Archives: Solution Manual

6.19 Component Concentration Equiv. Weight (mg/meq) Concentration (meq/L) Concentration (mg/L CaCO3) Ca2+ 90 mg/L 20 4.500 225.0 Mg2+ 30 mg/L 12.2 2.4596 123.0 HCO3 –165 mg/L 61.0 2.705 135.3 pH 7.5 – – – 348.0 135.3 0 225.0 0 Ca2+ […]

6.1 a. A primary standard is an enforceable limit on the concentration of a contaminant in water or an enforceable requirement that a particular treatment b. An MCL is a primary standard, whereas an MCLG is a maximum concentration goal […]

5.1 – 5.33 The solutions for these problems are the solutions for problems 5.1 – 5.33 in the 2nd edition Solutions Manual. 5.34 On a molar basis the C:N:P ratio for algae is 106:16:1 and on a mass basis it […]

4.1 – 4.10 The solutions for these problems are the solutions for problems 4.1 – 4.10 in the 2nd edition Solutions Manual. 4.11 a. b. Denver deaths due to cosmic radiation exposure: () yr deaths 8.6 rems 000,8 death 1 […]

3.1 – 3.17 The solutions for these problems are the solutions for problems 3.1 – 3.17 in the 2nd edition Solutions Manual. 3.18 a. rabbits 1,750 2 rabbits 3,500 2 *=== K N b. () () ( ) () rabbits/yr […]

2.1 – 2.14 The solutions for these problems are the solutions for problems 2.1 – 2.14 in the 2nd edition Solutions Manual. 2.15 EDTA (C10N2O8H16) has a molecular weight of 292 g/mole Calcium molar concentration: (20 mg/L)(40.1 mol/g)-1(103 mg/g)-1 = […]

1.1-1.7 The solutions for these problems are the solutions for problems 1.1-1.7 in the 2nd 1.8 The washing machine is a batch reactor in which a first order decay of grease on the clothes is occurring. The integrated form of […]

259 forces them to interpret their findings. While leaving the topic to each student’s discretion is more interesting, I find that many students flounder with an open-ended assignment until it is too late. For a second-semester course, or a senior […]

243 The forecasting section is heavily oriented towards regression methods and, in particular, autoregressive models. These can be estimated using any econometrics package, and forecasts and mean absolute errors or root mean squared errors are easy to obtain. The interest […]

231 C17.6 The results of an OLS regression using only the uncensored durations are given in the following table: Dependent Variable: log(durat) Independent Variable Coefficient (Standard Error) workprg .092 (.083) (.08221) married .239 (.099) educ −.019 (.019) age .00053 (.00042) […]

CHAPTER 17 TEACHING NOTES I emphasize to the students that, first and foremost, the reason we use the probit and logit models is to obtain more reasonable functional forms for the response probability. Once we move to a nonlinear model […]

more) variables are jointly determined does not mean that it is appropriate to specify and estimate an SEM. I have seen many bad applications of SEMs where no equation in the system can stand on its own with an interesting […]

187 A leading example is estimating the return to education when unobserved ability is in the error term. We are not thinking that education and wages are jointly determined; for the vast majority of people, education is completed before we […]

Choosing between the fixed effects transformation and first differencing is harder, although useful evidence can be obtained by testing for serial correlation in the first-difference estimation. If the AR(1) coefficient is significant and negative (say, less than −.3, to pick […]

156 Having more than two periods of panel data causes slight complications in that the errors in the differenced equation may be serially correlated. (However, the traditional assumption that the errors in the original equation are serially uncorrelated is not […]

143 Section 12.3, on GLS and FGLS estimation, is fairly standard, although I try to show how comparing OLS estimates and FGLS estimates is not so straightforward. Unfortunately, at the beginning level (and even beyond), it is difficult to choose […]

series regressions are the hallmark of many student projects that use time series data. Therefore, students need to be alerted to the dangers of using highly persistent processes in time series regression equations. (Spurious regression problem and the notion of […]

117 Although the text is careful in stating the assumptions, in class, after discussing strict exogeneity, I leave the conditioning on X implicit, especially when I discuss the no serial correlation assumption. As the absence of serial correlation is a […]

271 APPENDIX E SOLUTIONS TO PROBLEMS E.1 This follows directly from partitioned matrix multiplication in Appendix D. Write 1  x 1  y As shown in Section E.4, this expression is the basis for the asymptotic analysis of OLS […]

269 APPENDIX D SOLUTIONS TO PROBLEMS diagonal matrix with jth diagonal element ajbj. Similarly, BA is an n  n diagonal matrix with jth diagonal element bjaj, which, of course, is the same as ajbj. D.2 This result is easy […]

265 APPENDIX C SOLUTIONS TO PROBLEMS C.1 (i) This is just a special case of what we covered in the text, with n = 4: E( Y ) = µ and Var( Y ) =  2/4. (ii) Var(Wa) = […]

263 APPENDIX B SOLUTIONS TO PROBLEMS B.1 Before the student takes the SAT exam, we do not know – nor can we predict with certainty B.2 (i) P(X  6) = P[(X – 5)/2  (6 – 5)/2] = P(Z […]

with labor, such as capital and natural resources. The key to a rising standard of living is increased productivity. To foster productivity, developing nations must stimulate investment, support education and training programs, provide sufficient infrastructure, and foster supportive rules of […]

b. Merchandise import c. Merchandise import d. Net unilateral transfers e. Capital inflows f. Service imports g. Service exports © 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for […]

260 (ii) 3 + .2(5) = 4 classes. (iii) 10(.2) = 2 classes. A.3 If price = 15 and income = 200, quantity = 120 – 9.8(15) + .03(200) = –21, which is nonsense. This shows that linear demand functions […]

food production because the opportunity cost of producing one more unit of food in Fredonia is equal to the cost of one-seventh of a unit of clothing, compared with a cost of one-fourth of a unit of clothing in the […]

103 9.3 and 9.4. The first shows that controlling for IQ can substantially change the estimated return to education, and the omitted ability “bias” is in the expected direction. (Controlling for IQ lowers the return to education.) Interestingly, education and […]

© 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website […]

measures. The key is that these are estimates of the population R-squared, 1 – [Var(u)/Var(y)], where the variances are the unconditional variances in the population. The usual R-squared, and the adjusted version, consistently estimate the population R-squared whether or not […]

vertical line. At point a, the intersection of the supply of money, Sm, and the demand for money, Dm, determines the market interest rate, i. Following an increase in the money supply to S′m, the quantity of money supplied exceeds […]

In allowing for different slopes, it is important, as in Chapter 6, to appropriately interpret the parameters and to decide whether they are of direct interest. For example, in the wage equation where the return to education is allowed to […]

can make is ($4,000−$1,000 required reserves) = $3,000. The excess reserves would be ($3,000 − $1,000 required reserves) = $2,000. © 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except […]

54 I often have students and colleagues ask if there is a simple way to predict y when log(y) has been used as the dependent variable, and to obtain a goodness-of-fit measure for the log(y) model that can be compared […]

b. token money c. legal tender d. unit of account © 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a […]

consistency and asymptotic normality of OLS. (Conveniently, the same assumptions that work for finite sample analysis work for asymptotic analysis.) More advanced students can follow the proof of consistency of the slope coefficient in the bivariate regression case. Section E.4 […]

unemployment benefits rise. Also, many entitlement programs are indexed to inflation, so expenditures automatically rise. Inflation forecasts are therefore necessary to estimate expenditures. Interest on the national debt also depends on the state of the economy—whether interest rates rise or […]

34 CHAPTER 4 TEACHING NOTES At the start of this chapter is good time to remind students that a specific error distribution played no role in the results of Chapter 3. That is because only the first two moments were […]

employment, the price level, and economic growth. a. A decrease in government purchases decrease real GDP. b. An increase in net taxes decrease real GDP. c. A reduction in transfer payments decrease real GDP. d. A decrease in the marginal […]

19 I find extensive treatments of multicollinearity, where one “tests” or somehow “solves” the multicollinearity problem, to be misleading, at best. Even the organization of some texts gives the impression that imperfect collinearity is somehow a violation of the Gauss-Markov […]

the same. Note that this is the equilibrium real wage and corresponds to potential output. There is no frictional unemployment associated at this real wage. The money wage at point c is higher than that at point a. The reason […]

6 difference between an estimator that is unbiased conditional on the outcome of the covariates and one that is unconditionally unbiased. If the distribution of the 𝑥𝑖 is such that they can all equal the same value with positive probability […]

© 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website […]

i Chapter 15 Instrumental Variables Estimation and Two Stage 187 Least Squares Chapter 16 Simultaneous Equations Models 205 Chapter 17 Limited Dependent Variable Models and Sample 219 Selection Corrections CONTENTS PREFACE iii SUGGESTED COURSE OUTLINES iv Chapter 1 The Nature […]

© 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website […]

1 CHAPTER 1 TEACHING NOTES You have substantial latitude about what to emphasize in Chapter 1. I find it useful to talk about the economics of crime example (Example 1.1) and the wage example (Example 1.2) so that students see, […]

b. Cyclical c. Structural d. Frictional insurance provides a safety net for some and that’s good, but it may also reduce incentives to find work, as is the case in Europe, and that’s an unintended consequence. Research suggests that those […]

b. Net Domestic Product = GDP − depreciation = 280 − 10 = $270 billion c. Net investment = Gross investment − depreciation = 40 − 10 = $30 billion d. Net exports = X − M = 30 − […]

that individual item demanded and supplied. Aggregate demand and aggregate supply describe the relationship between the average price level of all goods and services and the total quantities of goods and services demanded and supplied throughout the entire economy. b. […]

b. Substitutes c. Substitutes d. Unrelated e. Complements inferior), a change in the price of a related good (an increase in the price of a substitute or a decrease in the price of a complement), the expectation of a higher […]

b. This would reduce household production because of the high price of land as well as other opportunity costs. c. This would increase household production because the high sales tax on food increases the cost of buying food. d. This […]