Econ 3010: Intermediate Price Theory (microeconomics)
Professor David L. Dickinson
PROBLEM SET #2………..ANSWERS
INPUTS AND PRODUCTION
1)
To prove increasing returns to scale, we must show that
f (tx1 , tx2 , tx3 )  t  f ( x1 , x2 , x3 ) (that is, multiplying all inputs by a factor t > 1yields
output that increasing by more than the factor t—for example, doubling the use of all
inputs will more than double the output produced).
2
2
2
f (tx1 , tx2 , tx3 )  tx1  tx2  tx3   t 2 x12 t 2 x22t 2 x32  t 2 t 2t 2 x12 x22 x32  t 6 x12 x22 x32  t 6  f ( x1 , x2 , x3 )
So, we have shown that f (tx1 , tx2 , tx3 )  t 6  f ( x1 , x 2 , x3 )  t  f ( x1 , x 2 , x3 ) , which we know
is true because t6 > t
2)
For the production function to reflect his technology, it must obviously be a
perfect substitute technology, and it must have the right amount of inputs producing a
unit of output (not quite like utility functions, where the utility number assigned to a
particular consumption bundle did not really matter).
The one that works is (assuming x1=humans, x2=robot)
f(x1,x2)=(1/50)x1+(1/10)x2
3)
Recall that a when you change the level of an input used, the resultant change in
production can be found by multiplying the marginal product, MP, of the input, times the
amount of the change in the input (for example, if MP=3, this means that each additional
unit of the input increases output by 3 units. If, however, we increase the use of the
input, x, by 4 units, then the change in output will be MP*x=3*4=12 units of output.
So, in general the Q=MP1*x1+MP2*x2. If, however, we are moving along the
same isoquant, it must be true that Q=0. So, for a tiny move along a given isoquant, it
x2  MP1
must be true that 0=MP1*x1+MP2*x2. Rearranging this equation yields
.

x1
MP2
Because the TRS is defined as the change in input x2 needed to compensate for a change
x
in input x1 in order to hold output constant, that is just TRS  2 . So, we have proven
x1
the result. You can think of the TRS as the rate at which the production technology
allows you to trade x1 for x2 to maintain a given production level.
1
1
1
For the production function f ( x1 , x 2 )  x12 x 2 2 , we have MP1  2 x1 x 2 2 and
4)
1
MP2  (1 / 2) x 12 x 2
2
x12

1
. So, the TRS=
2 x2 2
1
1
1
 2 x1 x 2 2
 2 x1 x 2 2 2 x 2 2  4 x1 x 2  4 x 2
 MP




MP2
1
x1
x12
x12
 x2

 1

 2 x 12 
2 

As usual, these often simplify down quite a bit.
5)
To find the equation for the general isoquant, we need to just solve
2
1
f ( x1 , x 2 )  x1 3 x 2 3 for x2 (because we usually plot the isoquant with x2 on the vertical
axis). I’ll call f(x1,x2)=Q to make it more simple. Solving for x2 yields
3
 Q 
Q3
Q  x1 3 x 2 3  x 2 3  2  x 2   2   x 2  2 . We can use this to plot
 3
x1
x1 3
 x1 
out the isoquant for Q=4 (I’ve done it by choosing x1=2,3,4,6,8 on the graph below (try
your best to draw to scale or use graph paper so that you can appreciate the x1-x2 tradeoffs along this isoquant).
2
1
Q
1
x2
16
7.1
Q=4
isoquant
4
1.8
1
2 3 4
6
8
x1
Supposing that wood is fixed at x 2 =8, we can now draw the production function for the
one variable input, x1. Below is the graph for f(x1, x 2 ).
2
Qoutput
74.2
Q=4x1(2/3)
Qoutput
46.8
37.1
37.1
32
Q=2x1(2/3)
Q=2x1(2/3)
23.4
23.4
16
16
8
8
8
24
40
80
8
24
40
Qlabor
PROFIT MAXIMIZATION AND COST MINIMIZATION
80
Qlabor
    
The production function would be f ( x1 , x2 )  min 1  x1 , 1  x2 . Given that
2
2
w1=$10, w2=$20 and P=$70, the profit maximizing outcome would be for Jiffy Lawn to
use infinite inputs, mow an infinite number of lawns, and it have infinite profits. This
strange sounding result come from the fact that it costs $60 worth of inputs to mow each
acre, it generates $70 in revenue, and this perfect complement technology never
experiences diminishing marginal returns.
Now, with a limit of producing Q=10, this is what Jiffy Lawn would produce. It
would take x1*=20, x2*=20. So, inputs will cost $600 altogether, and 10 acres of mowed
lawn will bring $700 in revenue. So, profits will be $100. This outcome is graphed
below.
1)
3
x2=riding
mower hours
JIFFY LAWN
x2=x1
30
Q*=10
x2*=20
x1*=20
60
x1=man hours
2)
This is one of those where it is just easier to talk through what is going on (you’ve
notice that this is often the case with perfect complement or perfect substitute
technologies). With production function f(x1,x2)=3x1+x2, the firm can produce one unit
of output with either 1/3 unit of x1 or 1 unit of input x2 (or some combination of the two).
So, which will it choose? Well, whichever is cheaper. So, if (1/3)w1<w2, it costs less to
produce each unit of output using only x1 (and so y=3x1, which means x1*=(1/3)y). So,
the conditional factor demand can be written as
1  y if 1  w1  w2 

3
3




*
1
x1 ( w1 , w2 , y )  
0
if
 w  w2 
3 1


 0, 13  y if 13  w1  w2 
Similarly, for x2, we have
 0
if 1  w1  w2 
3




*
1
x 2 ( w1 , w2 , y )  
y
if
 w  w2 
3 1


 0, y  if 13  w1  w2

 
 
 
 
  
 
3)
 
 
1
2
2
2
2
For the technology f ( x1 , x 2 )  x1 x 2 , we have MP1  (1 / 3) x 1 x2 
1
1
MP2  (2 / 3) x 1 3 x 2
3
3
3
3
x2 3
2
3x1
and
3
1
3

2 x1 3
1
3x2 3
.
The technical rate of substitution, the TRS is equal to the ratio -MP1/MP2, which
2
 x2 3
in this case means TRS=
2
3 x1 3
1
2 x1 3
1
2
1
 x2 3 3x2 3  x2

 1 
.
2
2 x1
3 x1 3 2 x1 3
3x2 3
4
For the conditional factor demands, first note that TRS= - w1/w2 at the optimal
 x 2  w1
wx
firm choice. So
, which can be rewritten as x1  2 2 . Now substitute this

2w1
2 x1
w2
1
2
into the production function y  x1 x 2
3
3
w x
to get y   2 2
 2w1
1
1
 3 2 3  w2  3
 x 2  
 x 2 . Finally,

 2w1 
1
 2w  3
just solve this for x2 to get x ( w1 , w2 , y )   1   y
 w2 
*
To find x1 solve the TRS= - w1/w2 for x2 and substitute back into the production
*
2
 w 
function. Then solve to get x ( w1 , w2 , y )   2 
 2w1 
*
1
2
3
y
    
Here, we realize that with technology f ( x1 , x2 )  min 1  x1 , 1  x2 , the firm
2
3
must use 2 units of x1 and 3 units of x2 to produce each unit of output, y (sorry, I realize
we’ve called output three different letters, but y is also standard and so I want to expose
you to all possibilities that you may see). Anyway, this means that to produce one unit of
output, we have to pay to use x1=2 and x2=3. So, we pay 2w1+3w2 for each unit of output
we produce. This shows us that our cost function is c*(w1,w2,y)= 2w1  3w2   y
4)
5)
I used to think that this implied perfect substitute technology. My reasoning was
that oil was oil and so the potato chip people would just use whatever oil was cheapest
for that production cycle. Then, I spoke with someone who knew a lot more (translation:
way too much!) about the potato chip industry, and he told me that it meant the exact
opposite. He said it implied a perfect complement technology for those inputs because
the used them in specific proportions to produce the exact flavor of the chip that they
wanted. In other words, not revealing which exact oil was used was an issue of not
revealing the “secret recipe” for their oil mixture, and not the fact that they were just
camping on whichever oil was cheapest that quarter.
This does make a big difference in terms of firm behavior, because if the price of
one of the oils goes up, the perfect substitution technology would just stop using that oil
if it was relatively more expensive than other oil options. The perfect complement
technology assumption says that the firm will keep using the oils in the exact same
proportions as always. Either way, costs will have gone up for the firm, but the
production implications are quite different.
5
COSTS CURVES AND FIRM SUPPLY
c ( y)
c ( y ) 10
c( y )
10
c( y )
1) ATC 
AVC  V
 3 AFC  F

 3
MC 
3
y
y
y
y
y
y
P
13
8
5
4
3
ATC
MC=AVC
1 2
10
Q
If P=$5 for the firm’s output, then since MC=$3, the firm would want to produce an
infinite amount of output. More realistically, the firm would produce to its capacity,
whatever that is—capacity would also determine the firm’s profits. If, on the other hand,
P=$2, then P<AVC, and so the firm is better off not producing anything in the short-run.
In this case, the firm’s profits would be -$10 (i.e., its losses are its fixed cost amount).
2)
To do this, note that the firm has two options, with an associated profit level in
each case. If the firm produces q*>0, (determined by finding the point where P=MC),
then its profits can be written as =TR-TC=TR-TVC-TFC. If the firm decides to produce
q=0, then its profits will be SD= - TFC. So, the firm should shut down only if
- TFC > TR-TVC-TFC.
This can be rewritten to say that the firm should shut down if TR<TVC. This can also be
written as P*Q<TVC, which can be written as P<TVC/Q. The question is: what is
TVC/Q? Well, this is just average variable costs by definition. So, we have shown that
the firm should shut down in the short-run if P<AVC.
c ( y)
c( y )
200
c( y )
AVC  V
 4s  20 MC 
 4s  20 
 8s  20
y
y
s
y
The short-run supply curve is highlighted with the squares on the graph below. Basically,
it is the MC curve down to where it equals AVC at the vertical axis intercept of $20.
Then, the supply curve goes straight down to the origin.
If P=$92, then Mr. Goodwrench maximizes profits by fixing cars until P=MC,
which implies 92=8s+20. So, the optimal number of cars to fix is s*=9 cars. This point is
highlighted on the second graph below, and TR, TC, and profits are highlighted on the
graph below. In the long-run, Mr. Goodwrench will require a price at least equal to his
minimum ATC in order to remain in the industry. So, he will need at least p=$76 in the
long-run (that’s about what you get for ATC at its minimum. Find the minimum by
200
noting that ATCmin is where MC=ATC, or 8s+20= 4s  20 
, which yields s=7
s
(about). MC (or ATC) at s=7 is $76). Notice, this is higher than the price at which Mr.
3)
ATC 
6
Goodwrench would still be willing to produce s>0 in the short-run (the shut-down point
is where MC=AVC at P=$20).
Mr. Goodwrench
$
MC= short-run supply
above $20 (p=AVC shut
down point)
Optimal production
point where MR=MC
224
ATC
AVC
128
p=92
76
market price($92)=D=MR
20
1 2
7
20
s*=9
40
S=cars fixed
Mr. Goodwrench
$
MC= short-run supply
above $20 (p=AVC shut
down point)
Total Revenue=
$828 (bold rectangle)
224
ATC
AVC
128
p=92
76
20
market price($92)=D=MR
Total Costs
=ATC*s
=78*9=$702
1 2
7
Profits=TR-TC
=$126
s*=9
20
40
S=cars fixed
4)
For this cost function, we have
7
c ( y)
c ( y ) 4500
c( y )
4500
AVC  V
 20 y AFC  F

 20 y 
y
y
y
y
y
c( y )
MC 
 40 y . These are graphed below, along with the firm’s optimal production
y
point. The firm’s optimal choice point is at y*=25.
ATC 
$
4520
optimal choice point
MC
ATC
1275
AVC
P=1000
750
600
1
15
q*=25 30
45
60
Q
5)
The firm’s profits at the optimum will be TR-TC, which are 25,000-c(y=25).
This can be solved to get $8,000. The area of profits is shaded in the first graph below
(recall that profits can also be written as (P-ATC)*y, which is useful for our graphing).
The shaded area is a rectangle 25 units long by $320 high (because ATC(Y=25)=$680,
though it is hard to see on the graph)). So the area of the rectangle is 25*320=$8000.
The graph below shades in the producer surplus, which is the area above the supply curve
(MC) and below the price received, out to the quantity being produced. So, it is, in this
case, a triangle with area (1/2)*base*height=(1/2)*25*1000=$12,500. This area is
obviously larger than the profit calculation, and it is larger by exactly the size of the fixed
costs of the firm (PS-profits=TFC or 12,500-8000=4500).
8
$
4520
optimal choice point
MC
ATC
1275
AVC
P=1000
750
600
profits
1
15
q*=25 30
60
45
Q
$
4520
optimal choice point
MC
ATC
1275
P=1000
750
600
AVC
Producer
Surplus
1
15
q*=25 30
45
60
Q
9
INDUSTRY SUPPLY AND EQUILIBRIUM
1)
The graphs below show the process. The firm starts out at p* q*, increases
production to q’ when market price rises to p’ (due to increase in market demand) leading
to positive SR profits, and then falls back down to q* when other firms enter the market
and push prices back down to p*. The points labels A,B,C describe the chronology of the
outcomes in the market graph. Notice that, due to our assumption of being in a constant
cost industry, the firm’s costs curves an unaffected by all this, and LR equilibrium settles
back down at point C—the LR supply curve for the market would be a perfectly
horizontal line running through points A and C.
P
Competitive #2-pencil Firm
P
#2 pencil Market
MC
S
ATC
P’
P*
SR Profits
D=MR
P’
P*
S’
B
A
C
D’=MR’
D’
D
q* q’
q
Q* Q’ Q’’
Q
2)
First, rewrite supply as y=(1/2)P. This is just MC=2y solved for y, and noting
that p=MC for the firm. Now, horizontally summing the MC curves, we get industry
supply to be Y=N(1/2)P, where N is the number of firms in the industry. The industry
supply curves are graphed below for 1-5 firms in the market. In the graph to the right, we
now highlight the LR industry supply curve after ruling out portions that would never
occur (e.g., all point below P=$2 since that would imply losses, and points where
quantity supplied is high enough so that another firm can profitably enter). Finally, in the
last graph, we add the demand curve. Industry supply=demand implies
25 5
1
 P  N   P . If we set P=$2, we find that the number of firms, N, that produces
4 4
2
this price in long-run equilibrium is 3.75. Assuming fractions of firms cannot enter, only
3 firms will enter, not 4, 5, or more, and the resultant equilibrium price will be about
P=$2.27. You can see this also in the final graph (where the D-curve is added).
10
P
P
S1
S1
S2
2=ATCmin
S2
S3
S3
S4
S4
2=ATCmin
S5
1
2
3
P
4
S5
1
5
Q
2
3
4
5
Q
S1
5
S2
S3
S4
P*=2.27
2=ATCmin
S5
D
1
2
3
4
5
Q
3)
The equilibrium is shown on the graph to the left (below). The graph to the right
shows the effects of the government policy (not shown is the highlighted producer and
consumer surplus areas, which would reveal that the policy inefficiently allocates wheat
in the market).
P
Wheat Market
S
4
P
Wheat Market
S
market surplus
4
of 7.5 bushels
of wheat
price
support
3.50
P*=3
P*=3
1
1
D
Q*=10
40 Q
D
5 Q*=10 12.5
40 Q
4)
11
P
S
CS
Ps
P*
Pb
Dsubsidy
PS
Size of
subsidy
D
Q* Qsubsidy
Q
Subsidy
Payments
P
Subsidy
Payments
S
Ps
P*
Pb
Dsubsidy
Size of
subsidy
D
Q* Qsubsidy
Q
As we can see here, both PS and CS rise as a result of the surplus. This is because
producers will receive a higher price, Ps, and consumers will pay a lower price Pb, than
in equilibrium, and the quantity traded rises to Qsubsidy. However, we now need to take
into account the gov’t as a player. Someone needs to pay for the subsidies, and so the
government has negative tax revenues (i.e., transfer payments) in the total amount of the
subsidy payments. Once we take this into account, we will see that there is a deadweight
loss triangle in the picture on the right. It is somewhat hard to see, but if you consider
new additions to CS and PS (not forgetting to count the overlapping regions of CS and PS
on the left-hand graph), the new surplus is the weird-shaped almost-rectangle. However,
subsidy payments are the entire (Ps-Pd)Qsubsidy rectangle than must be subtracted away
from total surplus. So, once taking this into account, we have
12
Equals DWL
minus
and so, similar to the case of a tax, there are winners and losers with subsidies, but the
policy will still reduce total surplus overall. The same result occurs whether you offer the
subsidy to buyers (as shown in graph above) or to sellers.
MONOPOLY, PRICE DISCRIMINATION, AND MONOPOLISTIC
COMPETITION
1)
Assuming the mafia really is a monopoly seller of heroin and assuming its goal is
to maximize profits, it would want to produce where MR=MC (and charge the price
given by the demand curve). We have seen, however, that where demand is inelastic,
MR<0, which implies that a profit maximizing monopolist would never produce at an
output level where demand is inelastic. Therefore, it can not be the case that both heroin
demand is highly inelastic and the mafia is a profit-maximizing monopoly seller (perhaps
they are a monopoly, and the just don’t do very well at profit maximizing. Or, maybe
they price discriminate. Here’s a free research topic for someone).
2)
A natural monopolist is one where ATC is decreasing over the relevant range of
output. This implies that MC<ATC over the relevant range of output. If forced to charge
P=MC (i.e., try to force the output to be competitive-like), the monopolist is guaranteed
to operate at an economic loss. So, the monopolist would rather not serve the market
than do this. An alternative would be to allow the monopolist to charge P=ATC. The
natural monopolist would at least break even, but there would be a DWL inefficiency in
the market (though not as bad as at the unregulated monopoly outcome, PM and QM).
This is shown in the graph below, where I assume constant MC as a useful representation
of the natural monopoly case).
P
P
Natural Monopolist
DWL at P=ATC
outcome
PM
PATC
ATC
Pmc
MC
MR
QM
QATC Qmc
D
Q
3) Start with the fact that marginal revenue for the monopolist, a change in revenue, R,
can come from either price and/or quantity, y, changing (because TR=py). So, we can
13
write: R  p  y  y  p . Because marginal revenue is R/y, we can rearrange to
solve for writeR/y. First, we employ a little trick and multiply the last term on the
right-hand side by the number y/y (just a special version of the number “1”). So,
y
This allows us to factor out y from each term to get
R  p  y  y  p 
y

p 
 Now we can divide both sides by y to get
R  y   p  y 
y 

R
p
. Do the trick one more time and multiply the second term in brackets
 p y
y
y
by p/p, and then factor out p from both terms to get

R
y p 
 . Notice, however, that the second term in brackets now is just the
 p  1  
y
p y 

R
inverse of the elasticity of demand. So, we can now write marginal revenue,
, as
y

R
1 
 p  1   . Because d < 0, we can pull the negative sign out front and write
y
 d 

R
1 
.
 p  1 
y
 d 

Finally, take the profit maximizing condition MR=MC, and now we can write that the

1 
monopolist will profit maximize where p  1 
 MC . This implies that
 d 

1
which is guaranteed to imply PM>MC because the monopolist will
p M  MC 


1
1 




d 

always produce where demand is elastic (and so  d  1 )
4)
Note that if TC=y2, the MC=2y. Also, ATC will be linear because there are no
fixed costs. Specifically ATC=y (we need ATC to calculate and graph profits). Also
note that demand, y=10-P can be written as P=10-y and, using our rule to calculate MR,
we therefore have MR=10-2y. The single-price best outcome is where MR=MC, which
implies 10-2y=2y or y=2.5. At this quantity, the price P=$7.50 can be charged (and ATC
at y=2.5 are $2.50). Profits are therefore (P-ATC)y=(7.50-2.50)2.5=$12.50. This is
graphed below. You can also see profits as the area of the rectangle highlighted below,
which is base*height, or 5*2.50=12.50.
14
P
Market for Relief-Trex
10
MC
PM=7.50
ATC
Profits
2.50
D
MR
QM=2.5
5
10
Q (or Y)
Placebo could do better, however, if it perfectly price discriminates. In this case, graphed
below, Placebo would charge prices along the demand curve (so, in this case, MR=D)
and capture the highlighted area in surplus. Profits are most simply calculated in this
case by just calculating producer surplus. Because there are no fixed costs, PS=profits.
So, we calculate the area of the highlighted PS triangle to get
½*b*h=1/2*10*3.33=16.65, which is greater than the profits at the single-price
monopoly outcome.
P
10
Market for Relief-Trex
MC
PS=Profits
ATC
D
QM=3.33
10
Q (or Y)
5)
15
Holiday Inn
P
P
MC
P*
Holiday Inn after entry lowers the
demand (and MR) for this firms
product. Profits are now zero.
ATC
MC
ATC
P’
Profits
MR
Q
*
D
MR
Q
Q’
D
q
The 20 percent vacancy rate is consistent with the fact that monopolistically competitive
firms are predicted to produce at a (profit maximizing) level of output that is less than the
output level that would minimize its ATC—this is different from what we predict in
competitive markets. The fact that the optimal Q is chosen with excess capacity to reach
ATCmin would explain why hotels might choose to maintain a vacancy rate greater than
0%.
OLIGOPOLY
1)
Market demand D(p)=60-P can be rewritten as P=60-Q or P=60-qpp-qpp. From
Pete’s perspective, his total revenue function is therefore Pqpp=(60-qpp-qGG)qpp or
TR
TR=60qpp-qpp2-qppqgg. So, Pete’s marginal revenue MR pp 
=60-2qpp-qgg.
q pp
TR
=60-2qgg-qpp. So,
q gg
Pete maximizes profit by setting MRpp=MCpp, which implies 60-2qpp-qgg=30. So, Pete’s
reaction function can be written as rpp(qgg)=qpp(qgg)=15-(1/2)qgg.
Similarly, we can solve for Gina’s reaction function rgg(qpp)=15-(1/2)qpp. We
simultaneously solve by substituting one into the other, so rgg(qpp)=15-(1/2)[15(1/2)qgg]=10. So qgg*=10 and we can then solve to find qpp*=10 also. This is shown in
the graph below (note: you should rewrite Pete’s reaction function as qgg=30-2qpp to have
it in slope-intercept form for the graph below).
Similarly, we can find that marginal revenue for Gina is MR gg 
16
qqq
30
Gina and Pete
rpp(qgg)
Cournot (Nash)
equilibrium
15
qpp*
=10
rgg(qpp)
qgg*
=10
15
qpp
30
2)
The graph (below) shows convergence to the Cournot equilibrium from the
starting point of qgg=25 and qpp=4. I assume that Gina first reacts to Pete’s qpp=4 (and she
produces qgg=13), then Pete reacts to Gina producing 13….etc.—the arrows show this
path to convergence).
qgg
30
Gina and Pete
rpp(qgg)
25
Cournot (Nash)
equilibrium
15
qpp*
=10
rgg(qpp)
qgg* 15
=10
4
30
qpp
3)
In the graph below we have the Cournot picture as a result of Gina’s tech
discovery that lowers her MC to 20. The new Cournot equilibrium now has Gina
producing qgg=16.7, and Pete producing qpp=6.7. Notice that as a result of Gina’s lower
MC, she now increases her market share, and the market price will fall (because together
they now produce about 23 units, as opposed to 20 before. So market price will now be
about P=$37, instead of P=$40 that it was before…..you get the market price by plugging
the quantities back into the demand function).
qgg
30
Gina and Pete
rpp(qgg)
New Cournot
(Nash) equilibrium
qpp*=
16.7
rgg
qgg*
=6.7
15
30
rgg’
40
qpp
4)
To solve this, we first must find the residual demand curve. The fringe would be
willing to supply a market equilibrium at P=$75 (Sfringe=Dmarket). Once price falls below
P=$75, then there is a residual amount that the leader will supply. So, the leader’s
17
demand curve starts at the point P=$75, Y=0, and then goes down to $P=0 at Y=100 (at
this price the fringe supplies nothing and the whole market demand belongs to Shilo).
So, writing the demand curve in slope intercept form gives P=75-(75/100)Y=75-(3/4)Y.
This implies that the MR (which has same P-intercept and slope twice as steep) is
MRleader=75-1.5Y. These are all graphed below. Now Shilo profit maximizes by setting
MRleader=MCleader, which means 75-1.5Y=10, so Y*leader=43.3. Shilo will charge the price
given by its residual demand curve, so P*leader=$42.50.
The fringe takes this price as given and therefore supplies Y*fringe=14.2
You’ll note that together, they supply 57.5 pairs of shoes, which is the total
market demand at P=$42.50.
P
Sfringe
100
75
42.5
Dleader
Market D
MCleader=10
10
MRleader
50
14.2
=Y*fringe
43.3
=Y*leader
100
Y=Output
5)
Shilo’s market share is 75% in the original example (it supplies 43.3 of the total
57.5 pairs of shoes). Now with the new fringe supply, the graph is as below: (you can
just do a new graph, but I kept the old information and highlighted the new with bold
lines for comparison. Basically, the leader and fringe go through the same decisionmaking as in question (4), but because of the new fringe supply, the outcomes are now
Y*leader=42.5, Y*fringe=19.2, P*=38.4. You will notice now that the price fell, and the
market share of Shilo drops from 75% to 69%. Thus, the additional fringe suppliers are
cutting into the market share of Shilo.
18
P
Sfringe
100
New Sfringe
75
66.7
42.5
New Dleader (bold)
38.4
Market D
MCleader=10
10
19.2
=Y*fringe
New MRleader (bold)
50
42.5
=Y*leader
100
Y=Output
19