What is maynards expected utility if he does not purchase

Question

Please provide your answers to questions in the form of a short essay. To prevent any misunderstanding, please note that a "short essay" answer:

 

a. consists of a series of complete sentences, in a reasonably logical order; and

 

b. provides a complete but concise explanation.

 

A short answer essay is notan outline, or a set of bullets, or a series of symbols or abbreviations with arrows.  A table, graph or equation may be integrated into an answer, but cannot be used as a substitute for written explanation

 

1. J. Wellington Wimpy eats 30 hamburgers and takes 30 Zocor (simvastatin) tablets every month.  His income is $150/month.  He pays $2 per hamburger and $3 per Zocor tablet.  The 30^th hamburger he eats increases his overall utility by 45 units, and the 30^th Zocor tablet he takes increases his utility by 20 units.

 

a. Does this combination of hamburgers and Zocor tablets maximize utility for Mr. Wimby?  Explain.

 

b. If not, what does Mr. Wimby need to do to increase his overall utility?  Explain.

 

c. At what point will he be unable to increase utility further?  Explain.

 

 

2. A dental clinic at a major academic health center noted that the fees they charged for dental care services generally were 15 to 20% lower than fees charged by private dentists in the community. [Most people in this community had no dental insurance and paid for dental care out of pocket.] The dental clinic decided to increase fees by about 15% (to just undercut the fees charged by private dentists by about 5%), assuming this would increase its patient care revenues by about 15%.  The clinic planned to use the additional revenue to offset losses from other clinic functions.  However, in the 12 months following the fee change, the clinic's patient care revenues declined substantially. In contrast, revenues for private dentists increased slightly over the same period. 

 

What might account for the decline in clinic revenues?  Elaborate.

 

1. In the theory of health insurance:  

 

Define "moral hazard"?  Why is moral hazard a potentially significant issue for health insurance markets?

1. Name two mechanisms in traditional insurance benefit design that are intended to ensure "risk sharing" between the insured and the insurer.  How might risk-sharing ameliorate the adverse effects of moral hazard? 
2. In "optimal" insurance design, the extent of risk sharing increases with the (magnitude of) the price elasticity of demand for the insured service.  Why?

Stickum, Inc. is a price-taking producer in the market for a diabetes testing supplies.  It can sell as many 100-count boxes of test strips at $3 per box as it wants to.  At present, Stickum employs 100 workers paid $50 per day in its sole production plant.  Unit costs of materials and other non-capital variable inputs used to produce the product are $0.10/box.

 

Stickum has determined that hiring another worker would increase output at the plant by 20 boxes per day.

1. Should Stickum hire the additional worker at $50 per day?  Explain. 
2. What if the additional worker couldn't be hired unless Stickum raised the wages it pays to all of its employees to $55/day per worker?  Explain

 

5. Maynard G. Krebs is considering the purchase of insurance.  Maynard faces an uncertain event where he receives wealth of $6000 with probability 0.75 and wealth of $1000 with probability 0.25.  His utility function with respect to wealth may be summarized as:

 

                U( $500)  =  200        U($1000) =  600

 

                 U($1500) =  900        U($2000) = 1080

 

                  U($2500) = 1210       U($3000) = 1320

 

U($4000) = 1415       U($5000) = 1500

 

 U($6000) = 1560       U($7000) = 1600

 

 

In other words, "U($500)  =  200" means that his utility of $500 of wealth with certainty is 200utils, U($1000) =  600 means his utility of $1000 of wealth with certainty is 600utils, his utility of $1500 of wealth with certainty is 900utils, and so on.      

 

a. What is Maynard's "expected utility" if he does not purchase insurance?  Explain.

 

b. If an insurance policy paid Maynard $5000 in the event he receives only $1000 of wealth, and zero otherwise, what would be the "actuarially fair premium" for such an insurance policy (assuming a large number of identical insureds)?  Explain.

 

c.  How much (at maximum) would Maynard be willing to pay for the insurance described above?  [In other words, at what total premium is he just as well-off without this particular insurance policy as with this insurance policy?]  Explain.