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Review Mid-term #2
Econ 344
Moral hazard
Adverse selection
Actuarially fair insurance premium
Pay as you go funding basis for Social security
Fully funded social security system
Asymmetric information
Risk premium
Risk aversion
Actuarially fair return on insurance
Wealth substitution effect in social security savings
In-kind transfers
Earned income tax credit
Labor leisure model
Calculating expected utility value of insurance(see example
Part 4
Tax shifting
Tax incidence
Regressive vs. progressive tax rates
Partial equilibrium model
General equilibrium model
Excess burden (dead weight loss)
Ramsey rule
Inverse elasticity rule
Vertical equity
Horizontal equity
Tax avoidance tax evasion
Lump sum tax, unit tax, ad valorem tax
Oct. 25, 2007
2.VinDiesel drives cars and is thinking about insurance. He has a 5% probability of an
accident that will cost him $10,000.
His utility ftn is U(I)=√I and his income is $40k
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a. What is the expected income
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c. What is the actuarially fair premium for insurance
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d. What is utility of full insurance
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e. What is utility of 50% partial insurance?
b. what is his expected utility of not buying ins.
• f. Should he insure?
1.VinDiesel drives cars and is thinking about insurance. He has a 5% probability of an
accident that will cost him $10,000.
His utility ftn is U(I)=√I and his income is $40k
• a. EU=p*U(inc if hurt) + (1-p)U(inc.not hurt)
(Expected utility is weighted average of utilities of incomes in different future states—
weights are probabilities) .05*√(40000-10000) + .95* √(40000) =198.66
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b. .05*10000 + .95*0=$500
(actuarially fair premium is the premium that allows insurance company to breakeven)
c. .05* √(40000-500) +.95(40000-500)=198.75
d..05* √(30000-250+5000) +.95* √(40000-250) =198.72
e. yes, full
2. Refer to Figure 14.2 in your textbook. Suppose the original before-tax demand curve is Xd = 49 –
P/2. Suppose further that supply is X = P/2 – 1. Now suppose a $3 unit tax is imposed on consumers.
(A) What is the before-tax equilibrium price and quantity?
(B) What is the after-tax equilibrium quantity?
(C) How much tax revenue is raised?
Ans:
(A) Setting before-tax demand equal to supply gives X* = 24, with P* = $50.
(B) The after tax analysis: new equilibrium price after a $3 consumer tax: 49-P/2=S98-(P+3)=P-2;
98-3-P=P-2; P=48.5; Substitute this price into the supply ftn: X=48.5/2-1 X=23.25
or a more tedious approach of first solving P in terms of X:
X=49-P/22X=98-P; $3 tax on consumers 2X=98-(P+3)2X=95-P
The after-tax demand curve is now P = 95 – 2X. (We then plug this expression for P into the supply
curve and solve for X
Setting the after-tax demand curve equal to supply gives X* = 23 ¼. :( S=D: 2X=P-22X=(95-2X)-2
4X=93; X=23.25
(C) Tax revenue is the after-tax equilibrium quantity multiplied by the tax rate. Therefore, 3(23 ¼) =
69 ¾.
D. From Question 2 above, calculate the economic incidence incurred by producers and the economic
incidence incurred by consumers.
Ans: The after-tax consumer price is now $51.5. The after-tax producer price is now $48.5. The
before-tax price was $50. The economic incidence for consumers is 1.5(23.25) = $34.875. For
producers, it is 1.5(23.25) = $34.875.
3. Suppose that the demand for medical services can be characterized by the equation X = 500 – P/3.
Suppose further that the supply of health services can be characterized by the equation X = P – 100.
(A) What is the equilibrium quantity and price in the market for health services?
(B) In an effort to make health services more affordable, the government restricts the price of health
services to be no greater than $250. What will happen to the quantity of health services in the market?
Ans: (A) Set 1,500 – 3X = 100 + X to get that X* = 350 and P* = $450.
(B) At a price of $250, a shortage of health services will occur. X* will now be only 150.
4. Suppose the government introduces an income maintenance program for low-income
people that offers a basic grant of $200 per month. For any earnings, the grant is
reduced dollar for dollar (100% tax)
a. Assume Lois can earn $10 per hour and has no other income. Sketch her monthly
budget constraint with and without the program in effect. Carefully label axes, intercepts
and all kink points. At how many hours of work is the grant reduced to 0?
b. According to economic theory, what would happen to Lois’ hour worked and total
income if the government instituted this program?
c. Suppose the government decides to keep the grant of $200 but to lower the implicit tax
rate to 50% (Lois can keep $.50 of each dollar she earns) Draw the new budget
constraint.
d. Which program provides more incentive for Lois to enter the work force?
--the 50% tax plan
(See diagram)
5. A voucher for housing is an example of an in-kind transfer. An individual with a
monthly income of $800 receives a housing voucher for $200.
a. Draw this person’s initial budget constraint for housing and all other goods.
b. Illustrate how the housing voucher affects his budget constraint.
c. Illustrate the cases where the voucher yields lower utility than a cash transfer and the
case where utility is the same as a cash transfer.
(see diagram below)