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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Hello! I just want to ask for help whether the answers in the given pictures are correct. If it's not, please help me recheck and resolve it. Please refer to the given pictures below for the answers.

After verifying the given answers shown in the subsequent picture, PLEASE ANSWER NUMBER 2: Compare the results of your calculations in item no.1 using a graphical illustration.

SITUATION/PROBLEM:

Consider two identical firms with similar cost functions given by C₁ = cq₁ and C₂ = cq₂ . The inverse demand function for the good Q is given by P = a - Q, where Q = q₁ + q_{2 .}

1. Solve for the equilibrium price, equilibrium quantity and the profit of each firm under a:

a.) quasi-competitive model

b.) cartel model

c.) cournot solution model

2. Compare the results of your calculations in item no.1 using a graphical illustration.

NOTE: Type only your answers. Please do not handwritten your answers.

Step 4
c. Profit of Firm 1: #1=pqi – c1
Profit of Firm 2: a2=pq2 – C2
Now, 71 is maximized with respect to q1:
dn
FOC :
2q1 – 92 – c = 0
dq
91= - 92
Now, 72 is maximized with respect to q2:
FOC :
dn
=a –
dq2
2q2 – q1 – c = 0
92=" - 1
а-с
Now, solving the above equations:
qı= -( -1)
а-с
91=
2
a-c
4
a-c
91*= units
Plugging in the value:
а-с
92 *=units
Now, price will be:
P-а —
*
+q2*)
За-2а+2с
3
a+2c
3
The profits will be:
A 1*=(P * –C)q1*
_ (a-c)
9
(а-с)?
9.

Step 2
a. The point of equilibrium occurs at: P = MC
Therefore,
– Q=c
а —
Q*=a
- C
Now,
P=a – Q
Р*-а — (а — с)
Profit is calculated as the difference between total revenue and total cost:
*=P * Q * –C*
—с (а — с) — с(а — с)
=0
Illustration:
APuice
MC = P
MR
Juanting
Step 3
b. The profit here is:
л3(а — Q(q1 + q2) — с1 — с2
=a(qı + 92) – (91² + qı² + 2q192) – c(qı + 92)
Now, profit is maximized with respect to q1
and
92:
FOC :
-(a – c) – 2q1 – 292 = 0
dqi
dn
%3(а — с) — 291 —242 3
= 0
dq2
Q*=units
Also, (q1 * -42*)=units
а-с
а-с
P*=a – Q*
a+c
T*=(P * –C)Q*
(а-с)?
4

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