Suggested Answers, Problem Set 5 Health Economics

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1 Suggested Answers, Problem Set 5 Health Eonomis Bill Evans Spring The graph is at the end of the handout. Fluoridated water strengthens teeth and redues inidene of avities. As a result, at all prie levels, people are willing to onsumer fewer dental visits. Therefore, the demand urve shifts in from D1 to D2. 2. a. This is an aute ondition that needs treatment now and there are few substitutes, so elastiity of demand should be low (in absolute value). b. Mammographies are typially preventative servies. Use of this servie an be delayed over time. Higher.. Length of a hospital stay. The patient typially has little ontrol over this deision. Lower d. These are typially non-aute (eletive) proedures that are expensive. Higher. 3. Please see the graph at the end of the handout. For the first $295, out of poket spending equals total spending. After that amount and through $2700 in total spending, the oinsurane rate falls to 25% and at $2700 in total spending, out of poket spending is now $ ( )=$ From that point until total spending reahes $ , the onsumer is on their own and the oinsurane rate now equals 1. After that level, the oinsurane rate falls to 5%. Note that with $ in spending, out of poket spending is $ ( )+( )=$ The graph is at the end of the handout. The demand urve without insurane is line (ab). With insurane and a zero dollar opayment, the osts of eah presription is $0, so demand is a vertial line (b). When the opayment is inreased to $9/presription, then demand urve now shifts to line (bde). If P=$15 and onsumers did not have insurane, onsumers would demand 15=45-5Q or 6 units. With a zero oinsurane rate (insurane pays for everything), demand would be 9 units sine P=$0. With a $15 prie and a $9 opay, eah presription osts $9, so they would demand 9=45-5Q, or 36=5Q and q= The graph is at the end of the handout. Demand without insurane is P d =150-30Q and the graph is illustrated by line (ab). With a oinsurane rate of, the prie faed by onsumers is P d = P s where P s is the prie reeived by sellers. In this ase, =0.25 so the prie paid to sellers is P d = P s (0.25) = Q whih means that the prie transated in the market is now P = (150/0.25) - (30/.25)Q = Q. This demand urve is line (a). With a prie of $60/unit, onsumers would demand 60=150-30Q or 90=30Q or Q=3 units. With a 25% oinsurane rate, if prie is $60, onsumers only pay $15/visit, so the demand is really $60 = Q, or 540 = 120Q and Q=4.5. DWL is this ase is area (def). Note that in order to sell 4.5 units to people without insurane, prie would have to fall to P=150-30(4.5) = $15. Therefore, the area of (def) is (½)(60-15)(4.5-3) = The graph is at the end of the handout. The demand urve without insurane is line (ab). At a prie of zero, 20 units will be demanded and the maximum prie that would be paid is $100. Without insurane, it is easy to establish that the equilibrium prie would be $60 and the equilibrium demand would be 8. P s =P d and therefore 20+5Q=100-5Q so 80-10Q and Q=8. Plug Q=8 into supply and you get P=20+5Q = $60. With insurane, the demand urve would now be equal to (100-5Q)/0.2 = Q and is represented by line a. Equilibrium prie and quantity in this market is generated by setting supply equals to demand and therefore 20+5Q=500-25Q so 480=30Q and Q=16 and therefore P=20+5Q =100. The dead weight loss assoiated with insurane is area (def) whih an be alulated as ½ height times base. The height is 8 (16-8) and the base is the differene between points e and f. Point e is $100 and point f is 20. (In order to sell Q=16 without insurane, prie would have to fall to P=100-5(16) = 20). Therefore, the dead weight loss is (1/2)(8)(80)=320. 1

2 7. Purhase of these insurane poliies are an anomaly and annot be explained well with eonomi theory. Sine a large fration of elderly meet their dedutible levels eah year, there is little risk : although they experiene a loss, the loss is fairly ertain. Sine poliy pries are based on the atuarial risk and loading fators suh as administrative expenses, in many ases, people would be paying large administrative osts to over a risk that almost surely will happen. 8. The ar elastiity of demand is defined as e d [(Q 2 -Q 1 )/(Q 2 +Q 1 )]/[(P 2 -P 1 )/(P 2 +P 1 )]. In eah ase, the denominator in the elastiity is the same. For free are, P 1 =0 and with a 50% oinsurane rate, P 2 =.50 so [(P 2 -P 1 )/(P 2 +P 1 )] = 1. Dotor Visits $ Hospital Care $ all are Q Q (Q2-Q2)/(Q1+Q2) [(P 2 -P 1 )/(P 2 +P 1 )] Ar elastiity A) Those that had insurane prior to the law will not experiene a hange in the opayment rate so their demand will not hange. Those without insurane before January 1 will experiene a drop in opayments of from 100 to 25 perent, a prie drop of (0.25-1)/1 = or a 75% drop in prie. Given an elastiity of -0.4, this will inrease demand by -0.4(-0.75) = 0.3 or 30%. The new level of demand for these people will then be $29*(1.3)= $37.7 billion. B) Everyone without insurane will now be overed and therefore, the government will end up paying 75% of $37.7 billion. Everyone with overage from another soure will now reeive overage from the federal government so the government will end up paying 75% of $73 billion, for a grand total of (0.75)($ )= $ billion. C) Outlays for the program will be $83 - $22 = $61 billion. D) An estimate from the CBO an be found at and these numbers suggest that the outlays should be roughly $55 billion a year. Not bad for bak of the envelope!!! 10. There are two potential answers. One an say the expenditures are high for those with insurane beause of moral hazard. However, it is hard to explain a three-fold differene in spending due to moral hazard elastiities of demand are typially not that large. A more likely explanation is adverse seletion -- those with insurane are those most likely to need insurane so it is no surprise that this groups spends more on presription drugs than those without insurane. 11. a) In the real world, people with and without insurane are very different. Those with insurane tend to be from higher inome families, have more years of eduation and have otherwise better health. In some situations however, the purhase of insurane is due to adverse seletion: people who need the insurane the most are most likely to purhase. Therefore, is one were to ompare health spending aross groups of people, some with and without insurane, it is impossible to tell whether the observed differenes in use are due to insurane or due to some of these other unobserved fators. By randomly assigning insurane to hildren, we do not have to worry about the underlying reasons they have insurane. 2

3 b) The authors identified the impat of insurane on demand by looking at the differene in insurane use before and after the students had insurane. They attribute all of the inrease in use over time to insurane. However, this ould be a biased estimate. Suppose for example that medial are use is naturally inreasing over time, either beause of market effets (maybe pries are going up) or beause as hildren age they onsume more medial are. In either of these ases, we would have expeted use to inrease over time anyway so the author's are overstating the impat of insurane on demand. The authors ould eliminate this problem by adding a 'ontrol' group where they ollet data on a group of hildren who were not offered insurane. Their hange in use over time would represent what would have happened to use in the absene of the treatment program. 3

4 P Question 1 Market for Dental Visits P 1 Q 2 Q 1 D2 D1 Q Out of Poket Question 3 45 o line $4350 $ $295 $295 $2700 $ Total osts 1

5 P Question 4 $45 a e $15 $9 d b Q P Question 5 $600 $150 b $60 $15 a Q 2

6 Prie Question b e Supply 60 d f g a Quantity 3