Intermediate Microeconomics
Prof. David Bjerk
Midterm 2 Practice Problems (answers)
1 – Felix just finished college and is deciding between two jobs. Job 1 pays $50,000 each
period, while Job 2 pays only $10,000 in period 1 but $93,000 in period 2. Suppose the
per period interest rate is 0.10. Further suppose Felix is a pretty patient guy. Specifically,
his intertemporal preferences are captured by the utility function U = c10.25c20.75.
(a) (8 pts) Which job will Felix take is he is a utility maximizer? Why? (Hint: you may
save time by thinking about this problem graphically)
PV(job 1) = 50,000 + 50,000/1.1 = 95,454
PV(job 2) = 10,000 + 93,000/1.1 = 94,545 c2
Since the PV of job 1 is higher, and
Felix faces the same interest rate at
both jobs, he should take Job 1. As
the graph shows, all bundles
available under job 2 are available
under job 1 but not vice versa.
93K
job 1
50K
job 2
10K
50K 94.54K 95.45K c1
(b) (8 pts) Now suppose that Felix is only offered Job 1 (i.e. paid $50,000 in each period).
Will he prefer the interest rate to stay at 0.10, rise to 0.15, or can’t you tell given the
information available? (show/describe why you give the answer that you do)
If we calculate Felix’s optimal bundle at the interest rate of 0.10 we get
c1 = 0.25(50,000 + 50,000/1.1) = 23,864
c2 = 0.75(50,000 + 50,000/1.1)/(1/1.1) = 78,749
Since Felix is a saver at the interest of 0.10, any rise in the interest rate will make him
even better off, so he will prefer an interest rate of 0.15. We can confirm this by
calculating his optimal bundle at 0.15
c1 = 0.25(50,000 + 50,000/1.15) = 23,369
c2 = 0.75(50,000 + 50,000/1.15)/(1/1.15) = 80,625
If we calculate the utility under both optimal bundles we get
U0.10 = (23,864)0.25(78,749)0.75 = 58,427
U0.15 = (23,369)0.25(80,625)0.75 = 59,158
Since he gets more utility from his optimal bundle given r = 0.15, he must prefer r = 0.15.
2 - Suppose a firm’s technology was such that their isoquants for 100 units of output and
125 units of output looked like the ones depicted below.
x2
20
18
16
14
12
10
8
6
4
q = 125
q = 100
2
2
4
6
8 10 12 14 16 18 20
x1
(a) (8 pts) If the price of input 1 and the price of input 2 are both $10/unit, can we tell
how much input 1 will be used to produce 100 units of output in the cost minimizing
way? If so, how much of input 1 should be used? If not, state why not.
Answer: If both inputs are priced the same, the isocost curves will have a slope of -1. As shown
on the graph above, given isocost lines with such a slope, the cheapest way to make 100 units of
output is with 6 units of x1 and 4 units of x2.
(b) (7 pts) Consider two situations: (i) the prices of both inputs are $10/unit and the firm
produces 100 units of output (same as above), (ii) the price of input 1 is twice the price of
input 2 and the firm produces 125 units of output. Under which situation will the firm’s
demand for input 1 be greater if the firm is a cost minimizer? (Briefly discuss why you
give the answer that you do)
Answer: if the price of input 1 is twice that of input 2, the isocost lines will have a slope of -2. As
shown on the graph above with the bold line, given isocost lines with such a slope, the cheapest
way to make 125 units of output is with 4 units of x1 and 12 units of x2. Therefore, the firm's
demand for input 1 will be greater under situation (i).
(c) (6 pts) Is it possible to find new input prices such that the price of input 1 is twice the
price of input 2, and under these prices it would now cost the firm the same amount to
produce 125 units in the cost minimizing way as it originally cost the firm to make 100
units in the cost minimizing way when each cost $10/unit? If so, state them, if not state
why not.
Answer: At $20/unit for each input, it originally cost the firm 10*6+10*4 = $100 to produce 100
units. Now suppose the price of input 2 is $5/unit and the price of input 1 stays at $10/unit. Then
it would cost the firm 10*4 + 5*12 = $100.
3 – Some of Joe’s indifference curves over work and leisure are shown below. Also,
assume Joe has no non-labor income and has 100 hrs/week he divides between working
and consuming leisure.
$
2000
1800
1600
1400
1200
1000
800
600
400
200
10 20 30 40 50 60 70 80 90 100
hrs of leisure
(a) (9 pts) If Joe could earn $10/hr in the labor market, how many hours will he choose to
work and how much will he earn? (Use the graph above to help explain your answer. Use
your best guess regarding number on the graph.)
At $10/hr, his budget constraint is shown as the thinner line above. Given this budget
constraint, he will work 70 hours.
(b) (7 pts) Now suppose Joe could earn $10/hr for the first 40 hrs per week he works, but
after that he earns overtime pay of time and a half (i.e. $15/hr for each hour worked after
40). Given this new pay structure, how many hours will he choose to work now and how
much will he earn? (Use the graph above to help explain your answer)
His new budget constraint if he gets paid time and a half is the original budget constraint
starting from the right, but at 60 hours of leisure (40 hours of work) it becomes the
thicker bold line with an intercept of $1300 (40*10 + 60*15). Given this new budget
constraint, his indifference curves suggest that he will now work about 100 – 35 = 65
hours.
4 - Consider the marginal cost, average variable cost, and average cost curves depicted
below.
$
10
MC(q)
AC(q)
8
6
AVC(q)
4
2
5
10
15
20
25
30 q
(a) (7 pts) What will be this firm’s economic profit if the price of its output is $8/unit and
the firm chooses to produce and supply 20 units to the market?
At q = 20, the firm’s Average cost per unit is $6. So total profits would be pq – qAC(q) =
q(p – AC(q)) = 20*(8 – 6) = 40.
(b) (8 pts) If the price of its output is $8/unit, will this firm maximize profits by
producing and supplying less than 20 units, more than 20 units, or exactly 20 units to the
market? (Briefly explain why you give the answer that you do)
A profit maximizing firm will produce until the marginal cost of the last unit produced
equals the price. At a price of 8, this does not occur until after 20 units of output. So a
profit maximizing firm with the cost curves above will produce more than 20 units of
output.
5 - Suppose Canadian Clothes makes suits using three inputs, fabric, capital and labor. In
particular, for each suit they must use 1 yard of fabric, which they can then turn into a
suit using a production technology q = L 0.25K0.25 (where q is the number of suits, L is the
hrs of labor they use, and K is the hours of Capital they use.) Furthermore, suppose fabric
costs $2/yard, Labor costs $4/hr and Capital costs $1 hr
(a) (8 pts) If Canadian Clothes produces a load of suits every month and doesn't have to
pay for any of its input costs until the end of the month, what is Canadian Clothes'
monthly cost function for producing suits?
First we have to find their conditional demands. For fabric this is easy, each suit needs a
yard of fabric, so F(q) = q. For labor and capital we can recognize the Cobb-Douglas
technology, so we know the cost minimizing input bundle will be given by the equations
below:
L(q) = (0.25/0.25*1/4)0.25/0.5q1/0.5 = 1/2 q2
K(q) = (0.25/0.25*4/1)0.25/0.5q1/0.5 = 2 q2
Therefore, the cost function will be
c(q) = 4L(q) + 1K(q) + 2(q)
c(q) = 4(q2/2) + 1(2q2) + 2q
c(q) = 4q2 + 2q
(b) (8 pts) If Canadian Clothes can sell their suits for $82, how many suits will they
produce each month if they are profit maximizers? Given this, how much labor and
capital will they use?
To find their profit maximizing supply, we first have to find their marginal cost function.
MC(q) = 8q + 2
Then we set MC(q) = p, which gives 8q + 1/2 = p, and solve for q
q(p) = (p – 2)/8
So at a price of $82, q(82) = (82-2)/8 = 10 suits.
Given the conditional demand for labor and capital above, this means they will use
L(10) = (10)2/2 = 50 hours of labor per month, and
K(10) = 2(10)2 = 200 hours of capital per month.
(c) (7 pts) Suppose in the short-run Canadian Clothes has a fixed amount of Capital
hours it can use, namely it must use 81 hours of capital. Will this cause them to increase,
decrease, or leave unchanged the amount they produce relative to your answer in (b), or
can’t you tell from the information given? (Please explain why you give the answer that
you do)
Having a fixed factor will raise their marginal cost of producing any given amount.
Assuming they can still sell suits for $81, this will mean that the quantity at which the
marginal cost equals the price will be lower, meaning they will optimally produce less
than they were in part (b).
To see this, with a fixed 81 hours of capital, their production function is q = L 0.25810.25,
or q = L 0.253. Therefore, the conditional demand for Labor will now be
L(q) = q4/81.
This means the cost function will now be C(q) = c(q) = 4(q4/81) + 1*(81)+ 2(q), giving a
marginal cost function of MC(q) = 16q3/81 + 2. Setting this equal to price we get
16q3/81 + 2 = 82
q = 7.4 or rounding down, q = 7.
6 – (9 pts) Do you think the demand for gasoline will be more or less price elastic is the
Los Angeles metropolitan area or the New York metropolitian area, or do you think it
will be the same in both places? (Please explain why you give the answer that you do)
Answer: Demand for gas will likely be more elastic in New York, as there are more
substitutes for driving (subway, commuter trains, buses, walking, biking). So, if price of
gas goes up, people can find other ways of transportation, causing a big change in
demand for gas. On the other hand, in LA, people often live far from work with no
subways, buses, or trains convenient to their work and home. So, even if gas prices go
way up, they cannot change their demand for gas very much.