Problem Set # 1
1) As part of an irrigation project, you need to install several thousand feet of irrigation
pipe in ditches dug in land you are improving. You have $2,000 to spend and you have to
both hire labor and rent shovels to do the job (you already have the pipe). You are given
the following information.
- A ditch digger is paid a wage of $60 a day. A ditch digger can dig 300 feet
of ditch in a day.
- A shovel rents for $5.00 per day.
- A pipe layer is paid a wage of $70 per day. A pipe layer can lay 600 feet
of pipe in a day.
- Each ditch digger needs to work with one shovel but pipe layers bring
their own tools.
a) Construct an efficient allocation of the $2,000 - that is, an allocation that allows you to
maximize the amount of pipe you can lay with $2,000. Explain your reasoning.
Answer: The key idea is that you don’t want to purchase resources that cannot be used.
– You don’t want ditch diggers standing around because they don’t have shovels.
This means you have to rent one shovel for every ditch digger you hire.
- Similarly, you don’t want pipe layers standing around because there are no
ditches into which they can lay pipe. This means you have to hire one pipe layer
for every two ditch diggers (who, together, can dig 600 feet of ditch in a day – the
same amount of ditch a pipe layer can fill).
Putting these together, an efficient “unit of input” is two ditch diggers, two
shovels and one pipe layer for a total cost of $65 + $65 +$70 or $200. So an
efficient allocation of $2,000 would be 10 of these “units” – i.e. 20 ditch diggers,
20 shovels and 10 pipe layers.
b) Construct one inefficient allocation of the $2,000 and explain why it is inefficient.
Answer: There are an infinite number of possibilities. The simplest is to hire something
like 30 ditch diggers ($1800), two pipe layers ($140) and 12 shovels ($60). This
combination would allow a lot of ditch diggers to stand idle because they had no shovels.
, It would also mean you ended up with empty ditch because there wouldn’t be enough
pipe layers to fill the ditches dug by the 12 ditch diggers who could use the shovels.
2) Nicholson and Snyder, 11’th edition, pp. 22, Problem 1.1 (for people using the
10’th edition, see the end of this problem set)
3) In two separate graphs, illustrate the following changes in the American consumer
market for coffee.
- In 2011, excessive rain and cold weather destroy 10 percent of the
world’s coffee crop. The coffee consumption of the typical American
household falls.
- In 2011, the New England Journal of Medicine publishes a study
showing that drinking more than 1 cup of coffee a day substantially
increases the likelihood of men and women of all ages going bald and
developing very wrinkled skin. The coffee consumption of the typical
American household falls.
There are various dimensions to graphs like these: whether the change in the market
equilibrium is caused by a shift in the supply curve or the demand curve, whether the
good’s price goes up or down, etc. We know that in one dimension – the quantity of the
coffee being purchased – the two graphs are similar: The amount coffee purchased falls in
both cases. Briefly explain how and why the graphs differ or are similar in their other
dimensions.
1) As part of an irrigation project, you need to install several thousand feet of irrigation
pipe in ditches dug in land you are improving. You have $2,000 to spend and you have to
both hire labor and rent shovels to do the job (you already have the pipe). You are given
the following information.
- A ditch digger is paid a wage of $60 a day. A ditch digger can dig 300 feet
of ditch in a day.
- A shovel rents for $5.00 per day.
- A pipe layer is paid a wage of $70 per day. A pipe layer can lay 600 feet
of pipe in a day.
- Each ditch digger needs to work with one shovel but pipe layers bring
their own tools.
a) Construct an efficient allocation of the $2,000 - that is, an allocation that allows you to
maximize the amount of pipe you can lay with $2,000. Explain your reasoning.
Answer: The key idea is that you don’t want to purchase resources that cannot be used.
– You don’t want ditch diggers standing around because they don’t have shovels.
This means you have to rent one shovel for every ditch digger you hire.
- Similarly, you don’t want pipe layers standing around because there are no
ditches into which they can lay pipe. This means you have to hire one pipe layer
for every two ditch diggers (who, together, can dig 600 feet of ditch in a day – the
same amount of ditch a pipe layer can fill).
Putting these together, an efficient “unit of input” is two ditch diggers, two
shovels and one pipe layer for a total cost of $65 + $65 +$70 or $200. So an
efficient allocation of $2,000 would be 10 of these “units” – i.e. 20 ditch diggers,
20 shovels and 10 pipe layers.
b) Construct one inefficient allocation of the $2,000 and explain why it is inefficient.
Answer: There are an infinite number of possibilities. The simplest is to hire something
like 30 ditch diggers ($1800), two pipe layers ($140) and 12 shovels ($60). This
combination would allow a lot of ditch diggers to stand idle because they had no shovels.
, It would also mean you ended up with empty ditch because there wouldn’t be enough
pipe layers to fill the ditches dug by the 12 ditch diggers who could use the shovels.
2) Nicholson and Snyder, 11’th edition, pp. 22, Problem 1.1 (for people using the
10’th edition, see the end of this problem set)
3) In two separate graphs, illustrate the following changes in the American consumer
market for coffee.
- In 2011, excessive rain and cold weather destroy 10 percent of the
world’s coffee crop. The coffee consumption of the typical American
household falls.
- In 2011, the New England Journal of Medicine publishes a study
showing that drinking more than 1 cup of coffee a day substantially
increases the likelihood of men and women of all ages going bald and
developing very wrinkled skin. The coffee consumption of the typical
American household falls.
There are various dimensions to graphs like these: whether the change in the market
equilibrium is caused by a shift in the supply curve or the demand curve, whether the
good’s price goes up or down, etc. We know that in one dimension – the quantity of the
coffee being purchased – the two graphs are similar: The amount coffee purchased falls in
both cases. Briefly explain how and why the graphs differ or are similar in their other
dimensions.
