ECN 100A Homework 8 (Due: Beginning of class, 12/4/24)
Professor Christoph Schlom
Circle your answers :)
Accounting costs measure things that would show up in a company’s financial statement,
like the costs of inputs (including labor). Economic costs, which are the kind we care
about in this class, are accounting costs plus opportunity costs, which are the costs of
missing out on the next best thing you could have done with your time and resources (for
example working in another industry). Economic profit is revenue minus economic costs.
1. Jimmy’s Deli is owned by Jimmy. Last year, the deli had the following statement
of revenues and costs:
Revenues
Deli Ingredients
Utility Bill
Employee Salaries
$350,000
$120,000
$20,000
$80,000
7T
A
Jimmy owns the building, and if he closed the deli, he could rent it out for $50,000 a year.
In addition, Jimmy has two other job o!ers that he could take. A competing deli would
pay him $60,000 per year; or he could tutor high school English full-time and earn $40,000
per year. Assume that Jimmy likes running his own deli no better or worse than he would
like either working for another deli or tutoring.
(a) What is the accounting (explicit) cost of running the deli?
(b) What is the full economic cost of running the deli, adding in Jimmy’s opportunity
costs?
(c) What is the economic profit of the deli (revenue minus total economic costs)?
(d) Should Jimmy stay or should he take another job?
.i.no
2. Consider the cost function,
C(Q) = 100 + 20Q + 10Q2 ,
from last week’s homework.
(a) Find the Q that minimizes the average cost, AC(Q).
(b) Find the value of this minimum average cost.
1
_oc
Economists think that what will happen in an industry consisting of many such identical firms is the following. Many small firms will operate, all producing the Q you found in
(a) (this is called e!cient scale). The price will equal the average cost you found in (b),
and so all will make zero (economic) profit.
Zero profit may sound surprising, but makes sense, because we think there are a bunch
of potential entrepreneurs out there who can make an identical company, and will, if the
industry is generating positive profits for firms, driving down profits. (Remember positive
profit means they are doing better than the next best thing they could have been doing.)
E”cient scale makes sense because if companies were operating at a di!erent scale than
the e”cient one, and making zero profit (meaning the price would be higher than the one
you found in (b)), any individual company could switch to operating at the e”cient scale
and make positive profit.
3. We will explore this “zero economic profit” idea in the context of a production economy.
Farmer John has 8 milk and 4 cheese, and Mary has 6 milk and 2 cheese. Both have utility:
__
u = mc.
Mary, inc., which is 100% owned by Mary, can turn milk into cheese using the production
technology:
c = m.
They will all operate in a competitive production economy, where the price of cheese is p
and of milk is 1.
(a) Show that Mary, inc.’s production technology has constant returns to scale (CRS).
[Think about what happens if you double all inputs.]
As mentioned above, we think that in an industry with free entry by many similar entrepreneurs, many small firms, each of the same size, will arise. This will lead to a CRS
industry production technology (if we are using twice the inputs, it is because we have
twice as many of these small firms operating, and hence the industry must have twice the
outputs). You should think of Mary, inc. as representing this competitive industry.
(b) Find Mary, inc.’s optimal use of milk and resulting profit, #, if p < 1, if p = 1 and
if p > 1. [Your answer may be something like m = 0, # = 0 or m = →, # = →, depending
on p. If multiple amounts of milk are optimal to use at some p, specify all of them.]
(c) In terms of p and #, find John’s and Mary’s optimal consumption of milk and cheese.
(d) Show that p < 1 and p > 1 will not clear the market (therefore p = 1 must be the
2
market-clearing price).
(e) Find John and Mary’s optimal consumption at p = 1. Then, find a production plan
for Mary inc. that is optimal at p = 1 and clears the market.
(f) In words, describe what is happening in this economy – specifically, what is Mary
inc. doing, and how much money is it making for its troubles?
1
a
120ooot
Accountinglost
20，000
80，00
220，000
b EonomicCost Accountingcosttopprtunitycost
233
三中
460，000
KI EconomicProfit Revenues
i
350，000
oooo
40，000
soocis toooosincethisisthebest
50，000
jobalternative
EconomicCost
330，000
20，000
d Jimmyshouldstaysince
Pr
fit isgreaterthan 0 positive
Economic
2
a
ALQ 㕺 20 10Q
day 是
ACQ 0
景 10Q 10 Q 丽
SinceQ50 Q To
b
3
a
ALL min ALTo
个
20 10
0 20丣 20
t productiontechnologyis c m
ifwedoubletinput 2 2m
sthattithasconstantreturnstoscale
Whichshow
b
if pcl
3
producingcheese isunprofitable
m o and7 0
If pil
if ps I
c
producingcheese
isindifferent
17 0 regardless t valueofm
duringcheeseasmuchaspossible
pro
mix Mex
John
Mary
BudgetConstraint 417 8
UtilityMaximization
Mtcp
CD m
So m
2Pt4
So m
C
2 145
c
doesn't producecheese
If P 1
If p 1
e
C Fm
UtiliyMaximization
If PCI Maryinc
d
2Pt6 7 mtcp
Budget Constraint
2
2
for
excessdemand
can
sing
t
doesn'tclear
themarket
Maryinc produceinfinitecheese causingexcess
supply which
Cheesesupplyequalsdemand Whichthemarketclears
ForJhn m c
升 6
ForMary m c
2
州
4t tM
4
ofmilk is 61814
Sincethetotal amount
14 16 4
So John's
4
consumption
is 6milkand 6cheese
andMary'sconsumption is 4milkand 4cheese
Mary Incneed convert4milkinto4cheese
f
TheEconomyat
p i themarket is at a equilibriumof acompetitive market
Resources
areefficiently allocated
MaryInc convert4milk into4cheesewithoutprofit
andJahnandMary
attheiroptimal consumption
themarket
cheese which
doesn'tclear