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
"TC=120-0.1Q^2"
MC= 0.2Q
"Q1=800-2P_1"
"P_1= 400-0.5Q_1"
TR= P.Q= Q(400-0.5Q"_1" )
=400Q-0.5Q1"^2"
MR"_1=400-0.1Q_1"
Equilibrium at market 1
MR=MC
0.2Q1=400-0.1Q1
0.3Q1= 400
Q1= 1333.33
"P_1= 400-0.5(1333.33)= 266.67"
Equilibrium at market 1
"Q_2=750-2.5P_2"
"P_2= 300-0.4Q_2"
MR= 300- 0.8Q2
300- 0.8Q2=0.2Q
Q= 300
"P_2= 300-0.4(300)= 180"
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