Please answer all parts and do not use ChatGPT or other AI tools. Please give me the solution and specific answers. Thanks! ## Problem (1)Firms 1 and 2 have total cost functions $ TC_1(q) = q^2 $ and $ TC_2(q) = \frac{q^2}{3} $ (with $ MC_1(q) = 2q $ and $ MC_2(q) = \frac{2q}{3} $ respectively). They are competing in quantities in a market with (inverse) demand $ p = 630 - 2Q $.Determine the market price in each of the following market organization scenarios:**(a) [C] Cournot-Nash Equilibrium**- They are competing in Cournot competition.**(b) [S] Stackelberg Equilibrium**- As in (a), but A is the leader and chooses the quantity first (and B chooses her quantity afterwards, observing A’s choice).**(c) [M] Collusion**- They collude as in a cartel, to maximize joint profits.**(d) [P] Perfect Competition Benchmark**- They behave perfectly competitively, as price takers.**(e) Calculate the DWL (dead-weight loss, inefficiency) in the Stackelberg equilibrium in (b).** - (WARNING: tedious calculations!)**(f) (MULTIPLE CHOICE QUESTION: NO calculation/explanation needed!)** Which of the following 6 market arrangements below …(i) Firm 1 operates as a monopoly (Firm 2 doesn’t exist at all)(ii) Firm 1 operates as a perfectly competitive firm (as a price taker!) (Firm 2 doesn’t exist at all)(iii) Firm 2 operates as a monopoly (Firm 1 doesn’t exist at all)(iv) Firm 2 operates as a perfectly competitive firm (as a price taker!) (Firm 1 doesn’t exist at all)(v) Firm 1 and Firm 2 collude (Scenario (c) above)(vi) Firm 1 and Firm 2 operate as perfectly competitive firms as price takers (Scenario (d) above)**Which scenario maximizes Total Surplus (TS)?** [ ]**Which scenario maximizes Producer Surplus (PS)?** [ ]**Which scenario minimizes Consumer Surplus (CS)?** [ ]

The cost function defines the relationship between two variables i.e. the inputs and their prices. It includes both fixed and variable costs. Total cost refers to the expenses incurred in the production of goods or services. Marginal cost refers to the additional cost incurred by the producer for producing an additional unit of output. “Since you have posted a question with multiple sub-parts, we will provide the solution only to the first three sub-parts as per our Q&A guidelines. Please repost the remaining sub-parts separately.”The total cost function of firm 1 is TC1=q12The total cost function of firm 2 is TC2=q223The demand function is P=630−2QUnder Cournot competition Q=q1+q2The profit function of Firm 1 will be π1=Pq1−TC1π1=(630−2q1−2q2)q1−q12π1=630q1−2q1q2−3q12The profit function of Firm 2 will be π2=Pq2−TC2π2=(630−2q1−2q2)q2−q223The profit function of firm 1 is π1=Pq1−TC1π1=(630−2q1−2q2)q1−q12π2=630q2−2q1q2−7q223Take the first-order derivative of the profit functions to ascertain the quantitiesdπ1dq1=630−2q2−6q16q1=630−2q2q1=105−q23 (1)dπ2dq2=630−2q1−14q2314q23=630−2q1q2=135−3q17 (2)Equating (1) and (2)q1=105−13(135−37q1)q1=105−45+q17q1−q17=60q1=70q2=135−3∗707q2=105The market price will be P=630−2(70+105)=$280Firm 1 is the leader and chooses the quantity firstThe profit function of Firm 1 will be π1=Pq1−TC1π1=(630−2q1−2q2)q1−q12π1=630q1−2q1q2−3q12Put equation (2) in the above profit functionπ1=630q1−2q1(135−3q17)−3q12π1=630q1−270q1+6q127−3q12π1=360q1−15q127Take the first-order derivative of the profit functiondπ1dq1=360−30q17360=30q17q1=84q2=135−3∗847q2=99The market price will be P=630−2(84+99)=$264Firm 1 and Firm 2 collude together to form a cartel. Since the cost of firm 2 is lowest, the total cost of firm 2 will be used to ascertain the price.The profit function will be π=PQ−TC2π=(630−2Q)Q−Q23π=630Q−2Q2−Q23π=630Q−7Q23Take the first-order derivative of the profit functiondπdQ=630−14Q314Q3=630Q=630(3)14Q=135The market price will be P=630−2(135)=$360(a) The market price under Cournot competition is $280(b) The market price under Stackleberg competition is $264(c) The market price under the cartel is $360

Business

Economics

PROBLEM (1) Firms 1 and 2 have total cost functions TC₁(q) = q² and TC₂ (q) = ²/3 (with MC₁(q) = 2q and MC₂ (q) =) respectively. They are competing in quantities in a market with (inverse) demand p = 630 - 20. Determine the market price in each of the following market organization scenarios: (a) [C] Cournot-Nash equilibrium They are competing in Cournot competition. (b) [S] Stackelberg Equilibrium As in (a), but A is the leader and chooses the quantity first (and B chooses her quantity afterwards, observing A's choice). (c) [M] Collusion They collude as in a cartel, to maximize joint profits.