Answer to Question #313048 in Microeconomics for Gotlhe

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=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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