Economics -Q66

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1. (26 pts) Consider the market for honey, which is in perfect competition. All firms have the same MC curve; it always costs $5 to make each jar of honey. The demand for honey is given by
 
D: P = 20 – 0.05Q
 
Each jar of honey generates $5 in positive externalities because honey bees pollinate nearby plants and crops, which we will model as increasing the social marginal benefit. For now, we will consider only what happens in the market equilibrium (not the market optimum).
 

a) (2 pts) What are the market equilibrium price and quantity?

b) (2 pts) In equilibrium, how much externality is created?
 
c) (2 pts) In equilibrium, what is the sum of CS and PS?

d) (2 pts) In equilibrium, how much TS is created?
 
e) (2 pts) Suppose we forcibly required five more consumers to buy at the market price, moving the total market quantity from Qmkt to Q’ = Qmkt + 5. How much consumer surplus do these additional consumers lose from being forced to participate in this market? (Assume these coerced consumers are the next people who would buy, so their WTP are given by the demand curve from quantityQmkt to Q’.)

f) (2 pts) How much externality is created, total, at Q’?
 
g) (2 pts) How much TS is there at Q’?

h) (4 pts) Now suppose the government institutes a subsidy of $7 per honey jar, paid to the suppliers. Using the same methods as the tax problems earlier in the term, solve for the post-tax equilibrium quantity, price received by suppliers, and market price.
 
i) (4 pts) What are the post-subsidy CS, PS, G, and X?

j) (2 pts) What is the post-subsidy DWL in the honey market?

 
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2. (16 pts) The market for SUVs is in perfect competition. Every time an SUV is driven, it creates pollution, congestion, and potential hazards to other drivers. Model this as a negative externality on consumption (so apply the externality to the demand curve).
 
Draw three graphs of this market on the same page, stacked vertically, NOT side-by-side.
a. (4 pts.) In the top graph, draw the normal supply and demand curves, indicate the market equilibrium price and quantity, and indicate the CS and PS regions.
 
b. (6 pts.) In the middle graph, draw the SMC and SMB curves, indicate the efficient quantity, and shade in the TS that would be realized at the efficient point. Draw a vertical line to indicate where the market quantity is (just taking the location from part a; do NOT represent the private curves on this graph). Indicate the DWL triangle.
 
c. (6 pts.) In the bottom graph, draw the PMC, PMB, SMC, and SMB curves. (Note: two of these curves are the same line.) Indicate the market quantity and price, the CS, the PS, the X region, and the DWL.
 
3. (30 pts) The Duke of SUNYia is considering a law mandating that everyone in the realm purchase health insurance (similar to the laws in the far-off mythical place called “Massachusetts”). The population of SUNYia suffers from exactly one potential malady, heart attacks. If a resident suffers a heart attack, then the hospital treatment will cost $130,000. If a resident buys insurance, she pays the premium, and then the insurer pays for ALL the expenses of the heart attack.
 
Actuarial tables show that 1,300 of the 8,000 residents of SUNYia face a 12% chance of a heart attack (the high-risk group), that 3,100 of the 8,000 residents face a 2% chance (the medium-risk group), and that the remaining 3,600 consumers face a 1% chance (the low-risk group). Each individual consumer’s Willingness-to-Pay for health insurance is TWICE the insurance company’s expected payout for that consumer. Each consumer knows her own type (so the WTP for a low-risk consumer is less than the WTP of a high-risk consumer). The insurer does NOT observe an individual’s type. The insurer has to charge the same price to everyone (community rating) and has NO access to any sort of screening mechanism.
 
We’ll assume that the insurance company follows a very simple rule for setting its premium (the price of the insurance). The premium is set at 130% of the insurance company’s average expected payout for the consumers the insurance company expects to buy the insurance. (In equilibrium, the insurer correctly judges which types will buy the insurance.) The insurance company cannot price discriminate or exclude anyone willing to buy their insurance at the stated price.
 
a. (6 pts) What is the insurance company’s expected payout if it insures a low-risk person? A medium-risk person? A high-risk person? What is each type’s WTP for insurance?
b. (4 pts) What is the insurance company’s expected per capita payout if it insures the entire population (assuming that everyone actually bought the insurance at the required price)? What premium would it set?
 
c. (3 pts) What is the insurance company’s expected per capita payout if it insures just the high-risk and medium-risk consumers, but not the low-risk consumers (assuming that those types actually bought the insurance at the required price)? What premium would it set?

d. (2 pts) If the insurer priced insurance on the assumption that everyone would buy it, who would actually buy it? Would the insurer make positive profits, zero profits, or negative profits?
 
e. (2 pts) If the insurer priced insurance on the assumption that only the high risk and medium risk types would buy it, who would actually buy it? Would the insurer make positive profits, zero profits, or negative profits?

f. (5 pts) In equilibrium, what price does a profit-maximizing insurer set (assuming it follows the given pricing rule)? What is the total CS for each type and the expected firm profits ? What is the total social surplus?
 
g. (6 pts) What would be the total CS for each type and the expected firm profits if the Duke passes a law requiring everyone to buy insurance? What is the total social surplus? Assume the insurer continues to price at the same formula as before (a fixed multiple of the expected cost of insuring the people expected to buy the insurance).
 
4. (8 pts) In Marron and Toder (2014)
 
a. (4 pts.) Describe how the issue of ‘standing’ affects assessment of the social marginal cost of carbon.

b. (4 pts.) What is one problem with using selective subsidies of renewables, instead of carbon taxes?

 
5. (20 pts) Suppose a project will provide the following costs and benefits.
 
Year 0: cost $300 million
Year 1: cost $200 million
Year 2: cost $150 million
Year 3: cost $100 million, benefit $140 million
Year 4: benefit $250 million
Year 5 to Year infinite: benefit $40 million
 
a. (10 pts) Write out the formula to compute the PDV of the project as a function of the interest rate, r. This should be something that I could use to calculate this with just a simple calculator; I do NOT want to see what you would enter into a fancy financial calculator. You may, of course, use exponents.
 
Hint: costs are just negative benefits. So year 0 has a value of -300.

For example, an answer might look like: PDV = 20/(1+r)2+ 10/r * 1/(1+r)
 
b. (10 pts) Create a line graph (what Excel calls an X Y scatter, but connect the points with a smooth curve) showing the PDV on the Y axis and the interest rate on the X axis, for the r values .01, .02, .03, .05, .07, .1, .12, and .15. You should see that the choice of interest rate makes a huge difference.
 
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