In a Cournot duopoly model, the market demand curve is given by P = 100 - yI -y where y, is the amount of output firm 1 produces and y2 is firm 2's level of output. The co- function of firm 1 is c(y1) 75 +8y1. The cost function of firm 2 is c(y2) = 100 +12y2. The reaction function of firm 1 is y1 = - 0.5y2. The reaction function of firm 2 is y2 -0.5y1- In the Cournot equilibrium, firm 2 produces units of output and makes a producer

A duopoly faces an inverse market demand of P(Q) = 150−Q.Firm 1 has a constant marginal cost of MC1 (q1) = ​$30.Firm​ 2's constant marginal cost is MC2 (q2) =​ $60.Assume fixed costs are negligible for both firms. Calculate the output of each​ firm, market​ output, and price if there is​ (A) a collusive equilibrium or​ (B) a Cournot equilibrium.   ​(A) Collusive equilibrium ​(Enter your responses rounded to two decimal​ places)   The collusive equilibrium occurs where q1  equals ?and q2 equals ?   Market output is ?   The collusive equilibrium price is ?     ​(B) Cournot equilibrium ​(Enter your responses using rounded to two decimal​ places)   The​ Nash-Cournot equilibrium occurs where q1 equals ? and q2  equals ?   Market output is ?   The equilibrium occurs at a price of ? ​

Consider an industry with N firms that compete by setting the quantities of an identical product simultaneously. The resulting market price is given by: p = 1000 − 4Q. The total cost function of each firm is C(qi) = 50 + 20qi  . (a) Derive the output reaction of firm i to the belief that its rivals are jointly producing a total output of Q-i . Assuming that every firm produces the same quantity in equilibrium, use your answer to compute that quantity. (b) Suppose firms would enter (exit) this industry if the existing firms were making a profit (loss). Write down a mathematical equation, the solution to which would give you the equilibrium number of firms in this industry. You don’t have to solve this equation.

A duopoly faces a market demand of p= 120 - Q. Firm 1 has a constant marginal cost of MC' =S10. Firm 2's constant marginal cost is MC = S20. Calculate the output of each firm, market output, and price if there is (a) a collusive equilibrium or (b) a Cournot equilibrium. The collusive equilibrium occurs where q, equals and q, equals (Enter numeric responses using real numbers rounded to two decimal places) Market output is The collusive equilibrium price is S The Cournot-Nash equilibrium occurs where q, equals and q2 equals Market output is Furthermore, the Cournot equilibrium price is S

Consider a duopoly market, where two firms sell differentiated products, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices p, and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = SG+P1)and D2 (P1, P2)= S(;+-P2), where S > 0 and the parameter t > 0 measures the 2t 2t degree of product differentiation. Both firms have constant marginal cost c> 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profit of the two firms. (b) From the demand functions, qi= D¡ (p; , p¡ )= SG+P), derive the residual inverse demand functions: p; = P; (qi , p¡) (work out: P; (qi , P;)). Show that for t > 0, P;(qi , P;) is downward 2t aPi (qi ,Pj) . sloping, i.e., c, i.e., firm į has market power. %3D (c) Calculate the limits of the equilibrium prices and profit as t → 0 ? What is P; (qi , p;) as t → 0? Is it downward sloping?…

Determine the reaction function for firm 1 in a Cournot duopoly with an inverse demand curve given by: P = 12 - (Q1+ Q2) and zero costs.

Suppose the iceberg lettuce industry is a Cournot duopoly with two firms: Xtra Leafy (a) and Yummy Farms (y). Xtra Leafy produces q units of output and Yummy Farms produces qy units of output. Aggregate market output is Q = x + y. The (inverse) market demand schedule is: p = 176 - 2Q Both firms have identical cost structures: MC = MC₁ = ATC₂ = ATC₁ = $12 Find Xtra Leafy's Cournot reaction function of the form: 9x = a + bay Where "a" is the reaction function's intercept and "b" is its slope. Note: Please review the formatting instructions above. If any value is negative, be sure to include its negative sign. a. a= b. b = Hint: One of your answers will be negative. Think about why.

The graph below presents the Short Run Aggregate Supply Curve and the Aggregate Demand Curve for Sanaton in 2001. Based on this graph, answer the questions: What is equilibrium output (Real GDP)? What is equilibrium price level?

(4) Firm l's cost function is C1(q1) = q1 and firm 2's cost function is C2(q2) = 2q2. Consider a duopoly selling in a market with inverse demand function p = 12 q. (a) Assume firms choose output simultaneously (Cournot model). Compute the equilibrium quantities and the market price in a Nash equilibrium. (b) Now assume that firm 1 is a leader and chooses its output q1 first. Then, firm 2 chooses its output q2 after observing q1 (Stackelberg model). Find a subgame-perfect Nash equilibrium of this game. Carefully specify the strategies for firm 1 and firm 2. What quantities are produced in equilibrium and what is the market price in equilibrium?

cost function is c(y) An industry has two firms. Firm 1's cost function is c(y) = 3y + 200 and firm 2's 3y + 100. The demand curve for the output of this industry is a downward-sloping straight line. In a Cournot equilibrium, where both firms produce positive amounts of output: = The firm with higher fixed costs produces more. Both firms produce the same amount of output. There is less output than there would be if the firms colluded to maximize joint profits. It is not possible to tell because the demand function is not specified. The firm with lower fixed costs produces more.