CHAPTER 33: Production
TRUE/FALSE
1. If there are constant returns to scale in an industry, then in competitive equilibrium, profits in that
industry must necessarily be zero.
2. When there is production, a competitive equilibrium is not Pareto optimal unless there are increasing
returns to scale.
3. The marginal rate of transformation between two goods indicates the rate at which an efficient
economy would have to give up one good to obtain more of the other.
4. There are two people and two goods, person A has comparative advantage in the production of good 1
if and only if it takes person A less time to produce good 1 than it takes person B.
MULTIPLE CHOICE
1. A small company produces two goods, swords and plowshares. The company has 100 type alpha
employees and 100 type beta employees. If an alpha devotes all his time to producing swords, he can
make 2 swords per week. If he devotes all his time to producing plowshares, he can make 4
plowshares per week. A beta can produce either 1 plowshare per week or 1 sword per week. The
company wants to produce 218 swords and as many plowshares as it can. How many type betas should
it employ at making swords?
a.
100
b.
18
c.
90
d.
0
e.
None of the above.
2. A small company produces two goods, swords and plowshares. The company has 100 type alpha
employees and 100 type beta employees. If an alpha devotes all his time to producing swords, he can
make 4 swords per week. If he devotes all his time to producing plowshares, he can make 20
plowshares per week. A beta can produce either 1 plowshare per week or 1 sword per week. The
company wants to produce 413 swords and as many plowshares as it can. How many type betas should
it employ at making swords?
a.
80
b.
0
c.
100
d.
13
e.
None of the above.
3. A small company produces two goods, swords and plowshares. The company has 100 type alpha
employees and 100 type beta employees. If an alpha devotes all his time to producing swords, he can
make 3 swords per week. If he devotes all his time to producing plowshares, he can make 6
plowshares per week. A beta can produce either 1 plowshare per week or 1 sword per week. The
company wants to produce 324 swords and as many plowshares as it can. How many type betas should
it employ at making swords?
a.
0
b.
85
c.
24
d.
100
e.
None of the above.
4. Ernie and Burt both make pizzas for a living. Making a pizza consists of two tasks: making the crust
and applying toppings. Ernie can make crusts at the rate of 30 crusts per hour. He can apply toppings
at the rate of 15 toppings per hour. Burt can make crusts at the rate of 15 crusts per hour. He can apply
toppings at the rate of 30 toppings per hour. After years of operating separate, one-man shops, they
realize they can produce more efficiently by combining operations and dividing the tasks between
them. How many more pizzas per hour can they make if they work together and allocate tasks
efficiently than they made when they worked separately?
a.
5
b.
10
c.
14
d.
25
e.
8
5. Mandy is a master wood-carver and Jerry is her apprentice. They will each work the same number of
hours making toy cars. Each car requires 4 wheels and 1 body. Mandy makes wheels at the rate of 25
per hour and bodies at the rate of 10 per hour. Jerry makes wheels at the rate of 10 per hour and bodies
at the rate of 10 per hour. If they wish to maximize output, how many wheels should Jerry make per
hour?
a.
3
b.
2
c.
10
d.
6
e.
There is not enough information to determine the answer.
6. Amy Canvas is an artist who produces sketches and paintings. She can produce 12 sketches a week if
she spends all of her workday sketching. She can produce 3 paintings a week if she spends all of her
workdays painting. The rate at which she produces either sketches or paintings is independent of how
many she makes. She can divide her time in any way she wishes between sketching and painting. If
you draw her production possibilities frontier with sketches on the horizontal axis and paintings on the
vertical axis, the production possibilities frontier will be
a.
the outer two sides of a rectangle.
b.
a downward-sloping curve that gets steeper as you move to the left.
c.
a downward-sloping straight line.
d.
an upward-sloping straight line.
e.
an upward-sloping curve that gets steeper as you move to the left.
7. Last year a pestilential fungus ravaged the cocoa fields. The price of chocolate has risen abruptly to $1
per ounce. The government is considering emergency measures to aid suffering chocolate addicts. One
plan being considered is the Chocolate Relief Plan (CRP). This plan would set a price ceiling of $.80
per ounce on chocolate. This would cause a shortage, so the CRP will limit consumption to no more
than 10 ounces of chocolate per person per week. At $.80 per ounce, enough chocolate would be
produced for everyone to have 10 ounces. Jill buys less than 10 ounces per week at $1 per ounce but
would buy more than 10 ounces if the price dropped to $.80.
a.
Jill is definitely better off without the CRP.
b.
Jill is better off without the CRP if $1 is the competitive equilibrium price without the
CRP.
c.
Jill is better off with CRP only if the industry is monopolized and the price exceeds
marginal cost in the absence of the CRP.
d.
Jill is definitely better off with the CRP.
e.
None of the above.
8. Robinson Crusoe’s preferences over coconut consumption, C, and leisure, R, are represented by the
utility function U(C, R) = CR. There are 48 hours available for Robinson to allocate between labor and
leisure. If he works L hours, he will produce the square root of L of coconuts. He will choose to work
a.
8 hours.
b.
12 hours.
c.
16 hours.
d.
20 hours.
e.
24 hours.
9. Robinson Crusoe spends 4 hours a day catching fish and picking coconuts. He can always catch 2 fish
per hour and he can always gather 3 coconuts per hour. His utility function is CF, where C is the
number of coconuts he eats per day and F is the number of fish he eats per day. How many fish will he
choose to eat per day?
a.
8
b.
6
c.
4
d.
2
e.
1
10. Tip can write 3 pages of term paper or solve 9 workbook problems in an hour, while Spot can write 4
pages of term paper or solve 4 workbook problems in an hour. If they each decide to work a total of 7
hours and to share their output, then if they produce as many pages of term paper as possible given that
they produce 18 workbook problems,
a.
Spot will spend all of his time writing term papers and Tip will spend some time at each
task.
b.
Tip will spend all of his time writing term papers and Spot will spend some time at each
task.
c.
both students will spend some time at each task.
d.
Spot will write term papers only and Tip will do workbook problems only.
e.
Tip will write term papers only and Spot will do workbook problems only.
11. Tip can write 2 pages of term paper or solve 4 workbook problems in an hour, while Spot can write 4
pages of term paper or solve 12 workbook problems in an hour. If they each decide to work a total of 6
hours and to share their output, then if they produce as many pages of term paper as possible given that
they produce 10 workbook problems,
a.
Spot will write term papers only and Tip will do workbook problems only.
b.
Spot will spend all of his time writing term papers and Tip will spend some time at each
task.
c.
both students will spend some time at each task.
d.
Tip will spend all of his time writing term papers and Spot will spend some time at each
task.
e.
Tip will write term papers only and Spot will do workbook problems only.
12. Tip can write 2 pages of term paper or solve 2 workbook problems in an hour, while Spot can write 2
pages of term paper or solve 6 workbook problems in an hour. If they each decide to work a total of 8
hours and to share their output, then if they produce as many pages of term paper as possible given that
they produce 14 workbook problems,
a.
Tip will spend all of his time writing term papers and Spot will spend some time at each
task.
b.
Spot will spend all of his time writing term papers and Tip will spend some time at each
task.
c.
Spot will write term papers only and Tip will do workbook problems only.
d.
both students will spend some time at each task.
e.
Tip will write term papers only and Spot will do workbook problems only.
13. Al and Bill are the only workers in a small factory which makes geegaws and doodads. Al can make 5
geegaws per hour or 15 doodads per hour. Bill can make 2 geegaws per hour or 12 doodads per hour.
Assuming that neither of them finds one task more odious than the other,
a.
Al has a comparative advantage in producing geegaws and Bill has a comparative
advantage in producing doodads.
b.
Bill has a comparative advantage in producing geegaws and Al has a comparative
advantage in producing doodads.
c.
Al has a comparative advantage in producing both geegaws and doodads.
d.
Bill has a comparative advantage in producing both geegaws and doodads.
e.
both have a comparative advantage in producing doodads.
14. Al and Bill are the only workers in a small factory which makes geegaws and doodads. Al can make 5
geegaws per hour or 15 doodads per hour. Bill can make 4 geegaws per hour or 8 doodads per hour.
Assuming that neither of them finds one task more odious than the other,
a.
Al has a comparative advantage in producing geegaws and Bill has a comparative
advantage in producing doodads.
b.
Bill has a comparative advantage in producing both geegaws and doodads.
c.
Al has a comparative advantage in producing both geegaws and doodads.
d.
Bill has a comparative advantage in producing geegaws and Al has a comparative
advantage in producing doodads.
e.
both have a comparative advantage in producing doodads.
15. Al and Bill are the only workers in a small factory which makes geegaws and doodads. Al can make 4
geegaws per hour or 12 doodads per hour. Bill can make 2 geegaws per hour or 8 doodads per hour.
Assuming that neither of them finds one task more odious than the other,
a.
Al has a comparative advantage in producing geegaws and Bill has a comparative
advantage in producing doodads.
b.
Bill has a comparative advantage in producing geegaws and Al has a comparative
advantage in producing doodads.
c.
Al has a comparative advantage in producing both geegaws and doodads.
d.
Bill has a comparative advantage in producing both geegaws and doodads.
e.
both have a comparative advantage in producing doodads.
16. Every consumer has a red-money income and a blue-money income and each commodity has a red
price and a blue price. You can buy a good by paying for it either with blue money at the blue price or
with red money at the red price. Harold has 7 units of red money to spend and 32 units of blue money
to spend. The red price of ambrosia is 1 and the blue price of ambrosia is 4. The red price of bubble
gum is 1 and the blue price of bubble gum is 2. If ambrosia is on the horizontal axis, and bubble gum
on the vertical axis, then Harold’s budget set is bounded by
a.
two line segments, one running from (0, 23) to (7, 16) and another running from (7, 16) to
(15, 0).
b.
two line segments one running from (0, 23) to (8, 7) and the other running from (8, 7) to
(15, 0).
c.
two line segments, one running from (0, 24) to (7, 16) and the other running from (7, 16)
to (14, 0).
d.
a vertical line segment and a horizontal line segment, intersecting at (7, 16).
e.
a vertical line segment and a horizontal line segment, intersecting at (8, 7).
17. Every consumer has a red-money income and a blue-money income and each commodity has a red
price and a blue price. You can buy a good by paying for it either with blue money at the blue price or
with red money at the red price. Harold has 40 units of red money to spend and 35 units of blue money
to spend. The red price of ambrosia is 4 and the blue price of ambrosia is 5. The red price of bubble
gum is 1 and the blue price of bubble gum is 1. If ambrosia is on the horizontal axis, and bubble gum
on the vertical axis, then Harold’s budget set is bounded by
a.
two line segments one running from (0, 75) to (7, 40) and the other running from (7, 40) to
(17, 0).
b.
two line segments, one running from (0, 42) to (10, 35) and the other running from
(10, 35) to (50, 0).
c.
a vertical line segment and a horizontal line segment, intersecting at (10, 35).
d.
two line segments, one running from (0, 75) to (10, 35) and another running from (10, 35)
to (17, 0).
e.
a vertical line segment and a horizontal line segment, intersecting at (7, 40).
18. Every consumer has a red-money income and a blue-money income and each commodity has a red
price and a blue price. You can buy a good by paying for it either with blue money at the blue price or
with red money at the red price. Harold has 12 units of red money to spend and 40 units of blue money
to spend. The red price of ambrosia is 1 and the blue price of ambrosia is 4. The red price of bubble
gum is 1 and the blue price of bubble gum is 2. If ambrosia is on the horizontal axis, and bubble gum
on the vertical axis, then Harold’s budget set is bounded by
a.
a vertical line segment and a horizontal line segment, intersecting at (12, 20).
b.
two line segments one running from (0, 32) to (10, 12) and the other running from (10, 12)
to (22, 0).
c.
two line segments, one running from (0, 32) to (12, 20) and another running from (12, 20)
to (22, 0).
d.
two line segments, one running from (0, 30) to (12, 20) and the other running from
(12, 20) to (24, 0).
e.
a vertical line segment and a horizontal line segment, intersecting at (10, 12).
19. Robinson Crusoe has exactly 14 hours per day to spend gathering coconuts or catching fish. He can
catch 4 fish per hour or he can pick 12 coconuts per hour. His utility function is U(F, C) = FC, where
F is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best
possible way between catching fish and picking coconuts, his consumption will be the same as it
would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1.
a.
His income is $168 and the price of fish is $3.
b.
His income is $56 and the price of fish is $4.
c.
His income is $224 and the price of fish is $4.
d.
His income is $168 and the price of fish is $.25.
e.
His income is $112 and the price of fish is $.25.
20. Robinson Crusoe has exactly 8 hours per day to spend gathering coconuts or catching fish. He can
catch 3 fish per hour or he can pick 6 coconuts per hour. His utility function is U(F, C) = FC, where F
is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best
possible way between catching fish and picking coconuts, his consumption will be the same as it
would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1.
a.
His income is $24 and the price of fish is $3.
b.
His income is $48 and the price of fish is $2.
c.
His income is $72 and the price of fish is $3.
d.
His income is $48 and the price of fish is $.33.
e.
His income is $36 and the price of fish is $.33.
21. Robinson Crusoe has exactly 10 hours per day to spend gathering coconuts or catching fish. He can
catch 3 fish per hour or he can pick 6 coconuts per hour. His utility function is U(F, C) = FC, where F
is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best
possible way between catching fish and picking coconuts, his consumption will be the same as it
would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1.
a.
His income is $60 and the price of fish is $2.
b.
His income is $60 and the price of fish is $.33.
c.
His income is $90 and the price of fish is $3.
d.
His income is $30 and the price of fish is $3.
e.
His income is $45 and the price of fish is $.33.
22. On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There
are 1,000 acres of land. An acre of land will produce either 14 units of milk or 15 units of wheat. Some
citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions
of the form U(M, W) = MW. At every Pareto optimal allocation,
a.
the number of units of milk produced equals the number of units of wheat produced.
b.
total milk production is 7,000 units.
c.
all citizens consume the same commodity bundle.
d.
every consumer’s marginal rate of substitution between milk and wheat is −1.
e.
None of the above is true at every Pareto optimal allocation.
23. On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There
are 1,000 acres of land. An acre of land will produce either 8 units of milk or 15 units of wheat. Some
citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions
of the form U(M, W) = MW. At every Pareto optimal allocation,
a.
every consumer’s marginal rate of substitution between milk and wheat is −1.
b.
the number of units of milk produced equals the number of units of wheat produced.
c.
total milk production is 4,000 units.
d.
all citizens consume the same commodity bundle.
e.
None of the above is true at every Pareto optimal allocation.
24. On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There
are 1,000 acres of land. An acre of land will produce either 3 units of milk or 32 units of wheat. Some
citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions
of the form U(M, W) = MW. At every Pareto optimal allocation,
a.
the number of units of milk produced equals the number of units of wheat produced.
b.
all citizens consume the same commodity bundle.
c.
every consumer’s marginal rate of substitution between milk and wheat is −1.
d.
total milk production is 1,500 units.
e.
None of the above is true at every Pareto optimal allocation.
25. In the process of producing 1 hormone-free, stress-free, happy cow, the New Age Cattle Ranch
produces 1 ton of natural, organic plant fertilizer. Demand for the ranch’s cattle is given by
Pc = 2,000 − 20Qc, and demand for fertilizer is given by Pf = 500 − 4Qf. The cost of producing Q
cow-fertilizer bundles is C = 5,000 + 400Q. To maximize profits, the ranch should
a.
produce 40 cow-fertilizer units, sell 40 cattle, and sell 40 tons of fertilizer.
b.
produce 40 cow-fertilizer units, sell 40 cattle, and sell 12.50 tons of fertilizer.
c.
produce 62.50 cow-fertilizer units, sell 40 cattle, and sell 62.50 tons of fertilizer.
d.
produce 43.75 cow-fertilizer units, sell 43.75 cattle, and sell 43.75 tons of fertilizer.
e.
produce 50 cow-fertilizer units, sell 50 cattle, and dispose of all the fertilizer in an
environmentally friendly manner.
26. In the process of producing 1 hormone-free, stress-free, happy cow, the New Age Cattle Ranch
produces 1 ton of natural, organic plant fertilizer. Demand for the ranch’s cattle is given by
Pc = 2,000 − 5Qc, and demand for fertilizer is given by Pf = 500 − 4Qf. The cost of producing Q
cow-fertilizer bundles is C = 5,000 + 400Q. To maximize profits, the ranch should
a.
produce 160 cow-fertilizer units, sell 160 cattle, and sell 62.50 tons of fertilizer.
b.
produce 160 cow-fertilizer units, sell 160 cattle, and sell 12.50 tons of fertilizer.
c.
produce 160 cow-fertilizer units, sell 160 cattle, and sell 160 tons of fertilizer.
d.
produce 116.67 cow-fertilizer units, sell 116.67 cattle, and sell 116.67 tons of fertilizer.
e.
produce 200 cow-fertilizer units, sell 200 cattle, and dispose of all the fertilizer in an
environmentally friendly manner.
27. In the process of producing 1 hormone-free, stress-free, happy cow, the New Age Cattle Ranch
produces 1 ton of natural, organic plant fertilizer. Demand for the ranch’s cattle is given by
Pc = 2,000 − 5Qc, and demand for fertilizer is given by Pf = 500 − 2Qf. The cost of producing Q
cow-fertilizer bundles is C = 5,000 + 200Q. To maximize profits, the ranch should
a.
produce 164.29 cow-fertilizer units, sell 164.29 cattle, and sell 164.29 tons of fertilizer.
b.
produce 180 cow-fertilizer units, sell 180 cattle, and sell 125 tons of fertilizer.
c.
produce 180 cow-fertilizer units, sell 180 cattle, and sell 75 tons of fertilizer.
d.
produce 180 cow-fertilizer units, sell 180 cattle, and sell 180 tons of fertilizer.
e.
produce 200 cow-fertilizer units, sell 200 cattle, and dispose of all the fertilizer in an
environmentally friendly manner.
28. For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is
smelted. The cost of mining and processing 1 carload of ore is C(Q) = 400 + 2Q + 0.04Q2. The demand
for silver (per ounce) is Ps = 30 − 0.30Qs and the demand for lead (per pound) is Pl = 6 − 0.02Ql. What
should the owners of the Matchless Mine do to maximize profits (in the long run)?
a.
Mine and process 47.22 carloads of ore, sell 47.22 ounces of silver, and sell 47.22 pounds
of lead.
b.
Mine and process 50 carloads of ore, sell 50 ounces of silver, and sell 33.33 pounds of
lead.
c.
Mine and process 150 carloads of ore, sell 41.18 ounces of silver, and sell 150 pounds of
lead.
d.
Mine and process 150 carloads of ore, sell 50 ounces of silver, and sell 150 pounds of
lead.
e.
Shut down the mine.
29. For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is
smelted. The cost of mining and processing 1 carload of ore is C(Q) = 300 + 3Q + 0.02Q2. The demand
for silver (per ounce) is Ps = 30 − 0.10Qs and the demand for lead (per pound) is Pl = 6 − 0.03Ql. What
should the owners of the Matchless Mine do to maximize profits (in the long run)?
a.
Mine and process 150 carloads of ore, sell 150 ounces of silver, and sell 30 pounds of
lead.
b.
Mine and process 150 carloads of ore, sell 150 ounces of silver, and sell 100 pounds of
lead.
c.
Mine and process 110 carloads of ore, sell 110 ounces of silver, and sell 110 pounds of
lead.
d.
Mine and process 112.50 carloads of ore, sell 112.50 ounces of silver, and sell 100 pounds
of lead.
e.
Shut down the mine.
30. For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is
smelted. The cost of mining and processing 1 carload of ore is C(Q) = 700 + 2Q + 0.09Q2. The demand
for silver (per ounce) is Ps = 40 − 0.30Qs and the demand for lead (per pound) is Pl = 5 − 0.02Ql. What
should the owners of the Matchless Mine do to maximize profits (in the long run)?
a.
Mine and process 52.44 carloads of ore, sell 52.44 ounces of silver, and sell 52.44 pounds
of lead.
b.
Mine and process 66.67 carloads of ore, sell 66.67 ounces of silver, and sell 13.64 pounds
of lead.
c.
Mine and process 125 carloads of ore, sell 66.67 ounces of silver, and sell 125 pounds of
lead.
d.
Mine and process 125 carloads of ore, sell 48.72 ounces of silver, and sell 125 pounds of
lead.
e.
Shut down the mine.
PROBLEM
1. On a certain small island, there are 100 units of labor and 200 units of capital. Two goods can be
produced. Good A is produced with fixed coefficients, using 1 unit of labor and 3 units of capital per
unit of output. Good B is produced with fixed coefficients, using 1 unit of labor and 1 unit of capital
per unit of output. Let X a denote the quantity of good A and X b be the quantity of good B that is
produced. The set of feasible output combinations for this economy is restricted by the fact that it
cannot use more than 100 units of labor or 200 units of capital.
a. Write down two inequalities expressed in terms of X a and X b that must be satisfied at feasible
output combinations.
b. Draw a graph showing the economy’s production possibility set. Put numerical labels on your
graph so that this graph is precisely described.