Question #313048

firm has the production function: TC=120-0.1Q^2 , and sells its output in two separate markets with demand functions: Q1=800-2p1


Q2=750-2.5p2



;


(i) Find the profit-maximizing output and sales in each market [8 marks]


(ii) Use the Hessian matrix to check if the second-order conditions for a maximum a



1
Expert's answer
2022-03-17T09:38:18-0400

TC=1200.1Q2TC=120-0.1Q^2

MC= 0.2Q

Q1=8002P1Q1=800-2P_1

P1=4000.5Q1P_1= 400-0.5Q_1

TR= P.Q= Q(400-0.5Q1_1 )

=400Q-0.5Q12^2

MR1=4000.1Q1_1=400-0.1Q_1

Equilibrium at market 1

MR=MC

0.2Q1=400-0.1Q1

0.3Q1= 400

Q1= 1333.33

P1=4000.5(1333.33)=266.67P_1= 400-0.5(1333.33)= 266.67

Equilibrium at market 1

Q2=7502.5P2Q_2=750-2.5P_2

P2=3000.4Q2P_2= 300-0.4Q_2

MR= 300- 0.8Q2

300- 0.8Q2=0.2Q

Q= 300

P2=3000.4(300)=180P_2= 300-0.4(300)= 180


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