QUESTION 1 QUESTION 2

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1 QUESTION 1 Consider a two period model of durable-goods monopolists. The demand for the service flow of the good in each period is given by P = 1- Q. The good is perfectly durable and there is no production cost. The monopolist can either sell or lease in the first period. Let q 1 be the output in the first period and let λ be the proportion of the first period output that is sold. Note that in the second period there is no distinction between leasing and selling in a two period model. There is no discounting, that is, δ=1. (a) The monopolist cannot commit to the future production plan. Derive the dynamically consistent output levels in the first period and the second period, and the optimal λ (Use backward induction). (b) Now suppose that the monopolist faces a potential entrant in the second period. Once there is entry, they play a Cournot game. What are the optimal choices of q 1 and λ for the monopolist in the first period? Assume that the production cost for the entrant is also zero. Give an intuitive explanation for your answer. (Once again, use backward induction to solve this game). QUESTION 2 A system product requires n components, used in fixed proportions (e.g., a computer requires a microprocessor, disk drive, keyboard, etc.). There is no production cost. Let P be the price of the system. The demand for the system is Q= 1 P. (a) Assume that a single firm manufactures all of the components and sells only systems. What is the profit-maximizing price of the system, as a function of the number of components parts, n? (b) Assume that each component is manufactured and sold separately at price purchase the components and assemble them into a system with a total price P= p j. Consumers n j 1 p j. The component manufacturers set prices simultaneously. What is the total system price as functions of the number of components, n? (c) Compare the results in (a) and (b) as a function of n. Why do they differ?

2 QUESTION 3

3 QUESTION 4 Clemens and Gottlieb coauthored a paper entitled Do Physicians Financial Incentives Affect Medical Treatment and Patient Health? that recently appeared in the American Economic Review (AER). In this paper, these economists consider how changes in physicians financial incentives influence not only the quantity of health care provided but also technology adoption - investment in a Magnetic resonance imaging (MRI) machine. They estimate these effects using Medicare payment rate changes due to an overhaul of geographic adjustments to provider reimbursements in the Medicare program. In 1997, Medicare consolidated the areas across which it adjusts physician payments, reducing the number of payment regions nationally from 210 to 89. This consolidation led to area-specific price shocks that are plausibly exogenous with respect to other changes in local health care demand and supply. Below is an excerpt from the article that presents the model of a physician s decision in terms of the quantity of health care to provide and the decision of whether to adopt a technology (like an MRI machine) that reduces per unit costs from to c. To obtain the technology, a physician must incur a fixed cost of k (price of an MRI machine). In our framework, physicians can practice medicine using a standard practice style (S) that has a variable cost of per unit of care, or an intense practice style (I) that reduces unit costs to c but costs k > 0 to adopt. The crucial property of these technologies is not quality or sophistication, but rather that they lower the marginal cost of producing medical services. Such investments involve up-front costs, subsequently allowing practices to generate revenue with low marginal costs and minimal use of its physicians valuable time. Because insurance diminishes or eliminates price sensitivity (Feldstein 1973) and consumers lack information about treatment options, physicians make many health care decisions on their patients behalf (Arrow 1963). We assume that demand is unsatiated, so that physicians supply decisions drive the quantity of health care their patients receive. Since physicians act, at least in part, as agents on each patient s behalf, the patient s benefit curve influences supply decisions. Using Q to denote the market s aggregate supply, we let b(q) capture the health benefit of marginal care. This benefit enters directly into the physician s utility function. Marginal benefits are decreasing in Q and individual physicians take b(q) as given. A continuum of physicians has productivity γ i distributed over (0, ) according to F( ), already known when they make investment decisions. Doctor i takes 1/γ i units of time to produce one unit of care. Each must choose a technology, S or I, and quantity of care, q. Medicare compensates providers for this care according to administratively set payments at reimbursement rate r per unit of care (Newhouse 2003). With quasilinear utility in income, utility in the standard and intense practice regimes is where e is an increasing and convex function of physician time that captures decreasing returns to leisure. The last term captures physicians desire to provide beneficial care. This agency benefit is linear in the value of care, the amount supplied, and the weight placed on patient benefits. (a) Show that if γ j < γ k, then it cannot be the case that doctor k selects the standard practice style (i.e., does not invest in the technology) while doctor j selects the intense practice style (i.e., does invest in the technology). (b) Suppose the equilibrium is such that there exists a threshold productivity level, denoted as γ * where physicians only invest if their productivity is greater than γ *. Show that this threshold productivity level decreases in the reimbursement rate (r) and decreases with the weight placed on patient benefit (α).

4 Clemens and Gottlieb empirically test the implications of the above model using data on health care provision from claims submitted by providers to Medicare for reimbursement. The data consist of all claims associated of a 5 percent random sample of the Medicare beneficiary population for each year from 1993 through The data contain itemized reports of the services purchased for them by Medicare along with health outcomes. Table 5 below reports coefficients from ordinary least squares regressions for the following patient care and health-related outcomes: a measure of total care (column 1), an indicator for whether the patient dies within 4 years (column 2), and an indicator for whether the patient is hospitalized for a heart attack (MI) during the first year following the initial diagnosis of cardiovascular disease (column 3). These outcomes are regressed on the reimbursement rate shocks (price changes) resulting from the consolidation of Medicare's fee schedule areas in 1997 interacted with an indicator for years after the consolidation. All specifications include county fixed effects, state-by-year fixed effects, and indicators for the patient's age, being black, Hispanic, female, being eligible for Medicare due to end-stage renal disease, and being eligible for Medicare due to disability. The coefficients estimates in Table 5, Panel A pertain to the price change interacted with a Post-1997 indicator variable. Panel B contains estimates from the identical specification as Panel A but includes an additional covariate the price change/post-1997/over age 74 interaction term. (c) Are the results in Table 5 consistent with the model s predictions? Explain. Also, briefly discuss alternative explanations for the estimates in Table 5. The authors also present empirical evidence that a doctor s investment in an MRI machine is related to Medicare reimbursement rates (price change) in an manner consistent with the theoretical model.

5 QUESTION 5 Kostol and Mogstad coauthored a paper entitled How Financial Incentives Induce Disability Insurance Recipients to Return to Work that recently appeared in the American Economic Review (AER). In this paper, these economists considered the incentives provided by a Disability Insurance (DI) Program initiated in Norway. Disability Insurance is a form of insurance that insures the beneficiary's earned income against the risk that a disability creates a barrier for a worker to complete the core functions of their work (due to a physical or mental impairment). Disability Insurance programs have long been criticized for apparent work disincentives. The Kostol and Mogstad paper analyzes the consequences of providing financial incentives to DI recipients to encourage them to return to work. In January 2005, the Norwegian government introduced such a program: the benefits of DI recipients would be reduced by approximately $0.6 for every $1 in earnings that they accumulated. However, only recipients who had been awarded DI before January 1, 2004 were eligible for the return-to-work program. Therefore, the cutoff date for eligibility was set retroactively. The paper uses this eligibility date in a sharp RD design where assignment to the return-to-work program is a deterministic function of the assignment variable, the date of the DI award (X): only recipients who had been awarded DI before January 1 of 2004 were eligible for the return-to-work program. As Kostol and Mogstad state when describing this regression discontinuity The RD design uses separate regressions on each side of this cutoff date (c). The regression model for the treatment group is applied to the left side of the cutoff date (X < c) (1) Y = α l + f l (c X) + ε l, whereas the regression model for the control group is applied to the right side of the cutoff date (X > c) (2) Y = α r + f r (X c) + ε r, where f r and f l are unknown functional forms. The RD estimate of the return-to-work program is then given by the difference between the estimated regression intercepts on the two sides of the cutoff date (3) RD = l r. To implement the RD design, Kostol and Mogstad specify multiple functional forms for f r and f l. The paper uses this sharp regression discontinuity design to empirical compare the behavior of the treatment group and the control group over the period Using administrative data collected by the Norwegian government, Kostol and Mogstad find that DI recipients aged who are eligible for the return-to-work program (those awarded DI before January 1, 2004) are more likely to participate in the labor market and have higher average earnings from than DI recipients aged in the control group. Among DI recipients aged 50 61, there is no evidence of any impact of the program. (a) Why is it important for identification to have the cutoff date for eligibility in the return-to-work program set retroactively? What concerns would arise if a cutoff date was set but not retroactively? (b) Do you have any concerns with the regression discontinuity design described above? Describe two identification concerns with using this empirical strategy to estimate the effect of the Norwegian return-to-work program. (c) Why might the program have a differential effect in terms of labor market participation and average earnings for recipients aged compared to recipients aged 50-61? Discuss in the context of a single crossing property.