Please help with a 3-part question for managerial economics... Notation: O = Aee

Question

Please help with a 3-part question for managerial economics...

Notation: O = Aeereeate Quantity and q = individual firm quantity Suppose we have a perfect competitive market for apple. The market demand for apple is given by Pc = 100 - 2Qc . The cost for each firm i in this competitive market to produce an apple is $10, so that the cost function for each firm is C= 10qi. What is the price Pc and quantity Qc in this competitive market? (Note that Qc =q1+...+qi) Now, suppose Firm 1 is the monopoly in the apple market. The market demand and cost function that is faced by Firm 1 is given by Pm = 100 - 2Qm and C = 10Qm respectively. What is the profit maximizing price Pm and Qm for Firm 1? Now, suppose Firm 2 enter the market such that the apple market become a duopoly. The demand function that is faced by both firms are Pd = 100 - 2Qd, where Qd is the sum of quantity that is produced by both Firm 1 and Firm 2 or (Qd = qx + q2). The cost function for Firm 1 and Firm 2 areC1 = 10q1 and C2 = 10q2 respectively. What is the price Pd and quantity Qd in this duopoly market ?

Explanation / Answer

1) In perfect competiton th edemand is equal to supply. Supply is nothing but marginal cost

100-2Q = 10

2Q=90

Q = 45

P =$10

2) Monopolist produces where MR = MC and chrages price where this quantiity cuts the demand function.

P =100-2Q

TR = PQ = 100Q-2Q2

MR = 100-4Q

MC = 10

100-4Q=10

4Q=90

Q = 22.5

P = 100-2x22.5

P = $55

3) Duopoly will behave same like monopoly. They will produce where MR = MC

P =100-2q1-2q2

TR = PQ = 100q1-2q12-2q1q2

MR1 = 100-4q1-2q2

MR2=100-4q2-2q1

MC = 10

MR1=MC

100-4q1-2q2=10

45=2q1+q2 Firm 1

45=2q2+q1 Firm 2

q2 = 45-2q1

SUbstitutte in second equation

45=2(45-2q1)+2q1

2q1=45

q1 = 22.5

q2=22.5

P = 100-2x45

P= $10

BOth firms will divide the market quantity where each will supply 22.5 units each at price $10.

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