20. Two hospitals want to merge. The price elasticity of demand is -0.20, and ea
ID: 1197921 • Letter: 2
Question
20. Two hospitals want to merge. The price elasticity of demand is -0.20, and each clinic has fixed costs of $100,000. One clinic has a volume of 9,200, marginal costs of $70, and a market share of 3 percent. The other clinic has a volume of 15,800, marginal costs of $80, and a market share of 6 percent. The merged firm would have a volume of 18,000, fixed costs of $80,000, marginal costs of $60, and a market share of 6 percent. (5 pts)
What are the total costs, revenues, and profits for each clinic and the merged firm?.
How does the merger affect markups and profits?
21.Explain your understanding of this notion: “Misunderstanding the dangers of risky behavior and the likelihood of those dangers is a major problem for younger people” as it relates to aversion. What happens as we get older? (3 pts).
Explanation / Answer
Answer 21
The simplest way to depart from separable preferences, in order to introduce interactions between consumptions at different periods of the life cycle, is to perform a non linear transformation f(.) of an intertemporal sum of instantaneous utilities. This gives the following specification for the (vonNeumann Morgenstern) utility of a consumption profile2 C = (C1,...,CN ) : U(C) = f N i=1 iu(Ci) , (1) where 1,...,N are positive discount factors that sum to one3, and u(.) (with u > 0, u” < 0) is the instantaneous utility function4. When f is linear, U is intertemporally separable. However when f is strictly concave (respectively convex), goods become specific substitutes U CiCj = iju (Ci)u (Cj )f” N k=1 ku(Ck) , (2) which has the same sign as f”. However f does not affect ordinal preferences, and thus consumption behavior (in a deterministic context) is still given by : (P1) maxN i=1 iu(Ci) N i=1 piCi = W. The indirect utility function is denoted6 v(W) for the separable preferences specified in P1, and V (W) = f(v(W)) for the utility function U. Notice that the nonlinear transformation f modifies risk aversion : W V ”(W) V (V ) = W v”(W) v (W) W v (W) f”(v) f (v) . (3) The risk aversion index is thus increased when f” < 0 (f concave) and decreased when f” > 0 (f convex). Our focus here is on the variations of risk aversion along the life cycle. This is why we define the (relative) risk aversion index Rn of an individual of age n, along a consumption path C = (C 1 ,...,C N ).
Thus, Age is a demographic characteristic that has long been hypothesized to affect an individual’s degree of risk aversion. The lifecycle risk aversion hypothesis predicts that risk aversion will increase over the lifecycle – the older a person gets, the more risk averse they become. The underlying explanation for this lies in the relative importance of labor income and asset income over the lifecycle. It is believed that the further a person is from retirement the more risk they are willing to accept in their investments since the number of paychecks they expect to get is large and labor income can offset any adverse investment outcomes. The closer to retirement a person gets, the fewer paychecks they have to cover any such adverse investment outcomes.
Several studies that have considered the effects of age on risk aversion claim to test the lifecycle risk aversion hypothesis but do not. Most studies have used cross sectional rather than longitudinal data and therefore can only draw inferences about the effects of age across a cross section of the population – at any given time younger people may be more or less risk averse than older people. For example, Morin and Suarez [1983] conclude that risk aversion increases with age such that older people are more risk averse than younger people. Palsson [1996] finds the same results. Riley and Chow [1992] find that risk aversion decreases with age up to 65 years, then increases significantly. Bellante and Saba [1986] attempt to distinguish between the effects of human capital and age on risk aversion and find evidence of increasing relative risk aversion with human capital but decreasing relative risk aversion with age. Although they interpret their results as evidence of a pure lifecycle effect of age that is independent of the human capital effect, the cross sectional nature of their study cautions against such a conclusion.
A rare study using time series data, Bakshi and Chen [1994] find evidence to support the lifecycle risk aversion hypothesis. Focusing on the effects of demographic changes on capital markets, they find an increase in the risk premium associated with an increase in the average age of investors.
The effects of age on risk aversion are further complicated by the possibility of cohort effects. There has been some suggestion that young people today may be less risk averse than young people a decade ago, for example. A study by Brown [1990] examines the effect of the distribution of wealth across age cohorts on security prices taking into account the non-marketability of human capital earnings. He finds that middle age investors were less risk averse than young investors and that older investors were more risk averse than middle age investors.
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