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You are a member of a team of economists working for the Highway Safety Division of the Ministry of Transportation in a Latin American country. Your primary objective in your work is to minimize the number of highway deaths.1 The total annual budget for highway safety is 10 million pesos. You have two means at your disposal to prevent highway deaths: the construction of guard-rails and the repairing of road surfaces. On average, the cost of guard-rails is 20 thousand pesos per mile. On average, the cost of road surface repairing is 10 thousand pesos per mile. 1. Given this information, construct a graph of all the different combinations of miles of guard-rail construction and miles of road surface repair you could achieve per year. In this graph, place road surface repair on the horizontal axis. 2. What is the maximum number of miles of guard-rail construction you could achieve per year? What is the maximum number of miles of road surface repair you could achieve per year? 3. What is the opportunity cost of road surface repair in terms of the number of miles of guard-rail construction forgone? What is the opportunity cost of guard-rail construction in terms of the number of miles of road surface repair forgone? What is the mathematical relationship between these two opportunity costs? 4. The Highway Safety Division has been collecting data for a number of years on the effectiveness of guard-rails and road surface repairs on lives saved. These data indicate that on average: 2 One mile of guard-rail construction saves 0.2 lives per year. One mile of road surface repair saves 0.1 lives per year. Pick four combinations of guard-rail construction and road surface repair on you graph from question 1, including the two endpoints. Calculate the number of lives you would save on average for each of these budget allocations. Does it matter how you allocate your budget between guard-rail construction and road surface repair? 1 Latin America has the highest rate of road fatalities in the world. 2 Clearly, there is no such thing as factions of a life, but safety policy is often conducted in terms of statistical lives. 2 5. Now suppose that, in contrast to question 4, your data indicate that: One mile of guard-rail construction saves 0.1 lives per year. One mile of road surface repair saves 0.1 lives per year. Use the same four combinations of guard-rail construction and road surface repair on your graph as you did in question 4. Calculate the number of lives you would save on average for each of these budget allocations. Does it matter how you allocate your budget in this new case? 6. Suppose your annual budge falls to 8 million pesos. Draw a new graph of all the different combinations of guard-rail construction and road surface repair you could administer. 7. In question 6, what is the new opportunity cost of road surface repair in term of the number of miles of guard-rail construction forgone? What is the opportunity cost of guard-rail construction in terms of the number of miles of road surface repair forgone? 8. Suppose your annual budget remains at 10 million pesos, but the cost of road surface repair rises to 20 thousand pesos per mile. Draw a new graph of all the different combinations of guard-rail construction and road surface repair you could administer. 9. In question 8, what is the new opportunity cost of road surface repair in term of the number of miles of guard-rail construction forgone? What is the opportunity cost of guard-rail construction in terms of the number of miles of road surface repair forgone? 10. Do changes in your budget affect opportunity costs? Do changes in the costs of safety strategies affect opportunity costs?

ITRN 504- Microeconomics and Trade
Problem Set #1
Resource Scarcity and Linear Equations
You are a member of a team of economists working for the Highway Safety Division of
the Ministry of Transportation in a Latin American country. Your primary objective in
your work is to minimize the number of highway deaths.1 The total annual budget for
highway safety is 10 million pesos. You have two means at your disposal to prevent
highway deaths: the construction of guard-rails and the repairing of road surfaces. On
average, the cost of guard-rails is 20 thousand pesos per mile. On average, the cost of
road surface repairing is 10 thousand pesos per mile.
1. Given this information, construct a graph of all the different combinations of miles of
guard-rail construction and miles of road surface repair you could achieve per year. In
this graph, place road surface repair on the horizontal axis.
2. What is the maximum number of miles of guard-rail construction you could achieve
per year? What is the maximum number of miles of road surface repair you could
achieve per year?
3. What is the opportunity cost of road surface repair in terms of the number of miles of
guard-rail construction forgone? What is the opportunity cost of guard-rail
construction in terms of the number of miles of road surface repair forgone? What is
the mathematical relationship between these two opportunity costs?
4. The Highway Safety Division has been collecting data for a number of years on the
effectiveness of guard-rails and road surface repairs on lives saved. These data
indicate that on average:2
One mile of guard-rail construction saves 0.2 lives per year.
One mile of road surface repair saves 0.1 lives per year.
Pick four combinations of guard-rail construction and road surface repair on you
graph from question 1, including the two endpoints. Calculate the number of lives you
would save on average for each of these budget allocations. Does it matter how you
allocate your budget between guard-rail construction and road surface repair?
1
Latin America has the highest rate of road fatalities in the world.
Clearly, there is no such thing as factions of a life, but safety policy is often conducted in terms
of statistical lives.
2
1
5. Now suppose that, in contrast to question 4, your data indicate that:
One mile of guard-rail construction saves 0.1 lives per year.
One mile of road surface repair saves 0.1 lives per year.
Use the same four combinations of guard-rail construction and road surface repair on
your graph as you did in question 4. Calculate the number of lives you would save on
average for each of these budget allocations. Does it matter how you allocate your
budget in this new case?
6. Suppose your annual budge falls to 8 million pesos. Draw a new graph of all the
different combinations of guard-rail construction and road surface repair you could
administer.
7. In question 6, what is the new opportunity cost of road surface repair in term of the
number of miles of guard-rail construction forgone? What is the opportunity cost of
guard-rail construction in terms of the number of miles of road surface repair
forgone?
8. Suppose your annual budget remains at 10 million pesos, but the cost of road surface
repair rises to 20 thousand pesos per mile. Draw a new graph of all the different
combinations of guard-rail construction and road surface repair you could administer.
9. In question 8, what is the new opportunity cost of road surface repair in term of the
number of miles of guard-rail construction forgone? What is the opportunity cost of
guard-rail construction in terms of the number of miles of road surface repair
forgone?
10. Do changes in your budget affect opportunity costs? Do changes in the costs of safety
strategies affect opportunity costs?
2
...

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