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by giving you easy access to your money, either by writing a check or by using a debit card (that is, a card which works like a credit card, except that purchases are immediately deducted from your checking account rather than billed separately through a credit card company). A savings account typically pays some inter...
r borrowers than the federal government, the rates tend to rise and fall together. Treasury bonds typically pay more than bank accounts, and corporate bonds typically pay a higher interest rate than Treasury bonds. This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Chapter 17 \| Financial Ma...
s rising or falling. Even investors who buy an indexed mutual fund designed to mimic some measure of the broad stock market, like the Standard & Poor’s 500, had better prepare against some ups and downs, like those the stock market experienced in the first decade of the 2000s. In 2008 average U.S. stock funds declined ...
isk, and the liquidity of each investment. Table 17.3 summarizes these characteristics. Financial Investment Return Risk Liquidity Checking account Savings account Very low Low Very little Very little Certificate of deposit Low to medium Very little Stocks Bonds High Medium Medium to high Low to medium Very high High M...
saving money early in life obviously will not make you rich overnight. Additional education typically means deferring earning income and living as a student for more years. Saving money often requires choices like driving an older or less expensive car, living in a smaller apartment or buying a smaller house, and maki...
tors and venture capital firms. A bond is a financial contract through which a borrower agrees to repay the amount that it borrowed. A bond specifies an amount that one will borrow, the amounts that one will repay over time based on the interest rate when the bond is issued, and the time until repayment. Corporate bond...
000 in ten years? 40. Many retirement funds charge an administrative fee each year equal to 0.25% on managed assets. Suppose that Alexx and Spenser each invest $5,000 in the same stock this year. Alexx invests directly and earns 5% a year. Spenser uses a retirement fund and earns 4.75%. After 30 years, how much more wi...
ndidates agree to abide by certain spending limits. Of course, candidates can also voluntarily agree to set certain spending limits if they wish. However, government cannot forbid people or organizations to raise and spend money above these limits if they choose. In 2002, Congress passed and President George W. Bush si...
he tax passes, so each should be willing to spend up to that amount to prevent the passage, a combined sum of $2 million. Of course, in the real world, there is no guarantee that lobbying efforts will be successful, so the factory owners may choose to invest an amount that is substantially lower. Step 2. There are 10,0...
median voter is in the middle of the spectrum. This theory argues that actual policy will reflect “middle of the road.” In the case of sugar lobby politics, the minority, not the median, dominates policy. Sometimes it is not even clear how to define the majority opinion. Step aside from politics for a moment and think ...
t with outrage expressed via social media, traditional media, or mass protests? Were there “Occupy Wall Street-type” demonstrations? The answer is a resounding “No”. Most U.S. tire consumers were likely unaware of the tariff increase, although they may have noticed the price increase, which was between $4 and $13 depen...
medicines that pharmacies are allowed to sell in the United States. Sometimes this means a company must test a drug for years before it can reach the market. We can easily identify the winners in this system as those who are protected from unsafe drugs that might otherwise harm them. Who are the more anonymous losers w...
tiate between corn or oil from either country. There is only one resource available in both countries, labor hours. Saudi Arabia can produce oil with fewer resources, while the United States can produce corn with fewer resources. Table 19.1 illustrates the advantages of the two countries, expressed in terms of how many...
d after 100% specialization — Oil (barrels) Quantity produced after 100% specialization — Corn (bushels) United States 0 Total World Production 100 Table 19.6 How Specialization Expands Output 100 100 What if we did not have complete specialization, as in Table 19.6? Would there still be gains from trade? Consider anot...
ng only 3,500 shoes but 26,000 refrigerators. If the United States can export no more than 6,000 refrigerators in exchange for imports of at least 1,500 pairs of shoes, it will be able to consume more of both goods and will be unambiguously better off. The range of trades that can benefit both nations is shown in Table...
s to and from the United States, the European Union, and Japan? There are two reasons: (1) The division of labor leads to learning, innovation, and unique skills; and (2) economies of scale. Gains from Specialization and Learning Consider the category of machinery, where the U.S. economy has considerable intra-industry...
limited possibilities for trade inside their countries or their immediate regions. Without international trade, they may have little ability to benefit from comparative advantage, slicing up the value chain, or economies of scale. Moreover, smaller economies often have fewer competitive firms making goods within their ...
t is splitting up the value chain? 16. Are the gains from international trade more likely to large or small to be relatively more important countries? CRITICAL THINKING QUESTIONS 22. You just got a job in Washington, D.C. You move into an apartment with some acquaintances. All your roommates, however, are slackers and ...
on to countries with loose or nonexistent pollution standards, trading a clean environment for jobs. Some politicians worry that their country may become overly dependent on key imported products, like oil, which in a time of war could threaten national security. All of these fears influence governments to reach the sa...
0.3 (b) shows consumers in the United States benefit from the lower price and greater availability of sugar. Consumers in Brazil are worse off (compare their no-trade consumer surplus with the free-trade consumer surplus) and U.S. producers of sugar are worse off. There are gains from trade—an increase in social surplu...
127,000 jobs, or more than seven times the total employment in sugar production. While the candy industry is especially affected by the cost of sugar, the costs are spread more broadly. U.S. consumers pay roughly $1 billion per year in higher food prices because of elevated sugar costs. Meanwhile, sugar producers in lo...
bsite (http://openstaxcollege.org/l/fairtradecoffee) to read an article on the issues surrounding fair trade coffee. One concern is that while globalization may be benefiting high-skilled, high-wage workers in the United States, it may also impose costs on low-skilled, low-wage workers. After all, high-skilled U.S. wor...
Brazilian consumers and industries that would have benefited from up-to-date computers paid the costs and Brazil’s computer industry never competed effectively on world markets, Brazil phased out its infant industry policy for the computer industry. Protectionism for infant industries always imposes costs on domestic u...
to countries with weak standards, thus reducing their costs and increasing their profits. Faced with such behavior, countries reduce their environmental standards to attract multinational firms, which, after all, provide jobs and economic clout. As a result, global production becomes concentrated in countries where fir...
etween countries is “very good” or “somewhat good,” Americans had the least favorable attitude toward increasing globalization, while the Chinese and South Africans ranked highest. In fact, among the 47 countries surveyed, the United States ranked by far the lowest on this measure, followed by Egypt, Italy, and Argenti...
gar producers. One of the jobs of the United States Department of Commerce is to determine if there is import dumping from other countries. The United States International Trade Commission—a government agency—determines whether the dumping has substantially injured domestic industries, and if so, the president can impo...
w occurs in countries other than the United States. 488 Chapter 20 \| Globalization and Protectionism KEY TERMS anti-dumping laws laws that block imports sold below the cost of production and impose tariffs that would increase the price of these imports to reflect their cost of production common market economic agreemen...
s international trade likely to have roughly the same effect on the number of jobs in each individual industry? 25. How is international trade, taken as a whole, likely to affect the average level of wages? Is international trade likely to have about the same 26. effect on everyone’s wages? 27. What are main reasons fo...
escribe cause and effect. The variable on the left-hand side is what is being explained (“the effect”). On the right-hand side is what is doing the explaining (“the causes”). For example, suppose your GPA was determined as follows: GPA = 0.25 × combined_SAT + 0.25 × class_attendance + 0.50 × hours_spent_studying This e...
$2/$10 = 0.20 or 20%. To compute the growth rate for data over an extended period of time, for example, the average annual growth in GDP over a decade or more, the denominator is commonly defined a little differently. In the previous example, we defined the quantity as the initial quantity—or the quantity when we start...
In columns 2–4, the first number shows the actual number of people in each age category, while the number in parentheses shows the percentage of the total population comprised by that age group. Year Total Population 19 and Under 20–64 years Over 65 1970 2000 2030 205.0 million 275.4 million 351.1 million 77.2 (37.6%) ...
mx, where x is the variable on the horizontal axis and y is the variable on the vertical axis, the b term is the y-intercept and the m term is the slope. The slope of a line is the same at any point on the line and it indicates the relationship (positive, negative, or zero) between two economic variables. Economic mod...
flatter on the right—the specific shape of indifference This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Appendix B 511 curves can be different for every person. Figure B1, for example, applies only to Lilly’s preferences. Indifference curves for other people would probably travel throug...
ewer haircuts to be consumed. For pizza, in this case, the substitution effect and income effect cancel out, leading to the same amount of pizza consumed. The price of haircuts rises to $30. Ogden starts at choice A on the higher opportunity set and the higher indifference curve. After the price of haircuts increases, ...
ing to Petunia’s preferences, the income effect that encourages choosing more leisure is stronger than the substitution effect that encourages choosing less leisure. Figure B5 represents only Petunia’s preferences. Other people might make other choices. For example, a person whose substitution and income effects on lei...
See Figure B11. Figure B11 In sketching substitution and income effect diagrams, you may wish to practice some of the following variations: (1) Price falls instead of a rising; (2) The price change affects the good on either the vertical or the horizontal axis; (3) Sketch these diagrams so that the substitution effect...
hat the present value of a $3,000 bond, issued at 8%, is just $3,000. After all, that is how much money the borrower is receiving. The calculation confirms that the present value is the same for the lender. The bond is moving money around in time, from those willing to save in the present to those who want to borrow in...
including energy, which is used in the production of virtually everything. A decrease in demand for energy will be reflected as a decrease in the demand for oil, or a leftward shift in demand for oil. Since the demand curve is shifting down the supply curve, both the equilibrium price and quantity of oil will fall. e. ...
÷ 2 ×100 ×100 = 5 97.5 = 5.13 % change in price = $13 – $12 ($13 + $12) ÷ 2 × 100 × 100 = 1 12.5 = 8.0 Elasticity of Supply = 5.13% 8.0% = 0.64 The supply curve is inelastic in this region of the supply curve. 3. The demand curve with constant unitary elasticity is concave because the absolute value of declines in pric...
ous. All that is required to get into the business is a truck (not an inexpensive asset, though) and a commercial driver’s license. To exit, one need only sell the truck. All trucks are essentially the same, providing transportation from point A to point B. (We’re assuming we not talking about specialized trucks.) Inde...
oly because average costs decline over the range that satisfies the market demand. For example, at the point where the demand curve and the average cost curve meet, there are economies of scale. 8. Improvements in technology that allowed phone calls to be made via microwave transmission, communications satellites, and ...
rams that either pay for education directly or that provide loans or reduced tax payments for education could create positive spillovers. A city might allow its businesses to form a group that would coordinate business efforts with schools and local colleges and universities—allowing students to obtain real-world exper...
oping. 11. For the second hypothesis, a well-funded social safety net might make people feel that even if their company goes This OpenStax book is available for free at http://cnx.org/content/col12170/1.7 Answer Key 551 bankrupt or they need to change jobs or industries, they will have some degree of protection. As a r...
You can also spot this conclusion by noticing that Poland’s absolute disadvantage is relatively lower in televisions, because Poland needs twice as many workers to produce a television but three times as many to produce a video camera, so the product with the relatively lower absolute disadvantage is Poland’s comparati...
ary 2015." Accessed March 27, 2015. http://www.bls.gov/news.release/pdf/empsit.pdf. Williamson, Lisa. “US Labor Market in 2012.” Bureau of Labor Statistics. Accessed December 1, 2013. http://www.bls.gov/opub/mlr/2013/03/art1full.pdf. The Heritage Foundation. 2015. "2015 Index of Economic Freedom." Accessed March 11, 20...
d March 12, 2015. http://www.digitaltrends.com/mobile/judge-tosses-out-googleantitrust-lawsuit/. Monopolistic Competition and Oligopoly Kantar Media. “Our Insights: Infographic—U.S. Advertising Year End Trends Report 2012.” Accessed October 17, 560 References 2013. http://kantarmedia.us/insight-center/reports/infograph...
=1&. Kolesnikova, Natalia A., and Yang Liu. Federal Reserve Bank of St. Louis: The Regional Economist. “Gender Wage Gap May Be Much Smaller Than Most Think.” Last modified October 2011. http://www.stlouisfed.org/ publications/re/articles/?id=2160. Podmolik, Mary Ellen. “HUD Finds Housing Discrimination ‘Hidden’ But Pre...
Becoming a Publicly Traded Company.” U.S. Small Business Administration: Community Blog (blog). Publication date March 23, http://www.sba.gov/community/blogs/community-blogs/business-law-advisor/should-your-small2010. business-go-public-consider-0. Howley, Kathleen M. Bloomberg. “Home Value Highest Since ’07 as U.S. Ho...
flow diagram, 16, 23 Civil Rights Act of 1964, 340 Civil Rights Act of 1991, 342 Clayton Antitrust Act, 258 Clean Air Act, 280, 283, 285 Clean Water Act, 280 coinsurance, 390, 396 collateral, 387, 396 collective bargaining, 330, 347 collusion, 244, 250 command economy, 18, 23 command-and-control regulation, 280, 291 co...
), 33, 42 production possibility frontier (PPF), 289, 446 production technologies, 172, 181 Productive efficiency, 36, 206 productive efficiency, 42, 242, 292 productivity, 450 Profit, 165 profit, 189 profit margin, 171, 194 profit-maximizing, 239 profits, 247 progressive tax system, 371, 375 property rights, 284, 291 ...
tions Many economic models start from the assumption that the economic actors being studied are rationally pursuing some goal. We brieﬂy discussed such an assumption when investigating the notion of ﬁrms maximizing proﬁts. Example 1.1 shows how that model can be used to make testable predictions. Other examples we will...
d price. To Smith, for example, the value of a commodity meant its ‘‘value in use,’’ whereas the price represented its ‘‘value in exchange.’’ The distinction between these two concepts was illustrated by the famous water–diamond paradox. Water, which obviously has great value in use, has little value in exchange (it ha...
d curves would show. For example, Figure 1.3 shows that when the constant 7 term, a, in the demand equation increases to 1,450, equilibrium price increases to p% [ ¼ QUERY: How might you use Equation 1.16 to ‘‘predict’’ how each unit increase in the exogenous constant a affects the endogenous variable p%? Does this equ...
is economy does not work well and that 20 workers are permanently unemployed. Now the production possibility frontier becomes 0:25y2 x2 þ ¼ 180, (1:20) Chapter 1: Economic Models 17 and the output combinations we described previously are no longer feasible. For example, if x ¼ 10, then y output is now y 17.9. The loss ...
. Discusses ﬁrst basic notions of marginalism. Smith, A. The Wealth of Nations. New York: Modern Library, 1937. First great economics classic. Long and detailed, but Smith had the ﬁrst word on practically every economic matter. This edition has helpful marginal notes. Walras, L. Elements of Pure Economics. Translated b...
book we shall be less interested in how the point is discovered than in its properties and how the point changes when conditions change. A mathematical development will be helpful in answering these questions. Rules for ﬁnding derivatives Here are a few familiar rules for taking derivatives of a function of a single v...
ts in which y and x are measured cancel out in the deﬁnition of elasticity; the result is a ﬁgure that is a pure number with no dimensions. This makes it possible for economists to compare elasticities across different countries or across rather different goods. You should already be familiar with the price elasticitie...
se implicit relationships can often provide another analytical tool for drawing conclusions from economic models. ¼ Probably the most useful result provided by this approach is in the ability to quantify the trade-offs inherent in most economic models. Here we will look at a simple case. f (x1, x2). If we hold the valu...
f x only, and the 1 2 and, for value of x that maximizes y can be calculated. For example, if a 1 these values of x and a, y 1 and y$ 4 (its maximal value). Similarly, if a 1. Hence an increase of 1 in the value of the parameter a has increased the maximum ¼ value of y by 3 4. In Table 2.1, integral values of a between...
ined maximum value of f is equivalent to ﬁnding a critical value of +. Let’s proceed then to do so, treating l also as a variable (in addition to the x’s). From Equation 2.50, the conditions for a critical point are: ¼ Þ @+ @x1 ¼ @+ @x2 ¼ . .. @+ @xn ¼ @+ @k ¼ f1 þ kg1 ¼ 0, f2 þ kg2 ¼ 0, fn þ kgn ¼ 0, x1, x2, g ð . . ....
, from 10 to 8. 0, x2 ¼ QUERY: Suppose this individual could tolerate two doses per day. Would you expect y to increase? Would increases in tolerance beyond three doses per day have any effect on y? EXAMPLE 2.8 Optimal Fences and Constrained Maximization Suppose a farmer had a certain length of fence, P, and wished to ...
s ensures that any solution will obey these conditions. The ﬁrst two equations also resemble the optimal conditions developed earlier. If l2 and l3 were 0, the conditions would in fact be identical. But the presence of the additional Lagrange multipliers in the expressions shows that the customary optimality conditions...
bey Equations 2.97 and 2.98, so both necessary and sufﬁcient conditions for a local maximum are satisﬁed.16 (2:102) QUERY: Describe the concave shape of the health status function, and indicate why it has only a single global maximum value. 2=f11 to Equation 2.95 and factoring. But this approach is 15The proof proceeds...
ges in all the arguments in a function. Homogeneity and derivatives If a function is homogeneous of degree k and can be differentiated, the partial derivatives of the function will be homogeneous of degree k 1. A proof of this follows directly from the deﬁnition of homogeneity. For example, differentiating Equation 2.1...
Integration of this differential yields udv duv ¼ þ duv uv ¼ ð ¼ ð u dv þ ð v du or u dv uv ¼ ð % ð v du: (2:136) Here the strategy is to deﬁne functions u and v in a way that the unknown integral on the left can be calculated by the difference between the two known expressions on the right. For example, it is by no me...
er periods. Hence one must explicitly take account of this interrelationship in choosing optimal paths. If decisions in one period did not affect later periods, the problem would not have a ‘‘dynamic’’ structure—one could just proceed to optimize decisions in each period without regard for what comes next. Here, howeve...
e consumption is continuously decreasing, we must use integration to calculate wine consumption in any particular year (x) as follows: x x consumption in year x dt ,580 79e% 0:05t dt 1,580e% 0:05t ¼ % 0:05 e% ð x 1 % Þ ð % 0:05x e2:165) 1, consumption is approximately 77 bottles in this ﬁrst year. Consumption then decr...
indicated on the graphs of the functions’ PDFs in Figure 2.6. 1. Binomial. In this case: (2:182) 72 Part 1: Introduction For the coin ﬂip case (where p ¼ this random variable is, as you might have guessed, one half. 0.5), this says that E(x) ¼ 0.5—the expected value of p ¼ 2. Uniform. For this continuous random variabl...
wever. A zero covariance does not necessarily imply statistical independence. Finally, the covariance concept is crucial for understanding the variance of sums or differences of random variables. Although the expected value of a sum of two random variables is (as one might guess) the sum of their expected values: E x ð...
y up to a constant of integration, which repre- sents ﬁxed costs. b. As you may know from an earlier economics course, if a ﬁrm takes price ( p) as given in its decisions then it will produce 15? MC(q). If the ﬁrm follows this proﬁt-maximizing rule, how much will it produce when p that output for which p Assuming that ...
age of the two X How much is the variance of this sum reduced by setting k properly relative to other possible values of k? 1 is minimized when k (1 – k)x2, 0 kx1 þ ¼ - - ¼ k e. How would the result from part (d) change if the two variables had unequal variances? 2.16 More on covariances Here are a few useful relations...
¼ Example 2 The Cobb–Douglas function xayb where a, b (0, 1) is used to illustrate utility functions and production functions in many places in this text. The ﬁrst- and second-order derivatives of the function are 2 fx ¼ fy ¼ fxx ¼ fyy ¼ axa 1yb, % bxayb 1, % 2yb, xa 1 a a % Þ ð 2: xayb 1 b b % Þ ð % % Hence the Hessi...
ceeds the utility assigned to B, U(B). ¼ ¼ 5 and U(B) 4, or that U(A) 1,000,000 and U(B) Nonuniqueness of utility measures We might even attach numbers to these utility rankings; however, these numbers will not be unique. Any set of numbers we arbitrarily assign that accurately reﬂects the original preference ordering ...
bundles all provide the same level of utility. The slope of the indifference curve in Figure 3.2 is negative, showing that if the individual is forced to give up some y, he or she must be compensated by an additional amount of x to remain indifferent between the two bundles of goods. The curve is also drawn so that th...
ar 100 y, x ’ ¼ (3:10) 100=x, y ¼ (3:11) FIGURE 3.73Indifference Curve for Utility ¼ yp x ’ ﬃﬃﬃﬃﬃﬃﬃﬃﬃ This indifference curve illustrates the function 10 ¼ implying that this person is willing to trade 4y for an additional x. At point B (20, 5), however, the MRS is 0.25, implying a greatly reduced willingness to trade....
degrees of substitutability of x for y. The Cobb– Douglas and constant elasticity of substitution (CES) functions (drawn here for relatively low substitutability) fall between the extremes of perfect substitution (b) and no substitution (c). Quantity of y Quantity of y U2 U1 U0 Quantity of x (a) Cobb-Douglas (b) Perfe...
ion 3.34 look like? Why might this approximate a situation where y is a speciﬁc good and x represents everything else? 106 Part 2: Choice and Demand The Many-Good Case All the concepts we have studied thus far for the case of two goods can be generalized to situations where utility is a function of arbitrarily many goo...
aph. c. Suppose an individual obtains utility only from amounts of x and y that exceed minimal subsistence levels given by x0, y0. In this case, Is this function homothetic? (For a further discussion, see the Extensions to Chapter 4.) U x, y ð Þ ¼ x ð % x0 a y ð Þ y0 b Þ % 3.11 Independent marginal utilities Two goods ...
y), provided that the blends do not decrease fuel efﬁciency. E3.2 Quality Because many consumption items differ widely in quality, economists have an interest in incorporating such differences into models of choice. One approach is simply to regard items of different quality as totally separate goods that are relativel...
t appears to be extremely selﬁsh; no one, according to this complaint, has such solely self-centered goals. Although economists are probably more ready to accept self-interest as a motivating force than are other, 117 118 Part 2: Choice and Demand more Utopian thinkers (Adam Smith observed, ‘‘We are not ready to suspec...
straint is not precisely tangent to the indifference curve U2. Instead, at the optimal point the budget constraint is ﬂatter than U2, indicating that the rate at which x can be traded for y in the market is lower than the individual’s psychic trade-off rate (the MRS). At prevailing market prices the individual is more ...
on 4.23? Explain your answer mathematically. Also develop an intuitive explanation based on the notion that the share of income devoted to good y is given by the parameter of the utility function, b. EXAMPLE 4.2 CES Demand To illustrate cases in which budget shares are responsive to economic circumstances, let’s look a...
he income tax is a clear net income to $6, and indirect utility would be 1.5 [ improvement in utility over the case where x alone is taxed. The tax on good x reduces utility for two reasons: It reduces a person’s purchasing power, and it biases his or her choices away from good x. With income taxation, only the ﬁrst ef...
on, demand functions are homogeneous of degree zero in all prices and income. 2. Expenditure functions are nondecreasing in prices. This property can be succinctly summarized by the mathematical statement @E @pi + 0 for every good i: (4:55) This seems intuitively obvious. Because the expenditure function reports the mi...
purchasing power needed to increase this person’s utility from U 2 to U 3. ¼ ¼ c. Use Equation 4.52 again to estimate the degree to which good x must be subsidized to increase this person’s utility from 3. How much would this subsidy cost the government? How would this cost compare with the cost calcu- U 2 to U lated ...
ons are x b bI/py. Therefore, ¼ a and b, ¼ ¼ and budget shares are constant for all observed income levels and relative prices. Because of this shortcoming, economists have investigated a number of other possible forms for the utility function that permit more ﬂexibility. (i) þ ¼ ¼ xayb (where a aI/px and y sx ¼ sy ¼ p...
f demand. Demand Functions As we pointed out in Chapter 4, in principle it will usually be possible to solve the necessary conditions of a utility maximum for the optimal levels of x1, x2, …, xn (and l, the Lagrange multiplier) as functions of all prices and income. Mathematically, this can be expressed as n demand fun...
dget constraint would have motivated a move to point B, even if choices had been conﬁned to those on the original indifference curve U1. The dashed line in Figure 5.3 has the same p2 but is drawn to be tangent to U1 xx slope as the new budget constraint because we are conceptually holding ‘‘real’’ income (i.e., utility...
t 2: Choice and Demand assumption is in accord with our general conclusion that, except in the unusual case of Giffen’s paradox, @x/@px is negative. In Figure 5.5b, information about the utility-maximizing choices of good x is transferred to a demand curve with px on the vertical axis and sharing the same horizontal ax...
er either demand concept. For prices below p00x, however, the individual suffers a compensating reduction in income on the curve xc that prevents an increase in utility arising from the lower price. Assuming x is a normal good, it follows that less x is demanded at p00x along xc than along the uncompensated curve x. Al...
at the utility-maximizing @x @px # # # # 162 Part 2: Choice and Demand This equation allows a more deﬁnitive treatment of the direction and size of substitution and income effects than was possible with a graphic analysis. First, as we have just shown, the substitution effect (and the slope of the compensated demand cu...
Marshallian counterparts Let the compensated demand function be given by xc( px, py, U). Then we have the following deﬁnitions. 1. Compensated own-price elasticity of demand . This elasticity measures the proportionate compensated change in quantity demanded in response to a proportionate change in a good’s own price: ...
the Cobb–Douglas. sxex, I ¼ ’ 1 and sx ¼ exc, px ¼ (5:52) 0.5): 1 ð 0:5 1:5 þ 1, Case 3: CES (s 0.5; d ¼ 1). U(x, y) 1 – x’ y’ 1. ¼ ’ ¼ ’ Referring back to Example 4.2, we can see that the share of good x implied by this utility function is given by 7Notice that this substitution must be made after differentiation bec...
ure the welfare loss from the price increase as we did in Figure 5.8 using the compensating variation (CV) associated with the initial comarea p1 , or should we perhaps use this new compensated pensated demand curve ð demand curve and measure the welfare loss as area p1 x? A potential rationale for using the area under...
however, substitution and income effects work in opposite directions, and no unambiguous prediction is possible. • Similarly, an increase in price induces both substitution and income effects that, in the normal case, cause less to be demanded. For inferior goods the net result is again ambiguous. • Marshallian demand...
P i n j c. Cournot aggregation: P 0. ei, j þ 1 ¼ ¼ n i ei, I ¼ siei, I ¼ 1. 1 siei, j ¼ ’ ¼ sj. 5.12 Quasi-linear utility (revisited) Consider a simple quasi-linear utility function of the form U(x, y) P x ln y. ¼ þ a. Calculate the income effect for each good. Also calculate the income elasticity of demand for each g...
hat people were actually paying. Assessing the magnitude of error introduced by these cases where incorrect prices are used in the CPI can also be accomplished by using the various demand concepts in Figure E5.1. For a summary of this research, see Moulton (1996). E5.4 Exact price indices In principle, it is possible t...
ct of a change in the price of x. Now let’s look at the cross-price effect of a change in y prices on x purchases. Remember that the uncompensated and compensated demand functions for x are given by Chapter 6: Demand Relationships among Goods 189 and px, py, I x ð Þ ¼ 0:5I px (6:3) xc px, py, V Vp0:5 y p% x 0:5 : (6:4)...
her this intuition is justiﬁed. The British economist John Hicks studied this issue in some detail more than 70 years ago and reached the conclusion that ‘‘most’’ goods must be substitutes. The result is summarized in what has come to be called Hicks’ second law of demand.3 A modern proof starts with the compensated de...
nchanged by making the substitutions represented by Equation 6.36? Chapter 6: Demand Relationships among Goods 197 Home Production, Attributes of Goods, and Implicit Prices Thus far in this chapter we have focused on what economists can learn about the relationships among goods by observing individuals’ changing consum...

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