Consider aduopolistic market wheredemand is given byP= 36 - 3Q, where Q = Q1 + Q2....

Consider aduopolistic market wheredemand is given byP= 36 - 3Q, where Q = Q1 + Q2. For each duopolist, the constant per unit marginal cost is $18/unit and fixed costs are zero. a. Assume first that the duopolists hold Cournot conjectures when they make their choices. Find the Cournot equilibrium price, quantity, and profits. b. Now find the equilibrium price, quantity, and profits assuming the duopolistic competition as Bertrand. c. Find the equilibrium um price, quantity, and profit for each firm, assuming the firms act as a Stackelberg leader and follower, with Firm 1 as the leader.

Expert Solution

Rahul Sunny answered 5 months ago

Consider a market where the inverse demand function is p =100 – Q, Q = q1+q2....

Consider a market where the inverse demand function is p =100 – Q, Q = q1+q2. Both firms in the market have a constant marginal cost of $10 and no fixed costs. Suppose these two firms are engaged in Cournot competition. Now answer the following questions: a) Define best response function. Find the best response function for each firm. b) Find Cournot-Nash equilibrium quantities and price. c) Compare Cournot solution with monopoly and perfect competitive solutions.

Given a utility function: U(q1, q2) = q1 + q 2^2 where q1 and q2 is...

Given a utility function: U(q1, q2) = q1 + q 2^2 where q1 and q2 is the consumption of good 1 and good 2 respectively. and the budget constraint: p1q1 + p2q2 = Y where p1 and p2 are prices of good 1 and good 2 respectively, Y is the consumer’s income a. Holding p2 and Y fixed, find the demand function for good 2. b. Holding p1 and p2 fixed, find the functional form of the Engel curve for...

Market demand curve for a pair of Cournot duopolist is given as P = 36-3Q where...

Market demand curve for a pair of Cournot duopolist is given as P = 36-3Q where Q = q1 + q2. The constant per unit marginal cost is 18 for each firm. Find the best response function for each firm, the Cournot equilibrium price and market quantity. What is the Cournot Lerner Index?

Consider the following inverse demand function, p(Q) = a-bQ, Q = q1 +q2, where a and...

Consider the following inverse demand function, p(Q) = a-bQ, Q = q1 +q2, where a and b are positive parameters and qi denotes firm i's output, i = 1, 2. Assume that the total cost of firm i is cqi2/2, with c > 0. Firms choose quantities simultaneously and non cooperatively (Cournot competition). The Cournot game described above is infinitely repeated. Firms use grim trigger strategies (infinite Nash reversion). Firms discount future profits at a rate r > 0. a)...

Duopoly quantity-setting firms face the market demand: P = 300–Q where Q = Q1 + Q2....

Duopoly quantity-setting firms face the market demand: P = 300–Q where Q = Q1 + Q2. Each firm has a marginal cost of $30 per unit and zero fixed costs. (a) What are the quantities chosen by each firm in the Cournot equilibrium? What is the market price? (b) What are the quantities chosen by each firm in the Stackelberg equilibrium, when Firm 1 moves first? What is the market price? How does this market price compare to the market...

Consider a market where inverse demand is given by P = 40 − Q, where Q...

Consider a market where inverse demand is given by P = 40 − Q, where Q is the total quantity produced. This market is served by two firms, F1 and F2, who each produce a homogeneous good at constant marginal cost c = $4. You are asked to analyze how market outcomes vary with industry conduct: that is, the way in which firms in the industry compete (or don’t). First assume that F1 and F2 engage in Bertrand competition. 1....

Given a utility function: U(q1,q2)=q1 +βlnq2 where q1 and q2 is the consumption of good 1...

Given a utility function: U(q1,q2)=q1 +βlnq2 where q1 and q2 is the consumption of good 1 and good 2 respectively, β is a positive constant, and the budget constraint: p1q1 + p2q2 = Y where p1 and p2 are prices of good 1 and good 2 respectively, Y is the consumer’s income a. Holding p2 and Y fixed, find the demand function for good 2. b. Holding p1 and p2 fixed, find the functional form of the Engel curve for...

Consider three point charges q1=q2=q3=Q. If q1 and q2 are located on the Y-axis at y=+a...

Consider three point charges q1=q2=q3=Q. If q1 and q2 are located on the Y-axis at y=+a and y= -a and the third charge is located at a point x on the X-axis. (a) find the force E exerted by q1 and q2 on q3 when q3 is located at the origin (b) what is the force F on q3 when q3 is located at an arbitrary value of x on the X-axis? (c) for what value of x is the...

1. Consider two firms facing the demand curve P=50-5Q where Q = Q1 + Q2. The...

1. Consider two firms facing the demand curve P=50-5Q where Q = Q1 + Q2. The firms’ cost functions are C1(Q1) = 20+10Q1 and C2(Q2) = 10+12Q2. Suppose both firms entered the industry. a) What is the joint profit-maximizing level of output? b) What is total production (Q1+Q2) at the joint profit-maximizing level? c) What is firm 1's output if they behave non-cooperatively (Cournet Model)? d) What is firm 2's output if they behave non-cooperatively (Cournet Model)? e) How much...

Consider a perfectly competitive market where the market demand curve is given by Q = 76−8P...

Consider a perfectly competitive market where the market demand curve is given by Q = 76−8P and the market supply curve is given by Q=−8+4P. In the situations (d), determine the following items (i-viii) (d) A market with price ceiling C = 5. i) The quantity sold in the market. ii) The price that consumers pay (before all taxes/subsidies). iii) The price that producers receive (after all taxes/subsidies). iv) The range of possible consumer surplus values. v) The range of...

Question