4.(a) Consider a homogeneous goods industry where two firms operate and the lineardemand is given by p(y₁ + y2) = a - b(y₁ + y2), where p is the market price, and y₁ (y2) is theoutput produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the bestresponses (reaction curve) for firm 1 and firm 2. Explain the term best response (reactioncurve). Illustrate the best responses in a diagram.ANDc) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantitydemanded and p is the market price. Firm 1 is the leader and has a cost function c₁(y₁)=cy₁while firm 2 is the follower with a cost function c₂(y2Firm 1 sets its price tomaximise its profit. Firm 1 correctly forecasts that the follower takes the price leader'schosen price as given (price taker) and chooses output so as to maximise its own profit.Write down the profit function of the follower. Calculate the profit maximising quantity thatthe follower selects given the leader's chosen price p (i.e., calculate the follower's supplycurve S(p)). Interpret the solution to the profit maximising problem.d) The leader is facing the residual demand curve R(p)=D(p)-S(p) with D(p) and S(p) asdefined in (c) above. Calculate the leader's residual demand curve using the result in (c).Solve for p as a function of the leader's output y₁, i.e. the inverse demand function facing theleader. Write down the profit function of the leader and find the profit-maximising level ofoutput.

(a) Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y₁ + y2) = a - b(y₁ + y2), where p is the market price, and y₁ (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram.

(a) Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y₁ + y2) = a - b(y₁ + y2), where p is the market price, and y₁ (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram.

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter13: Firms In Competitive Markets

Section: Chapter Questions

Problem 8PA

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Suppose that each firm in a competitive industry has the following costs: Total cost: TC = 50 + q2 Marginal cost: MC = q where q is an individual firms quantity produced. The market demand curve for this product is Demand:QD = 120 P where P is the price and Q is the total quantity of the good. Currently, there are 9 firms in the market. a. What is each firms fixed cost? What is its variable cost? Give the equation for average total cost. b. Graph average-total-cost curve and the marginal-cost curve for q from 5 to 15. At what quantity is average-total-cost curve at its minimum? What is marginal cost and average total cost at that quantity? c Give the equation for each firms supply curve. d. Give the equation for the market supply curve for the short run in which the number of firms is fixed. e. What is the equilibrium price and quantity for this market in the short run? f. In this equilibrium, how much does each firm produce? Calculate each firms profit or loss. Is there incentive for firms to enter or exit? g. In the long run with free entry and exit, what is the equilibrium price and quantity in this market? h. In this long-run equilibrium, how much does each firm produce? How many firms are in the market?
2) Cost functionsConsider the following total cost function for an individual firm: C(q)= 10 +q + ¼ q^2 a- At what level of output is average cost at its lowest?b- Draw a graph showing firm average cost against quantity.c- Suppose that there is an industry with two identical firms, with this cost function. What is the industry total cost curve? What is the industry marginal cost curve?d- Suppose these two firms together act in a perfectly competitive manner. What is the price level in the case where these firms act perfectly competitively? What are the profits of the firms given perfectly competitive pricing?
1. In principle, how do we determine a perfectly competitive firm's profit-maximizing output and maximum profits given information about the market clearing price, and about the marginal cost and average total cost curves of the firm? Explain in words. 2. Can a firm make losses by producing the rate of output at which marginal revenue equals marginal cost? Why? 3. What determines the perfect competitor's supply curve? How is the industry supply curve found? 4. Why would it be economically inefficient for a firm to charge the price of a good greater than its marginal cost? 5. What is a price taker? Discuss the assumptions used to obtain the perfectly competitive model. 6. Why would economies of scale be a barrier to entry? 7. What is the main difference between the demand curves for the perfect competitor and the monopolist? 8. How does a monopoly maximize profits? What price does it charge? 9. Explain what will happen if firms in a monopolistically competitive industry are earning…
Question #1: Assume agricultural products are identical and there are many sellers and buyers of agriculture products:a. State the profit maximizing condition for each seller of agricultural products.b. Graphically, show the market equilibrium of the industry and a seller where economic profits equal zero. Please include marginalrevenues, demand curve, price and quantity at the equilibrium.c. From part b above, if the number of buyers increases, show the new short run equilibrium for a seller and the industry as awhole.
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A5 5. Suppose the market is perfectly competitive. The equilibrium market price P = $20. A consumer's willingness to pay (WTP) is WTP = 30 - q. (a) How much this consumer will buy and wh (b) How much a typical firm will produce the firm's marginal cost MC = 2q. If the average total cost is ATC = q, can you tell if this firm is making positive, negative, or zero economic profit (c) It is assumed here that all firms are identical. In what sense are they identica (d) Suppose now that one firm's marginal cost is: MC = 25/q. Can this industry still remain perfectly competitive? Why not?l?s?y?
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Figure 7.1 shows a ﬁrm’s total revenue and total cost curves. If the ﬁrm were producing Q1, it should a. expand output to Q2 to maximize proﬁt. b. reduce output to zero to maximize proﬁt. c. expand output to Q3 to maximize proﬁt. d. expand output beyond Q3 to maximize proﬁt. e. continue to produce Q1, which is the proﬁt-maximizing output.
5) If average total cost is $50 and average fixed cost is $15 when output is 20 units, then the firm's total variable cost at that level of output is The equilibrium price is likely to increase and profits are likely to increase The equilibrium price is likely to remain unchanged and profits are likely to increase The equilibrium price is likely to decrease and profits are likely to decrease The equilibrium price is likely to increase and profits are likely to remain unchanged