1. Two profit-maximising firms call them firm 1 and firm 2- compete in quantities.Before the firms choose their quantities, firm 1 has the option to spend money onadvertising, which allows differentiating the two products. That is, firm 1 choosesa € [0, 1] (i.e., 0≤ a ≤ 1) and pays ca, with c> 0. The two firms then face the followinginverse demand functions:P₁ = 1-q₁ (1-a)q2 and p2=1-92-(1-a)9₁.There is no cost of production so the profit of firm 1 is #₁ = pigi - ca and the profit offirm 2 is #2 = P292.(a)(c)(d)(b)Without doing any calculation, briefly explain what the market struc-ture would be if firm 1 one chose not to advertise at all (a = 0) and if it chose themaximal amount of advertising (a = 1). [max: 50 words]For any value of a € [0, 1], calculate the equilibrium quantities.Calculate the optimal level of advertising for firm 1.Briefly provide intuition for your results. [max: 50 words]And here is an example. When solving for the question given above, You can refer to theformat:There are three profit-maximising firms that compete in prices. Each firm i = 1,2,3produces good i and faces the demand function qi= 12-3pi+ji Pj. For each firm i,the cost of producing a quantity q is cq, where c₁ = 2, c2 = 4, and c3 = 6.(a) Find the equilibrium prices and quantities.(b) Suppose that firms 2 and 3 merge to become firm A and that their merger resultsin efficiency gains that halve the cost of producing goods 2 and 3; that is, c₂ = 2and c3 = 3. Calculate the new equilibrium prices and quantities.(c) How much profit did the merger generate for the firms involved?(d) i. Did the outsider (firm 1) benefit from the merger?ii. Provide intuition for your result in (i). [max: 50 words](e) Without doing any additional calculations, determine whether a competition au-thority would be likely to block this merger. [max: 50 words] 1. (a) The profit of firm 1 isThe first-order condition givesThe profit of firm 2 isThe profit of firm 3 is₁ (123p1 + P2 + P3) (P12)=071дру6p₁ = P2 + P3 + 18.The first-order condition gives= −3p₁ +6+12 - 3p1 + P2 +P3 = 0T2 (12-3p2 + P₁+P3) (P24)On1др16p2 = P1+P3 + 24.TA ==The first-order condition gives-3p2+12+12-3p2 + P₁+P3 = 0T3 = (12-3p3 + P1+P2) (P3-6)ӘлзOp36p3 = P1+P2 + 30.= 92(P2 − 2) + 93 (P3 − 3) == -3p3 +6+12-3p3 +P1+P2 = 0(3)Using Wolfram Alpha to solve the system of linear equations (1)-(3) for p₁, p2, andP3 gives(P1, P2, P3) =The equilibrium quantities are36 48,6,10891 = 12-3p1 +p2 + P3 = 12-792 = 12-3p2 + P1+P3 = 12-18+(e) The joint profit of firms 2 and 3 before the merger is7₂ +3 = 92₂(P2 - 4) + 93 (P3 − 6) =The profit of firm A after the merger is76 141 54 119+11 44 11 44The profit generated by the merger is8571 696242 4936793 = 12-3p3 + P1 + P2 = 12 - + +6=144 367 7= 6-2+≈(5.14, 6, 6.86).251, 54711,858=+6+186 69677 4921.21.48 668787+18(91,92,93)= (60,6, 1/0) ≈ (9.43, 6, 2.57).48= 614.20.10716 6426 8571+484 484 242189.432.57(1)≈35.42.

"since you have posted the question with multiple subparts , we will solve the first three subparts…

1. Two profit-maximising firms call them firm 1 and firm 2- compete in quantities. Before the firms choose their quantities, firm 1 has the option to spend money on advertising, which allows differentiating the two products. That is, firm 1 chooses a € [0, 1] (i.e., 0≤ a ≤ 1) and pays ca, with c> 0. The two firms then face the following inverse demand functions: P₁ = 1-q₁-(1-a)q2 and p2=1-92-(1-a)g₁. There is no cost of production so the profit of firm 1 is #1 = P191-ca and the profit of firm 2 is #2 = P292- (a) (c) (b) Without doing any calculation, briefly explain what the market struc- ture would be if firm 1 one chose not to advertise at all (a = 0) and if it chose the maximal amount of advertising (a = 1). [max: 50 words] For any value of a € [0, 1], calculate the equilibrium quantities. Calculate the optimal level of advertising for firm 1.

1. Two profit-maximising firms call them firm 1 and firm 2- compete in quantities. Before the firms choose their quantities, firm 1 has the option to spend money on advertising, which allows differentiating the two products. That is, firm 1 chooses a € [0, 1] (i.e., 0≤ a ≤ 1) and pays ca, with c> 0. The two firms then face the following inverse demand functions: P₁ = 1-q₁-(1-a)q2 and p2=1-92-(1-a)g₁. There is no cost of production so the profit of firm 1 is #1 = P191-ca and the profit of firm 2 is #2 = P292- (a) (c) (b) Without doing any calculation, briefly explain what the market struc- ture would be if firm 1 one chose not to advertise at all (a = 0) and if it chose the maximal amount of advertising (a = 1). [max: 50 words] For any value of a € [0, 1], calculate the equilibrium quantities. Calculate the optimal level of advertising for firm 1.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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