Answers to Numerical Questions in
Public Economics
Chapters 1 to 19
Peter Abelson
Chapter 3
Competitive Markets: Efficiency and Welfare
5
Equilibrium is achieved when demand equals supply: Q
S
= 20 + 4P = 65 – 5P
= Q
D
. Hence 9P = 45; P = $5 and Q = 40. This point is Pareto efficient.
Suppose that the quantity supplied were 50 units. Firms would require a price
of $7.5. However, consumers would require a price of only $3 to absorb this
supply.
At this level of output, some firms would lose money and be worse
off.
Only at equilibrium would the marginal benefit derived by consumers
(represented by the demand curve) equal the marginal cost of supply
(represented by the supply curve in a competitive industry).
Chapter 4
Market Failures, Equity and Government
4
(i) A monopolist produces at the point where marginal revenue equals
marginal cost ($6 per unit). The firm will select P = $15, sell 10 units and
receive marginal revenue of $6.
(ii) Under perfect competition, P = MC = $6. Q = 19 units.
(iii) DWL = 0.5 (1910) (156) = $40.5
See also Excel sheet
5
(i) In a competitive market, the price of a vaccination would be $60 and there
would be 400,000 vaccination per annum
(ii) Given the positive externality, the price of a vaccination should fall to $10
($60  $50) and there would be 900,000 vaccinations per annum.
Chapter 6
Valuing Individual Preferences
8
The budget constraint: p
1
b+p
2
c = M
And the utility function is S = min[b/2,c]
The solution will be at the corner where b/2=c, that is b=2c
Putting this in the budget equation
2p
1
c+p
2
c=M
or c(2p
1
+p
2
)=M
thus c=M/(2p
1
+p
2
)
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This is the demand function of cheese.
The demand for sandwich will be
equal to the demand for cheese.
Thus D
S
= M/(2p
1
+p
2
)
9
Given p
1
t + p
2
s =200.
Initially prices (p
1
, p
2
) are (1, 2) and then becomes (1.5,
2).
To find out initial consumption basket: t+2s = 200 and from the utility
function consumption will be at the corner where t = 2s.
Solving t = 100 and s
= 50.
After the price change the budget line is 1.5t + 2s = 200.
Solving this for the
given utility function t = 80 and s = 40
To find EV we are to find out the income that person needs at the original
price to reach the new consumption bundle: that is 80×1+40×2 = 160.
So the
maximum amount the person will pay to avoid price increase (that is EV) is
200160 = 40.
To find CV we need to find out the income the person needs at the new prices
to reach the original consumption bundle: that is 100×1.5+50×2 = 250.
Thus
in order to be as well off as the individual was with the original bundle, his/her
original income would have to rise by: 250200 = 50.
That is the CV.
Graphically to get the EV draw compensated budget line (parallel to the old
budget line, downwards) tangent to the new indifference curve which will be
at the corner.
The vertical distance between these two budget lines is (10080)
×2=40 = EV
Chapter 7
Social Welfare and Economic Evaluation
3
With
W
i
, equal weight is attached to a unit change in the utility of Anne and
Bruce. With
W
2
twice as much weight is attached to a change in Anne’s utility.
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 Three '10
 PeterAbelson
 Economics, Supply And Demand, DWL

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