Consider an industry with identical firms and production function y= (x12 + x22)1/2 The demand function...

Consider an industry with identical firms and production function y= (x1² + x2²)^1/2

The demand function is qD (p) = a − bp, where a > 0, b > 0. Compute the long run equilibrium number of firms in the market, and the quantity of output that each firm produces.

Solutions

Expert Solution

Assuming that the production function is

Each firm's cost minimization problem is to minimize where w and r are price of factors and respectively, subject to the constraint that

At equilibrium, the Marginal Rate of Technical Substitution (MRTS) = Ratio of the factor prices

Hence, the cost function of the firm is

Each firm's profit function is

The is the quantity of output produced by one firm. In the long run, let there be n such firms. The total output is:

Substituting the value of Q in the market demand function:

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider a competitive industry where all firms have identical cost functions C(y) = y^2 +1 if...

Consider a competitive industry where all firms have identical cost functions C(y) = y^2 +1 if y > 0 and C(0) = 0. Suppose that the demand curve for this industry is given by D(p) = 52 − p. (a) Find the individual supply curve of each firm. (b) Suppose there are n firms in the industry. Find the industry supply curve. (c) Find the price and quantity corresponding to a short-run market equilibrium assuming there are n firms in...

Consider an industry with n identical firms competing a l´a Cournot. Demand is P(Q) = 1...

Consider an industry with n identical firms competing a l´a Cournot. Demand is P(Q) = 1 − Q, and each firm’s total cost function is T C(qi) = cqi . (a) Find the limit of the total equilibrium output Q∗ (n) as n goes to infinity. (b) Suppose that n > 3 and 3 firms decide to merge. The new firm has the same total cost function as its predecessors. What is the condition on n that ensures that the...

Consider an industry with demand Q = a − p where 3 identical firms that compete...

Consider an industry with demand Q = a − p where 3 identical firms that compete a la Cournot. Each firm’s cost function is given by C = F + c q. Suppose two of the firms merge and that the merged firm’s cost function is given by C = F'+C'q, where F<F'<2F (a) Determine each firm’s market share before and after the merger. (b) Suppose that a = 10 and c = 3. Determine the Herfindahl index after the...

Consider two identical firms (no. 1 and no. 2) that face a linear market demand curve....

Consider two identical firms (no. 1 and no. 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 50 - 0.5Q. a. Find the Cournot equilibrium Q and P for each firm. b. Find the equilibrium Q and P for each firm assuming that the firms collude and share the profit equally. c. Contrast the efficiencies of the markets in (a) and (b) above.

Question 1: Demand in an industry is 1200 – Q/10. There are 20 identical firms in...

Question 1: Demand in an industry is 1200 – Q/10. There are 20 identical firms in a competitive fringe, each with the cost function: C(q) = 1000q + q2 . There is also a dominant firm with the cost function C(q) = b*q, where b is a constant, and b<1000. (a) What is the maximum possible value of b such that the fringe produces zero output? (b) Suppose b=500. Work out the equilibrium price and Consumer Surplus. (c) Suppose b=...

Consider an industry consisting of two firms which produce a homogeneous commodity. The industry demand function...

Consider an industry consisting of two firms which produce a homogeneous commodity. The industry demand function is Q= 100 − P, where Q is the quantity demanded and P is its price. The total cost functions are given as C1 = 50q1 for firm 1, and C2 = 60q2 for firm 2, where Q =q1 + q2. a. Suppose both firms are Cournot duopolists. Find and graph each firm's reaction function. What would be the equilibrium price, quantity supplied by...

1. There are identical firms with cost function ?(?) = ? 2 + 100. The market...

1. There are identical firms with cost function ?(?) = ? 2 + 100. The market demand is given by the following inverse demand function ? = −0.02? + 220. The industry is a constant cost industry. This is a competitive market where each firm takes the price as given, with $5 per unit tax levied on the producers. a) Calculate the firm’s MC, AC, AVC and supply ?(?). Graph the cost curves and the supply on a graph. b)...

Consider an industry with 2 firms whose total demand function is P(q1 +q2)=2 ,000−2(q1 +q2). The...

Consider an industry with 2 firms whose total demand function is P(q1 +q2)=2 ,000−2(q1 +q2). The marginal costs are fixed and equal to $400 for each firm; the fixed costs are zero. a. Find the Cournot equilibrium price and quantities. b. Find the Bertrand equilibrium price and quantities. c. Find the Stackelberg equilibrium price and quantities.

1. Suppose the demand function of an industry is P=100-0.5X and there are two firms A...

1. Suppose the demand function of an industry is P=100-0.5X and there are two firms A and B in it. Futher assume that the firm A has a constant cost function of CA = 5xA and firm B has an increasing cost function CB =0.5xB. (X= xA +xB ). a. What would the reaction function of each firm? b. What would be the profit of each firm? c. What would the out put of each firm? d. What would be...

In an industry where demand is Q = 120 – P and two identical firms have...

In an industry where demand is Q = 120 – P and two identical firms have MC = AC = 30 find the Cournot and the Stackelberg equilibriums and compare the corresponding market outcomes. Do consumers have a preference for one market structure over the other?

Subjects