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Department of Economics
University of California, Berkeley
Prof. Kenneth Train
Fall 2011
ECONOMICS 1
Problem Set 1 – Suggested Answers
1)
a)
Grapes (thousands)
125
115
A
B
C
95
D
70
E
40
0
F
0
200
400
Llamas
600 800 1000
b) The opportunity cost of these 200 llamas is the number of bushels of grapes that you
must forgo in order to get these 200 llamas. If you weren’t producing any llamas, you could
produce 125,000 bushels of grapes. Now you are producing only 115,000. So the opportunity
cost of these 200 llamas is 10,000 bushels of grapes.
c) The PPF is bowed outward due to the law of increasing opportunity costs. Imagine
you are producing at point A in the graph of part a). There you produce only grapes using all of
your land. Now you want to consider raising 200 llamas (which means moving to point B). To
raise llamas, you must allocate some land for grazing by the llamas and can’t produce grapes on
that part of your land. Since llamas graze equally well on any kind of land, you will allocate the
areas that are least good for grapes, that is, the rocky, hilly areas; production of grapes will be
reduced by only 10,000 bushels. But suppose now that you are producing at point D and want to
increase your production of llamas by 200 again. You will have to allocate more land to the
grazing of the llamas, probably some of the flat loamy areas since you are already producing 600
llamas. Those areas are better for producing grapes and the reduction in the production of grapes
is larger: it goes from producing 70,000 bushels to only 40,000. The opportunity cost of these
additional 200 llamas is now 30,000 bushels of grapes, 3 times larger than before. Since the slope
of the PPF represents this opportunity cost, its shape shows that the higher the production of
llamas (good on the x-axis) the higher the number of bushels of grapes (good on the y-axis) you
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must forgo to produce some additional number of llamas; that is, the higher the opportunity cost
of llamas in terms of grapes. If you draw the line tangent to points B and E in your graph, you
will see that the second line is steeper than the first, which means that the slope is higher,
showing higher opportunity costs.
d) Given your current production levels (point B), the opportunity costs of producing 200
more llamas is 20,000 bushels of grapes (you go from producing 115,000 bushels to producing
only 95,000). That is, if you produce 200 more llamas you must produce 20,000 fewer bushels of
grapes. The 200 extra llamas would increase your revenues by $24,000 ($120 each times 200).
The 20,000 fewer bushels of grapes would mean that you earn $20,000 less revenue from grapes
($1 for each bushel). Since $24,000 exceeds $20,000, you would make more revenue ($4000
more revenue to be exact) by producing 200 more llamas and 20,000 fewer bushels of grapes.
You have just figured out that you will make more revenues by shifting your production toward
more llamas and less grapes (that is, by moving along the PPF toward point C). Should you go
beyond point C to point D? No. At point C, the opportunity cost of 200 more llamas is 25,000
bushels of grapes. If you produced another 200 llamas your revenues from llamas would
increase by $24,000; however, your revenues from grapes would fall by $25,000. Overall you
would earn less revenue. So you will be better off by producing (and selling) at point C. If you
still don’t believe me, calculate total revenues at each point and you’ll find that:
Revenues
Point A
Point B
Point C
Point D
Point E
Point F
$125,000
$139,000
$143,000
$142,000
$136,000
$120,000
e) The new table will be:
Llamas
Grapes
0
200
400
600
800
1,000
137,500
126,500
104,500
77,000
44,000
0
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The graph looks like this:
Grapes (thousands)
A’
B’
A
125
B
115
C’
C
95
D’
D
70
E’
E
40
0
F
0
200
400
Llamas
600 800 1000
Notice that the point F remains the same: when you don’t produce grapes, the largest amount of
llamas you can get is still 1,000. This should be obvious since the improved method is for
production of grapes and not of llamas. If you don’t produce any grapes, you don’t get the
advantages of the new method. However, at any other point except F you can get more of both
goods even though the improved technology is used in only one sector. The reason for this is as
follows: to produce a certain amount of grapes, you need less land now that you did before, so
you can use the rest of the land (previously used to produce grapes) for the grazing of more
llamas, thus increasing the production of llamas. Also notice that the amount of land available to
you is the same. There was a technological change that made this shift of the PPF possible.
2)
a)
Fish
6
Coconuts
60
3
b) The opportunity cost of one fish is the amount of coconuts Robinson could be
collecting if he were not fishing. It takes him an hour to catch one fish (a lousy, fisher, no doubt).
Since he can collect 10 coconuts per hour, the opportunity cost of one fish is 10 coconuts.
c) If you drew the graph asked in part a), you may have already noticed that the PPF on
this island economy is a straight line instead of being bowed outward. The reason is that there is
only one factor of production: Robinson’s time (labor). If you remember the explanation in part
c) of problem 1, we said that the reason for the bowed out shape was the existence of two
different kinds of land (two factors of production). In this island economy, to produce one more
fish costs Robinson the same hour, which always translates into 10 coconuts. The law of
increasing opportunity costs does not apply here: regardless of how much of both goods
Robinson is producing, the opportunity cost of one more fish will always be 10 coconuts (1 hour
of labor). Also, that is why in part b) we could compute the opportunity cost of one fish without
setting a specific point for our calculation. In summary, the law of increasing opportunity costs
applies when there is more than one factor of production, each being better suited to produce one
good than the others.
3)
a) Since some people were probably eating oat bran because of this alleged characteristic,
they will quit eating it and the demand curve will shift leftward (a decrease in demand). There is
no change in the supply curve. Both the equilibrium price and the quantity of oat bran sold will
be lower.
P
S
P1
P2
E1
D1
E2
D2
Q
Q2
Q1
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b) This is an increase in the cost of producing vegetables. For each quantity produced,
agricultural producers will require a higher price (to cover the higher cost) in order to be
induced to supply that quantity. Because of this, the supply curve will shift upward (a
decrease in supply). There is no change in the demand curve. The equilibrium price will
rise and the quantity of vegetables sold will decrease.
P
S2
S1
E2
P2
E1
P1
D
Q
Q2
Q1
c) Since it takes some time to build a house even when prices go up, we can think of the
supply of housing at any point in time as being vertical (short term supply of housing).
Due to the earthquake, the stock of houses was reduced by 10% and the supply curve
shifts to the left (a decrease in supply). There is no change in the demand curve. The
equilibrium price of housing will go up and the quantity of housing sold will go down (by
10%).
S2
S1
P
P2
E2
E1
P1
D
Q
Q2
Q1
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d) As in part c), the supply of coffee is reduced, increasing the price of coffee. Therefore
some coffee drinkers will find it too expensive to drink and will switch to its substitutes,
one of which is tea. The demand for tea will increase (the demand curve for tea shifts to
the right) and there is no change in the supply curve of tea. Both the equilibrium price of
tea and the quantity of tea sold will increase.
P
S2
S1
P2
E2
P2
E1
P1
S
P
Coffee
D
E2
D2
E1
P1
D1
Q
Q2
Tea
Q
Q1
Q1
Q2
4)
a) What you observe in the real world (rising output and falling prices) are not points on
the supply curve, but equilibrium points, that is, intersections of a supply curve and a demand
curve. The observation is perfectly valid with an upward sloping supply curve that is shifting
downward (or to the right) showing lower costs of production and/or technological
improvements. When the supply curve shifts to the right, the equilibrium points will move along
the demand curve, showing lower prices and higher output produced and sold.
P
P70
S1980
S1970
S1990
E70
E80
P80
P90
E90
D
Q
Q70
Q80
Q90
b) The low rents in Berkeley are forced by the rent control here, creating an excess
demand for housing that will be unattended. These people will have to go to neighboring
communities to get an apartment, increasing the demand for housing in there above the level that
it would normally have. If prices are low in these communities, the reason is not rent control in
Berkeley.
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c) The city revenues for illegal parking equal the fine times the amount of illegal parking.
If fines are doubled and the amount of illegal parking is reduced, then total revenues for the city
will increase by less than double. We could even think of a situation in which doubling the fines
makes them so expensive that only the rich can afford to park illegally and the amount of illegal
parking will drop by a lot, say more than 50%. In this case, the city revenues from illegal parking
will drop.
d) Opportunity costs are not always measured in monetary terms. The retired person
doing volunteer work could have been doing something else (like reading, sleeping, or going to
the movies) instead of volunteering. These forgone activities constitute the opportunity cost for
the retired person of doing volunteer work.
5)
a) We can view the demand curve as showing the maximum price consumers are willing
and able to pay for each amount. Because of the government policy, consumers will be able to
pay a higher price (twice as much, in fact) for each quantity since the government is paying half
of it. For example, if consumers were willing to pay $10 per unity for 100 units, now they’ll be
willing to pay $20 for the same 100 units. They will in fact be paying only $10, since the
government is paying 50% of the market price. That will rotate the demand curve clockwise, that
is, the new demand curve will be shifted to the right, but it will be steeper.
P
D2
S
P2
D1
P1
Q
Q1
Q2
b) The equilibrium quantity of the drug sold will increase.
c) As you can see in the graph in part a), the equilibrium price will increase so producers
will obtain more money per unit sold.
d) Probably not, since the government is paying 50% of the new equilibrium price, which
is higher than before.
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