Midterm 2ECO 321Fall 2016Prof. CabralInstructions: There are 5 questions in total, each with several parts. Write your answers in a bluebook to be handed in at the end of the test. Only calculators with no 3G or wifi technology are permitted to be used on this test. Good luck!1. [18 pts] Suppose the preferences of the individuals of the town of Economica can be represented by the following utility function: U(E,C)=ln(E)+3ln(C) where E represents the number of dollars spent on Education and C represents the number of dollars spent on private consumption goods. Economica has 20 million dollars of total resources.a. [4 pts] Draw Economica’s budget constraint and solve for the town’s optimal spending bundle (and label this bundle on your graph). For your graph , put E on thex-axis and C on the y-axis. Clearly label the intercepts, the coordinates of the kink points, and the slopes of the line segments in your graph.Now suppose the federal government is considering intervening and offering the town of Economica some sort of grant (funded by some external source). For each of the scenarios described below, (i) draw the new budget constraint for the town, and (ii) solve for the optimal allocation of spending and label this point on your graph. For your graph , put E on the x-axis and C on the y-axis. Clearly label the intercepts, the coordinates of the kink points, and the slopes of the line segments in your graph.b. [4 pts] Economica is offered a block grant of 4 million dollars.c. [4 pts] Economica is offered a conditional block grant of 4 million dollars to be applied toward education.d. [4 pts] Economica is offered a matching grant with every $2 spent by Economica matched by $1 from the federal government.e. [2 pts] Which of the interventions(b)-(d), increases educational spending the most? Which is the lowest cost to the government? The matching grant in part d is both the lowest cost to the government and increases educational spending the most.2. [24 pts] Suppose there are an equal number of two types of people in the world: Type A and Type B. The Type A people have a probability of sickness next year of 15% and the Type B peoplehave a probability of sickness next year of 2%. Annual income for all is $60,000. In the case of sickness, individuals lose $15,000 of income. Utility of all types can be described by the following function, U(c)=ln(2c), where consumption c is defined as income net losses. Suppose that insurance companies have no markups (there is a competitively priced insurance market). Also suppose that government regulation allows for full insurance to be sold but not partial insurance. NOTE: When answering the following parts, do not round numbers at intermediate steps in your calculations.Suppose that individuals know that which type they are, but insurers do not know (and cannot verify) individual types.a. [4 pts] What is the expected utility of individuals without insurance?Type A: 0.85*U(60,000)+0.15*U(45,000)=11.65209Type B: 0.98*U(60,000)+0.02*U(45,000)=11.68949b. [5 pts] Calculate the willingness-to-pay for insurance for Type B individuals.Strategy is to solve for p such that person is indifferent between insurance at premium p and no insurance. This is the maximum premium they are willing to pay for insurance.U(60,000-p)= 0.98*U(60,000)+0.02*U(45,000)This implies p=344.23So, WTP=$344.23 c. [7 pts] Is insurance sold in this world? If so, describe the equilibrium price, product and purchasers. Justify your answer.Insurers cannot tell people apart. If insurance is sold to both types, it must be sold at pooling actuarially fair price. The pooling AF price is equal to the insurer’s expected payout: (1/2)*0.15*15,000+ (1/2)*.02*15,000=$1275. We know however from part b that the maximum the Type B people will pay is $344.23. So, Type B will not buy a pooled policy. Therefore, insurance is sold in this world only to the Type A people for the type A AF premium of $2,250. We know that Type A is willing to buy this policy because his expected utility under this policy is greater than with no insurance.EU under this policy: U(60,000-2,250)=11.65703EU no insurance: see part ANow suppose that insurers can verify whether individuals are Type A or Type B, and can use this information in contracting (setting premiums).d. [5 pts] Is insurance sold in this world? If so, describe the equilibrium price, product and purchasers. Justify your answer.Yes. The insurer will sell Type A and Type B people different policies since it can verify and contract on the Types.-Type A will get full coverage for $2250 (their AF premium). We know they will accept it because their utility under this policy is greater than under no insurance (see parts a andc above).-Type B will get full coverage for $300 (their AF premium). We know they will go for this policy since it is less than their WTP that we calculated in part b. e. [3 pts] Based on your answer to the above parts, should the government outlaw pricing health risk information (Type A or B status) if the government cares only about efficiency?No. In this context, the government should not outlaw contracting on health informationbecause outlawing such pricing would introduce inefficient under-insurance due to adverse selection.3. [20 pts] Suppose an individual’s demand curve for doctor’s visits is given by P=800-60Q, where Qis the number of doctor visits per year and P is the price per visit. Suppose also that the social marginal cost of each doctor visit is $200. a. [5 pts] How many visits per year would be efficient? Set 800-60Q=200 and solve to find that q=10 is efficient.b. [5 pts] Suppose that the individual obtains insurance, with no deductible and 10% coinsurance rate. Suppose it is a competitive market, so that doctors charge the social marginal cost for a visit. How many visits will occur? Set 800-60Q =20 (=0.10*200). Solve to find q=13. c. [5 pts] What is the magnitude of the deadweight loss caused by this insurance policy? (13-10)*(200-20)/2=$270d. [5 pts] Depict this market in a graph. Put doctor visits on the x axis and price per visit on the y axis. Be sure to label the SMC, PMC, SMB and PMB curves as well was the x – and y-intercepts. Also label the x-y coordinates of the equilibriums you derived in parts (a) and (b) along with the deadweight loss calculated in part (c). [Note: the PMC reflects the price paid by consumers for a doctor’s visit.]4. [20 pts, 2.5 pts each]