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microeconomics

Questions and Answers of Microeconomics

9. For a straight-line demand curve, what is the price elasticity at the revenue maximizing point?
6. To get the market demand curve for a product, why do we add individual demand curves horizontally rather than vertically?
5. Can the price-consumption curve for a normal good ever be downward-sloping?
4. Give two examples of what are, for most students, inferior goods.
3. Draw Engel curves for both a normal good and an inferior good.
2. Why is the quantity of education demanded in private universities much more responsive than salt is to changes in price?
1. Why does the quantity of salt demanded tend to be unresponsive to changes in its price?
13. If you were president of a conservation group, which rate structure would you prefer the Gigawatt Power Company to use: the one described in Example 3.1, or one in which all power sold for
1. The Acme Seed Company charges $2/lb for the first 10 lb you buy of marigold seeds each week and $1/lb for every pound you buy thereafter. If your income is $100/wk, draw your budget constraint for
7. Why are corner solutions especially likely in the case of perfect substitutes?
6. Explain why a consumer will often buy one bundle of goods even though he prefers another.
4. Construct an example of a preference ordering over Coke, Diet Coke, and Diet Pepsi that violates the transitivity assumption.
3. True or false: The downward slope of indifference curves is a consequence of the diminishing marginal rate of substitution.
2. True or false: If you know the slope of the budget constraint(for two goods), you know the prices of the two goods. Explain.
1. If the prices of all products are rising at 20 percent per year and your employer gives you a 20 percent salary increase, are you better off, worse off, or equally well off in comparison with your
10. How would the equilibrium price and quantity change in the market depicted below if the marginal cost of every producer were to increase by $2/pound? (Hint: Recall the vertical interpretation of
7. Give an example of a market in which the allocative function of price is not very important.
6. When there is excess supply, why is any single seller able to sell all she wants to by offering only a small reduction below the current market price?
4. What is the difference between “a reduction in supply”and “a reduction in the quantity supplied”?
3. Give two examples of actions taken by the administration of your college or university whose effect is to prevent specific markets from reaching equilibrium. What evidence of excess supply or
1. What is the difference between “scarcity” and“shortage”?
2. If her marginal benefit curve is again as given in Figure 1.1, how many minutes should Susan speak with Hal each month if the long-distance rate falls to 2 cents per minute?Why do manual
2. If the marginal cost of launching each boat had not been $100 but $150, how many boats should Tom have launched?
2. You are holding a discount coupon that will entitle you to a fare reduction on only one of the two trips you are scheduled to take during the coming month. You can either get $100 off the normal
Should you drive downtown to save $10 on a $1000 television set?
Should you drive to Wal-Mart to save $10 on a $20 clock radio?
2. Jim wins a ticket from a radio station to see a jazz band perform at an outdoor concert. Mike has paid $18 for a ticket to the same concert. On the evening of the concert there is a tremendous
1. How, if at all, would your answer to the question in Example 1.5 be different if the worth of avoiding the hassle of driving is $20 and you average one$28 traffic ticket for every 200 miles you
12. Suppose in Problem 11 the cost of RAM falls to $50 per gigabyte. How many gigabytes of memory should you purchase now? Suppose additionally that your benefit for an additional gigabyte of memory
11. Suppose that random access memory (RAM) can be added to your computer at a cost of $100 per gigabyte. Suppose also that the value to you, measured in terms of your willingness to pay, of an
10. Residents of your city are charged a fixed weekly fee of $6 for refuse collection. They may put out as many cans as they wish. The average household puts out three cans per week.Now, suppose your
9. A group has chartered a bus to New York City. The driver costs $100, the bus costs$500, and tolls will cost $75. The driver’s fee is nonrefundable, but the bus may be canceled a week in advance
8. Two types of radar weather-detection devices are available for commercial passenger aircraft: the “state-of-the-art” machine and another that is significantly less costly, but also less
7. Bill and Joe live in Ithaca, New York. At 2 PM, Bill goes to the local Ticketmaster and buys a $30 ticket to a basketball game to be played that night in Syracuse (50 miles north). Joe plans to
6. You loan a friend $1000, and at the end of 1 year she writes you a check for $1000 to pay off this loan. If the annual interest rate on your savings account is 6 percent, what was your opportunity
5. Al and Jane have rented a banquet hall to celebrate their wedding anniversary. Fifty people have already accepted their invitation. The caterers will charge $5 per person for food and $2 per
4. You are planning a 1000-mile trip to Florida. Except for cost, you are indifferent between driving and taking the bus. Bus fare is $260. The costs of operating your car during a typical
3. The meal plan at University A lets students eat as much as they like for a fixed fee of$500 per semester. The average student there eats 250 lb of food per semester. University B charges students
2. Tom is a mushroom farmer. He invests all his spare cash in additional mushrooms, which grow on otherwise useless land behind his barn. The mushrooms double in size during their first year, after
1. Jamal has a flexible summer job. He can work every day but is allowed to take a day off anytime he wants. His friend Don suggests they go to the amusement park on Tuesday.The admission charge for
6. How can the cost-benefit model be useful for studying the behavior of people who do not think explicitly in terms of costs and benefits?
5. Why should sunk costs be irrelevant for current decisions?
4. Why is the opportunity cost of attending college higher for a 50-year-old than for a 20-year-old?
3. Give three examples of activities accompanied by external costs or benefits.
2. Your roommate is thinking of dropping out of school this semester. If his tuition payment for this semester is nonrefundable, should he take it into account when making his decision?
1. What is your opportunity cost of reading a novel this evening?
Consider the linear regression model \(\mathbf{y}=\mathbf{X} \boldsymbol{\beta}+\mathbf{u}\), where \(\mathrm{E}[\mathbf{u}]=\mathbf{0}\) and \(\mathrm{E}\left[\mathbf{u u}^{\prime}\right]=\sigma^{2}
Using the sample of the McCall data set from the empirical exercise in the previous chapter, reestimate the Weibull model for those transiting to full-time employment \((C E N S O R 1=1)\) under the
Reconsider the Weibull-gamma model of Section 18.2.3 after replacing the gamma distributed heterogeneity assumption by the assumption that heterogeneity is distributed according to the log-normal
The analysis of Section 18.2 shows the effects of unobserved heterogeneity on the unconditional or averaged hazard function. The result that neglected heterogeneity leads to under-estimation of the
Show that the duration data model with Pareto density of the first kind f(t)=αkα/tα+1,α>0,t⩾k⩾0, is an accelerated failure time duration model but is not a proportional hazards model. [Show
Using a 50% random subsample of the RAND data on medical expenditure over a 12-month period used in this chapter, and using a similar model specification, we wish to consider the following broad
Consider the maximum score estimator with objective functions \(S_{N}(\beta)\) given in (14.29) and \(Q_{N}(\beta)\) given in (14.30).(a) Show that
Consider the censored regression or Tobit model (see Section 16.3) where y∗=x′β+ε,ε∼ iid N[0,σ2], and y is observed when y∗>0 but is not observed (censored) when y∗≤0. There are N0
For data generated from the dgp given in Section 6.6.4 with N=1,000, obtain NL2SLS estimates and compare these to the two-stage estimates. 6.4.4. Alternatives to Standard IV Estimators The IV-based
The MD estimator (see Section 6.7) uses the restriction π−g(θ)=0. Suppose more generally that the restriction is h(θ,π)=0 and we estimate using the generalized MD estimator that minimizes
Suppose we impose the constraint that E[wi]=g(θ), where dim⁡[w]>dim⁡[θ].(a) Obtain the objective function for the GMM estimator.(b) Obtain the objective function for the minimum distance
This question uses the probit model but requires little knowledge of the model. Let y denote a binary variable that takes value 0 or 1 according to whether or not an event occurs, let x denote a
Consider the Laplace intercept-only example at the end of Section 6.3.6, so y=μ+u. Then GMM estimation is based on E[h(μ)]=0, where h(μ)=[(y− μ),(y−μ)3]′.(a) Using knowledge of the central
Select a 50% random subsample of the Section 4.6.4 data on log health expenditure (y) and log total expenditure (x).(a) Obtain OLS estimates and contrast usual and White standard errors for the slope
Suppose the dgp is yi=β0xi+ui,ui=xiεi,xi∼N[0,1], and εi∼N[0,1]. Assume that data are independent over i and that xi is independent of εi. Note that the first four central moments of N[0,σ2]
Based on the information in the Botox Application, what would happen to the optimum price and quantity if the government had collected a specific tax of \(\$ 75\) per vial of Botox? What welfare
Consider the nonlinear panel data model \(y_{i t}=\alpha_{i}+\exp \left(\mathbf{x}_{i t}^{\prime} \beta\right)+u_{i t}\), where \(\beta\) are parameters to be estimated, \(\alpha_{i}, i=1, \ldots,
Show that MLE in a binary logit panel model is inconsistent, with plim of \(2 \beta\) in a simple \(T=2\) model.
Use the same model for the Patents-R\&D data as in Section 23.3, except vary the dependent variable and model as suggested in the following. In each case estimate random effects models and, if
(a) Verify the expression for \(\Sigma_{c}\) given at (24.25).(b) Prove the consistency property of the estimators \(\widehat{\sigma}^{2}\) and \(\widehat{ho}\) in the CSRE model.(c) Consider the
Consider the OLS cluster-robust variance estimator formula (24.33). Suppose there are two levels of clustering. Specifically, in the context of the empirical example of this chapter, clustering could
For this exercise use a \(50 \%\) sample of the VLSMS data. Define \(y=1\) if the subject has at least one pharmacy visit (PHARVIS) and \(y=0\) otherwise. This example presumes access to a program
Consider the treatment-outcome model \(y=\) \(\mathbf{x}^{\prime} \boldsymbol{\beta}+\alpha d+\varepsilon\), where \(d\) is a binary indicator variable taking the value 1 if treatment is assigned
In the previous problem randomization refers to treatment. Here we consider randomized eligibility for receiving the treatment. Now \(e=1\) means that an individual is randomly made eligible and
Consider the nonlinear treatment outcome model \(\mathrm{E}[y \mid \mathbf{x}, d]=\exp \left(\mathbf{x}^{\prime} \boldsymbol{\beta}+\alpha d\right)\), where \(d\) is a binary treatment indicator.
Consider the nonlinear treatment outcome model \(\mathrm{E}[\ln y \mid \mathbf{x}, d]=\mathbf{x}^{\prime} \boldsymbol{\beta}+\alpha d\), where \(d\) is a binary treatment indicator. Suppose that we
In this chapter the empirical illustration used the PSID control group and the NSW treatment group. Dehejia and Wahba (2002) used two control groups. There is another control group available based on
Consider the attenuation bias result for the slope parameter of the bivariate errors-in-variables model (Equation (26.9) in Section 26.2.3). Extend the model to include an intercept term.(a) Derive a
Consider a linear multiple regression model with scalar regressor \(x\) that is measured with error and a vector of other regressors \(\mathbf{z}\) that are free of measurement error.(a) Maintaining
Consider the quadratic regression model \(y=\alpha+\beta x^{*}+\gamma x^{* 2}+\varepsilon\), where the regressor \(x^{*}=x+v\), with \(x\) observed and \(v\) a measurement error. Assume that
The literature on intergenerational mobility uses the following model (Solon, 1992; Zimmerman, 1992):\[ \begin{equation*} Y_{i}^{\text {son }}=\alpha+\beta Y_{i}^{\text {father
Consider any regression model, linear or nonlinear, with dependent variable \(y\) and exogenous variables \(\mathbf{x}\), and iid errors \(\varepsilon\). Show that if the probability of missing data
Consider the regression model \(\mathbf{y}=\beta_{1} \mathbf{x}+\mathbf{Z} \boldsymbol{\beta}_{2}+\mathbf{u}\), where \(y\) is an \(N \times 1\) vector, \(\mathbf{Z}\) is an \(N \times K\) matrix,
Consider the point that when estimation of a model is undertaken after data imputation the precision of the estimates is likely to be overstated if no adjustment is made for the imputation step. In
This problem involves an example that illustrates the Cox-Tsiatsis nonidentification of the competing risks result mentioned in Section 19.2. Consider the following dependent competing risks model in
For the model specified in the preceding problem, write down the log-likelihood function for each model in terms of hazard rates and integrated hazard rates, if both \(T\) and \(\delta\) are
Consider two parallel durations, say duration of unemployment, \(T_{1}\), and the duration of a spell without private health insurance, \(T_{2}\). Assume that conditional on unobserved heterogeneity
Using the same subsample of the McCall data set as in Chapter 18, estimate using a two-state model with unemployment and employment as the two states, (i.e., ignoring the distinction between
Suppose that \(Y\) is Poisson distributed with mean \(\mu\).(a) Verify that the first four moments are, respectively, \(\mu, \mu, \mu\), and \(3 \mu^{2}+\mu\).(b) Show that there is a linear
Now consider overdispersion in the Poisson model.(a) Suppose \(Y \mid \mu \sim \mathcal{P}[\mu]\), where \(\mu=\exp \left(\beta_{0}+\beta_{1} x\right), \beta_{0}=\gamma_{0}+\varepsilon\), and
Consider the Poisson regression model with conditional mean \(\mu=\exp \left(\mathbf{x}^{\prime} \beta\right)\). Treat the estimation problem as an unweighted nonlinear squares problem in which
Consider a finite mixture density \(f(y \mid \theta)=\sum_{j=1}^{C} \pi_{j} f_{j}\left(y \mid \theta_{j}\right)\), an additive mixture of \(C\) distinct latent classes, or subpopulations, with
A simple test of overdispersion in a Poisson model given in Section 20.2.4 tests the null hypothesis of zero coefficient in the regression of
For this problem use a \(50 \%\) subsample of the data used in this chapter.(a) Estimate Poisson and negative binomial regression with MDU as the dependent variable and the following explanatory
Consider the panel model \(y_{i t}=\alpha+\beta x_{i t}+u_{i t}\), where \(\alpha\) and \(\beta\) are scalars.(a) Show by appropriate subtraction that this model implies\[ y_{i
Consider estimation of the fixed effects linear regression model \(y_{i t}=\alpha_{i}+\mathbf{x}_{i t}^{\prime} \beta+\) \(\varepsilon_{i t}\), where \(\alpha_{i}\) are fixed effects possibly
Consider the fixed effects, two-way error component panel data model\[ y_{i t}=\alpha+\mathbf{x}_{i t}^{\prime} \boldsymbol{\beta}+\boldsymbol{\mu}_{i}+\lambda_{t}+\varepsilon_{i t} \]where
Use a 50% random subsample of the wage-hours data in Section 21.3(a) Can \(\beta\) be directly interpreted as a labor supply elasticity? Explain.(b) For the following estimators: (1) pooled OLS, (2)
Consider the panel GMM estimator of Section 22.2.1.(a) Show that minimization with respect to \(\beta\) of the quadratic function \(Q_{N}(\beta)\) given after (22.3) yields the panel GMM esimator
Consider the panel data model \(y_{i t}=\alpha+\beta x_{i t}+\gamma w_{i t}+u_{i t}, i=1, \ldots, N, t=\) \(1, \ldots, T\), where for simplicity there is no individual-specific effect. Suppose the
Again with three periods of data, but now consider the panel data model \(y_{i t}=\alpha_{i}+\beta x_{i t}+\gamma w_{i t}+u_{i t}\), where \(\alpha_{i}\) is a fixed effect, and consider IV estimation
Consider the differences in differences (DID) estimator presented in Section 22.6. Suppose the time trend term \(\left(\delta_{t}-\delta_{t-1}\right)\) differs across the treated and untreated
Using the hours and wages data of Ziliak (1997) reproduce as much of Table 22.2 as you can, with appropriate discussion, when the instrument set is expanded to include the third lags of Inwg, kids,
For the example in Section 12.5 .6 consider the estimator α^ that solves ∑i=1N[yi− 1S∑s=1S(α+uiS)]=0. Obtain analytical expressions for this estimator and its variance. 12.5.6. Unobserved

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