Question 1.
P= 200-10(Q1+Q2)
Total revenue for firm 1= TR1= P x Q1= 200Q1-10Q1(Q1+Q2)
MR1= Differentiation of TR1 wrt Q1= 200-20Q1-10Q2
Total revenue for firm 2= TR2= P x Q2= 200Q2-10Q2(Q1+Q2)
MR2= Differentiation of TR2 wrt Q2= 200-10Q1-20Q2
TC of firm 1= 100+40Q1
MC for firm 1(MC1)= Differentiate TC wrt Q1= 40
TC of firm 2= 80+60Q2
MC for firm 2(MC2)= Differentiate TC wrt Q2= 60
1.
For reaction of firm 1:
MR1= MC1
200-20Q1-10Q2= 40
20Q1+10Q2= 160
2Q1+Q2= 16 Equation 1
Q1= (16-Q2)/ 2 Reaction curve of firm 1
For reaction curve of firm 2:
MC2=MR2
60= 200-10Q1-20Q2
Q1+2Q2= 14 Equation 2
Q2= (14-Q1)/2 Reaction curve of firm 2
2.
For equilibrium level of output: Solve equation 1 and 2
Multiply 2 in equation 1 and then subtract it from equation 2:
Q1+2Q2-4Q1-2Q2= 14-32
-3Q1 = -18
Q1 = 6 Equilibrium quantity of firm 1
Put Q1= 6 in reaction curve of firm 2:
Q2= (14-6)/2= 8/2= 4 Equilibrium quantity of firm 2
3.
For equilibrium price:
P= 200-10(Q1+Q2)= 200-10(6+4)= 200-100= 100 Equilibrium price
4.
Profit for firm 1= P x Q1 - (100+40Q1)
Profit of firm 1 = 100 x 6 - 100-40(6)= 600-100-240= 260
Profit of firm 2= P x Q2 - 80-60Q2= 100 x 4 - 80-60(4)= 400-80-240= 80
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