates many of the contingencies that a ﬁrm in a competitive market must face. For example, a ...
ttery costs are given by P Q where C 0(X) > 0. Show that, in this case, the monopoly will opt for the same level of X as does a competitive industry even though levels of output and prices may differ. Explain your result. Hint: Treat XQ as a composite commodity. C Q, X ð C X ð Q, Þ Analytical Problems 14.10 Taxation of...
der values of a and p such that a pqM 1 ¼ þ pMqM 1 or a pM " ¼ ð p qM 1 , Þ (viii) where qM represents consumption of person 1 under a single1 price policy. In this case, a and p are set so that person 1 can still afford to buy qM 1 under the new price schedule. Because p < pM, however, he will opt for q!1 > qM 1 . Bec...
he discussion of total welfare in this paragraph focuses on short-run considerations. As discussed in a later section, an imperfectly competitive market may produce considerably more deadweight loss than a perfectly competitive one in the short run yet provide more innovation incentives, leading to lower production cos...
ondition of Equation 15.3 with respect to qi gives @ @qi n 1 j X ¼ pj ! qj C 0i ð qiÞ $ ¼ 0: MR MC This ﬁrst-order condition is similar to Equation 15.2 except that the wedge term, \|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} \|ﬄﬄ{zﬄﬄ qj ¼ P 0 Q, Q ð Þ (15:3) (15:4) (15:5) is larger in magnitude with a perfect cartel than with ...
Q a cqi ¼ ð i $ $ Q qi $ Þ qi: c Þ (15:14pi @qi ¼ a 2qi $ Q $ i $ c $ ¼ 0, (15:15) 1, 2, . . . , n. which holds for all i ¼ The key to solving the system of n equations for the n equilibrium quantities is to recognize that the Nash equilibrium involves equal quantities because ﬁrms are symmetric. Symmetry implies that...
the usual marginal revenue from an increase in quantity, but rather the marginal revenue from an increase in price. The increase in price increases revenue on existing sales of qi units, but we must also consider the negative effect of the reduction in sales (@qi/@pi multiplied by the price pi) that would have been ea...
me: All charge the monopoly price v, which extracts all consumer surplus! This outcome holds no matter how small the search cost s is—as long as s is positive (say, a penny). It is easy to see that all stores charging v is an equilibrium. If all charge the same price v, then demanders may as well buy from the ﬁrst stor...
challenge certain mergers is that a merger may reduce n to a level such that Equation 15.49 begins to be satisﬁed and collusion becomes possible, resulting in higher prices and lower total welfare. QUERY: A period can be interpreted as the length of time it takes for ﬁrms to recognize and respond to undercutting by a ...
ave q1 þ ð BR2ð p1 ¼ q1 $ q1ÞÞ : q1Þ (15:56) C1ð P 11Mathematically, the notion of sunk costs can be integrated into the per-period total cost function as þ where S is the per-period amortization of sunk costs (e.g., the interest paid for funds used to ﬁnance capital investments), Ft is Ft; but if the production the pe...
parison of Figures 15.6 and 15.7 suggests the crucial difference between the games that leads the ﬁrst mover to play a ‘‘top dog’’ strategy in the quantity game and a ‘‘puppy dog’’ strategy in the price game: The best-response functions have different slopes. The goal is to induce the follower to compete less aggressiv...
ayoff of zero, and ﬁrm 1 again operates alone in the market. Assume there is no discounting between periods. $ ¼ 1 Firm 2 draws inferences about ﬁrm 1’s cost from the price that ﬁrm 1 charges in the ﬁrst period. Firm 2 earns more if it competes against the high-cost type because the 15The Query in Example 15.9 asks you...

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