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equilibrium pnces. QUESTION 3 inonopoli,Aic producer 0 two goods has a Jul H I IOW C0')1 Function ' XXXXXXXXXX (#+) () I I 0(:), where Qi and Q2 denote the quantities of Good I and Good 2....

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equilibrium pnces.
QUESTION 3
inonopoli,Aic producer 0
two goods has a Jul H I IOW C0')1 Function
' XXXXXXXXXX (#+) () I I 0(:),
where Qi and Q2 denote the quantities of Good I and Good 2. respectively. kind denote the corresponding prices then the demand equations are
P =5O0, 4-Q2 P2 = 30+2Q, —Qz Find the maximum profit if the firm is contracted to produce a total of 15 units of either type. Calculate the equilibrium value of 2 and interpret its meaning.
Answered Same Day Dec 20, 2021

Solution

Robert answered on Dec 20 2021
134 Votes
Q1
a.
maximise TR = P*Q
P= 20-2Q
TR= 20Q-2Q2
dTR/dQ= 0 = 20-4Q = 0
Q= 5
.
To maximise profits we need Mr = MC
MR = 20-4Q
Mc = 3Q2 -16Q +20.
20-4Q = 3Q2 -16Q +20.
3Q2 -12Q = 0
3Q*(Q- 4) = 0
So Q= 0 or Q= 4
MR at Q=4 = 20*4*4=4
MC at Q= 4 = 3*4*4 -16*4 +20= 4
Q2
We need to find total each MR and equate it to each MC
TR1= 50Q1-Q1^2
MR1= 50 -2Q1
MC1=2Q1 +3Q2
SO 50 -2Q1 =2Q +3Q21 or 50 = 4Q1 +3Q2
EQ 1
TR2= 95Q2-3Q2^2
MR2= 95-6Q2
MC2= 2Q2 +3Q1
SO 95-6Q2 = 2Q2 +3Q1 or 95 = 3Q1 +8Q2
eq 2
Solve Eq1 and 2 together to get
Q2= 10 and Q1 =5
So P1=50-5...
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