End of Chapter Exercises: Solutions
Chapter 7
1. A new publicly financed bridge is expected to reduce the cost of auto travel between
two areas by $1 per trip. This cost reduction to motorists consists of a reduction
in travel time, auto depreciation and petrol expenses totalling $1.50 per trip, less
the $0.50 bridge toll which the government will collect. Before the bridge was
built there were 1 million trips per year between the two areas. Once the bridge
is in operation it is estimated that there will be 1.5 million trips per year between
the two areas.
In terms of areas under the demand curve, what is the annual benefit of the
bridge:
(a) to motorists?
(b) to the government?
What other referent group benefits would need to be considered in a
social benefit/cost analysis?
Answer:
(a) $1.25 million
(b) $0.75 million
Other possible benefits include less congestion on other routes and lower levels of
air pollution.
2. (a) Briefly outline the model and principles you would use to conduct a benefitcost analysis of a highway project which will reduce the travel time between two
cities (include the appropriate diagram showing the demand for trips in your
explanation);
(b) Using the above framework, together with the following information and any
reasonable assumptions you need to make about the values of variables and the
timing of benefit flows, work out a rough estimate of the present value of the
benefit to users of an extension to the Pacific Motorway:
Current usage rate: 85,000 trips per day
Estimated future usage: 170,000 trips per day by 2020
Estimated time saved per trip at current usage rate: 10 minutes
(c) The capital cost of the project is reported to have a present value of $850
million. Using this value work out a rough estimate of the net present value of the
project;
(d) Briefly discuss the accuracy of your net present value estimate as an
measure of the net social benefit of the project, taking account of any significant
omissions from your analysis.
Answer:
(a) Draw a demand curve showing the original price and the new price of a trip
between the two cities. The annual benefit of the motorway is the area of
consumer surplus between the original and new prices.
(b) To estimate the annual benefit we need to estimate the difference between the
original and new prices of a trip and the amount of additional traffic generated by
the bridge. Time saved could be valued at 1/3 of the hourly wage – say $2.50 per
hour. While traffic doubles over the period to 2020 an average level of generated
traffic is 50% of the 2020 level – 42,500. Hence at a saving of $2.50 per trip the
annual consumer surplus gain is $2.50 times 85000 times 365 on existing trips
and $1.25 times 42500 times 365 on generated trips, giving a total of $77.6 plus
$19.4 million. Treating the benefit stream as a perpetuity the present value at a
real discount rate of 5% is $1940 million.
(c) The net present value is $(1940 – 850) = $1090 million.
(d) The estimate of the benefit stream was based on 42500 generated trips in
perpetuiy, whereas the actual stream of generated traffic may be different over
the period to 2020 and beyond. The time saved is based on today’s traffic flows
and is an underestimate of future time savings if traffic volumes continue to
grow. The calculation ignores the benefits of lower congestion on other routes,
lower exhaust emissions, fewer accidents etc.
3. The Headless Valley Water Control Board (HVWCB) will undertake an irrigation
project which will provide 10 million gallons of water annually to 100 wheat farms of
100 acres each. The HVWCB will charge $0.02 per gallon for the water, which will
be distributed equally among the 100 farms. It is estimated that:
(i)
(ii)
(iii)
land rent in Headless Valley will rise by $70 per acre per annum;
50 farm labourers will be attracted to work on Headless Valley farms, at
the market wage of $2000 per annum, from the vineyards of nearby
Sunshine Valley;
production of wheat on Headless Valley farms is subject to constant
returns to scale.
Assuming the referent group is the economy as a whole, work out the annual
social benefit of the irrigation project in terms of areas defined by demand and
supply curves for output or inputs. Explain your answer.
Answer:
Because of constant returns to scale, the value of the additional output in Headless
Valley is equal to the value of the additional income generated. Additional annual
incomes generated include: land $700000; labour $100000, HVWCB $200000. Hence
value of additional wheat production is $1000000. The labour diverted from Sunshine
Valley has an opportunity cost of $100000. Hence the annual social benefit is $900000.
4. Comment critically on the following approaches to measuring project benefits:
(a) an analyst measures the annual benefit of a bridge as the gain in consumer
surplus to bridge users plus the increase in annual rental value of properties
served by the bridge;
(b) an analyst measures the annual benefit of an irrigation project by the
increase in the value of food production, plus the increase in rental value of
the land served by the project. He takes the present value of the annual
benefit, calculated in this way, and adds the increase in capital value of the
land to obtain an estimate of the present value of the benefit.
Answer:
(a) If the demand for trips was based on the original level of rents this approach
involves double counting of benefits because the increase in annual rental value is a
transfer of benefit from users of the bridge to landlords.
(b) This approach involves triple counting. The annual benefit of the project is the value
of the extra food produced less the opportunity cost of any additional inputs. The
increase in land productivity is reflected in increased annual rental values, which, in
turn, result in higher capital values.
5. When a public project results in lowering the price of a particular commodity
(Commodity A) it impacts on the markets for complementary or substitute
commodities. Give some examples of this type of relationship. Choose one of the
examples (call it Commodity B) and use it to explain in detail the relevance of the
changes in the market for Commodity B for the benefit-cost analysis of the project
which results in a lower price for Commodity A.
Answer:
Consider question 4(a). Rental units in an area to be served by a bridge (Commodity
B) are complementary with the services of a bridge (Commodity A). Building the
bridge is equivalent to lowering the price of Commodity A, resulting in an increase in
demand for Commodity B. The benefit of the bridge is measured by an area of
consumer surplus under the demand curve for Commodity A. The shift in the demand
curve for Commodity B can be ignored in the benefit-cost analysis.
6.
Ellsworth spends all of his income on two goods, x and y. He always consumes
the same quantity of x as he does of y, Qx = Qy. Ellsworth’s current weekly
income is $150 and the price of x and the price of y are both $1 per unit.
Ellsworth's boss is thinking of sending him to New York where the price of x is
$1 and the price of y is $2. The boss offers no raise in pay, although he will pay
the moving costs. Ellsworth says that although he doesn't mind moving for its
own sake, and New York is just as pleasant as Boston, where he currently lives,
he is concerned about the higher price of good y in New York: he says that
having to move is as bad as a cut in weekly pay of $A. He also says he wouldn't
mind moving if when he moved he got a raise of $B per week. What are the
values of A and B?
a
b
c
d
e
A = 50 B = 50.
A = 75 B = 75.
A = 75 B = 100.
A = 50 B = 75.
None of the above.
Which is the compensating, and which the equivalent variation? Explain.
(Hint: see the Appendix to Chapter 7).
Answer:
(d). A is the equivalent variation and B is the compensating variation.