Show that the long-run equilibrium number of firms is indeterminate when all firms in the industry share the same constant returns-to-scale technology and face the same factor prices.
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4.5 Show that the long-run equilibrium number of firms is indeterminate when all firms in the industry
share the same constant returns-to-scale technology and face the same factor prices.
4.7 Technology for producing q gives rise to the cost function c(q) = aq + bg. The market demand for
qisp =a - Bq.
(a) If a>0, if b < 0, and if there are J firms in the industry, what is the short-run
market price
b) Ifa> 0 and b <0, what is the long-run equilibrium market price and number of firms? Explain.
() Ifa>0and b > 0, what is the long-un equilibrium market price and number of firms? Explain.
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- The figure deplcts the demand curve for Beautiful Cars, and the marginal cost and Isoprofit curves of the car manufacturer. The quantity and price at polnt E are (Q*. P*) - (30, 5,500). Suppose now that the firm Increases the price to 5,550 and chooses the corresponding level of output from the demand function at the new price. Based on this Information, whlch of the following Is correct? 8,000 Demand curve 100 Quantity of cars, O O The firm will sell 30 cars at the higher price. O The firm's profit remains the same. O The quantity of cars produced reduced. O Tho firm's profit is now incroasod Price, Marginal cost ($)Suppose that the market demand for a product is given by ( A > 0 and B > 0). Suppose QABP=-also that in a competitive industry the typical firm’s cost function is given by (k > 2()Cqkaqbq=++0, a > 0 and b > 0).(a) Calculate the long-run equilibrium market price and the output for the typical firm. (b) Calculate the equilibrium number of firms in the market.(c) Describe how changes in the demand parameters A and B affect the equilibrium number of firms in this market. Explain your results intuitively.Short-run supply and long-run equilibrium Consiber the competitive market for rhodium. Assume that no matter how many firms operate in the induatry, every firm is identical and faces the same marpinal cost (MC), averapt total cost (ATC), and average variable cost (AVC ) curves plotted in the following praph. The following graph plots the market demand curve for thodium. If there were 10 firms in this market, the short-run equilibrium price of rhodium would be per pound. At that price, firms in this industry would. Therefore, in the long run, firms would the rhodium market. Because you know that competitive firms earn economic profit in the long run, you know the long-run equilibrium price must be per pound. From the graph, you can see that this means there will be firms operating in the rhodium industry in long-run equilibrium. True or False: Assuming implicit costs are positive, each of the firms operating in this industry in the long run earns positive accounting profit. True False
- The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs MC ($) Quantity of Ear Buds 5 10 15 20 25 30 35 40 2.00 2.45 3.55 4.00 5.50 5.98 8.52 pairs ATC ($) 2.00 2.00 2.15 2.50 2.80 3.25 3.64 4.25 Check my work Instructions: In part a, enter your answer as the closest given whole number. In parts b-d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? b. At the profit-maximizing quantity, what is the total cost of producing ear buds? c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what will Buddies profit or loss be per week? d. Now assume the market price is $5.50 per pair, and Buddies produces the…Suppose that each firm in a competitive industry has the following costs: Totalcost:TC=50+1/2q2 Marginalcost:MC=q where q is an individual firm's 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 firm's 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 qfrom 5 to 15. Atwhat quantity is average-total-cost curve at its minimum? What is marginal cost and averagetotal cost at that quantity?c. Give the equation for each firm's 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 firm's profit or loss. Is there incentive for firms to…3. Assume that the manufacturing of generic medicine XYZ is a perfectly competitive industry. Suppose that the annual demand for this medicine is given by: QD = 1,450 - 30P. There are exactly a hundred manufacturers in the market. Each manufacturer has the same production costs. These are described by 5 total and marginal cost functions of: C(q) = q² + 25q + 2.5 and MC(q) = 5q + 25. a. Show that an individual firm in this industry maximizes profit by producing: q = -5 +0.2P. b. Derive the industry supply curve and show that it is: QS = -500 + 20P. c. Find the market price and aggregate quantity traded at the equilibrium price. d. How much output does each firm produce? e. f. Calculate each firm's profit. Using market demand and supply functions (QD, QS): i. Graphically represent the equilibrium in the market; ii. Calculate producer surplus; and iii. Consumer surplus in this competitive equilibrium. Li 11. total cost and demand of an individual firm in
- For Parts (A) through (C) below, refer to the figure and table below. The figure below displays the short-run MC, AVC, and AC for a firm. The table displays the MC, AVC, and AC at specific levels of output for the same firm. q 0 4 6 MC(q) AVC(q) 10 10 6 6 14 8 AC(q) ∞ 15 14 MC(q) B) If the price of the good is $15 (p = 15), select the statement below that is true: A. The firm's profit in the short-run will be negative ( 0) in the short-run, what is the lowest the price (p) could be? D. The firm's profit in the short-run will be positive (π > 0). E. There is not enough information to know whether the profit will be greater than, less than, or equal to zero. AVC(q) > 8 60.00 9An industry with many stores offer laminating as a service to their customers. Suppose that each store that offers this service has a cost function C(q)=50+0.5q+0.08q2 and a marginal costMC=0.5+0.16q. Suppose the going rate for laminating is R8.50 per sleeve which each store is compelled to charge. 1. Is the industry in long run equilibrium? Use calculations to either prove or disprove your findings.1. Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by P₁ and P₂. The production cost is C (Q₁, Q2) = Q +3Q/²2 where Q₁ and Q₂ represent the output levels of product 1 and product 2. (e) Find the maximum proifit that this firm can earn as a function of P₁ and P₂.
- The diagram illustrates the demand curve, isoprofit curves and the marginal cost curve of MQ2020, a luxury car manufactured by MQ Motors. Assume that MQ Motors currently chooses to operate at Point E. Which statement correctly describes the market of MQ2020? 10,000 Price, marginal cost ($) A P = $5,440 Po B 0 0 E 10 20 Q" = 32 D Qo Quantity of cars, Q Select one: a. Producer surplus is $63,360 as it equals MQ Motors' profits. Marginal cost Isoprofit curve: $150,000 Isoprofit curve: $63,360 Demand curve 120 O b. The amount of consumer surplus is the area ADP o. c. The amount of total surplus is the area ABD. Od. All possible gains from trade are being achieved as MQ Motors operates at its profit-maximising output and price. O e. The amount of MQ Motors' producer surplus is the area BCEP*.1. There is an industry consisting of 12 firms, each with total cost function given by TC(q) 3q² - 2q +867, where the fixed costs are non-sunk. The demand for the industry's product is given by Q¹ (p) = 448 - p per month. Firms are price takers. (a) Find the short-term equilibrium price, demand, the quantity produced by each firm, as well as firm's profit. What is the consumer surplus? What about the producer's surplus? (b) The government urgently needs to collect some extra tax revenues in the next four months to meet debt payments. This implies that it needs to collect the amount of T = 1000 per month from the industry. Calculate the tax level needed to raise this revenue depending on the type of tax. Which tax type is the better from a welfare perspective? i. An output tax of t per unit sold imposed on the firms. ii. 7-percent tax on firms' profits.Consider a competitive industry with a large number of firms, all ofwhich have identical cost functions c(y) = y2 + 1 for y > 0 and c(0) = 0. Supposethat initially the demand curve for this industry is given by D(p) = 52 − p.(a) What is the supply curve of an individual firm?(b) If there are n number of firms, what is the industry supply curve?(c) What is the smallest price at which the product can be sold?(d) Based on your answers to parts (a)-(c), explain in detail theequilibrium points based on the market activity with respect to the price, firmand industry.
