1. Consider the following functions faced by a perfectly competitive firm: Demand: Q = 100 – 2P Total cost: TC = Q3 – 10Q2 + 100Q + 5 A. Derive the total profit function of the firm. B. Determine the level of output at which the firm maximizes T. C. Determine the maximum total profit.
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- A firm in a perfectly competitive industry has patented a newprocess for making widgets. The new process lowers the firm’saverage cost, meaning that this firm alone (although still aprice taker) can earn real economic profits in the long run. a. If the market price is $20 per widget and the firm’s marginalcost is given by MC=0.4q , where q is the dailywidget production for the firm, how many widgets willthe firm produce? b. Suppose a government study has found that the firm’snew process is polluting the air and estimates the socialmarginal cost of widget production by this firm to be. If the market price is still $20, what is thesocially optimal level of production for the firm? Whatshould be the rate of a government-imposed excise tax tobring about this optimal level of production? c. Graph your results.The table below shows the average cost (AC) for a purely competitive market. The average revenue (AR) is constant at RM5 per unit and the firm’s total fixed cost (TFC) is RM4. If the average revenue falls to RM3 per unit, calculate the firm’s new profit or loss at the equilibrium. Based on your answer, should the firm continue or stop the production? Justify. Output (Units) Total Revenue (RM) Average Cost (RM) Total Cost (RM) Marginal Cost (RM) Marginal Revenue (RM) 1 8.0 2 5.5 3 4.0 4 3.5 5 3.8 6 4.5 7 6.0In a purely competitive market at its long-run equilibrium, which of the following is not true? a The marginal benefit of the last unit of the product equals the marginal cost of producing that unit. b The maximum willingness of buyers to pay for the last unit of the product equals the minimum acceptable price for the seller of that unit. c Price equals marginal cost, and they are equal to the lowest attainable average cost of production. d The combined amount of consumer and producer surpluses is at its minimum possible.
- Consider a competitive industry with a large number of firms, all of which have identical cost functions c(y) = y2 + 1 if y > 0 and c(y) = 0 ify = 0. The demand curve for this industry is D(p)= 52-p.1. Find marginal cost and average cost functions.2. What is the competitive price in this market?3. What will be the number of firms in the industry?Suppose the competitive market price is $60, and a competitive firm’s total costs = q^2 - 6q + 990 and marginal cost = 2q - 6. a. Solve for the profit-maximizing (or loss minimizing) quantity (q*). b. What is the market equilibrium price? c. Should the competitive firm produce q*? Explain why using one of the four key questions and solutions. d. Does the competitive firm make a profit? Explain why using one of the four key questions and solutions. e. How much profit (or loss) does the competitive firm make?A firm sells its product in a perfectly competitive market. Its total cost function is: TC = 900 - 20Q + Q2where TC is total cost and Q is output level.a. Find the firm’s average total cost function. b. Find the firm’s average variable cost function. c. Find the firm’s marginal cost function. d. Given the price is $100, what is the profit-maximizing output level? e. Given the price is $100, what is the profit level? f. Over time, is there going to be entry or exit in this competitive market? Why?
- Suppose the market for coffee is characterized by perfect competition. Assume that all firms are identical.The long run average total cost (LATC) and long run Marginal cost function (LMC) functions for arepresentative firm are given as: LATC = Q + 5 + 25/Q and LMC = 2Q + 5. Total demand from all consumers in this market is given by P = 500 – Q What quantity will a firm produce in the long run?a. 10 unitsb. 15 unitsc. 20 unitsd. Zero unitse. 5 units 2. What is the price that each firm will change in the long run?a. $15b. $20c. $30d. $40e. $50 How many units will be traded in the market in the long run?a. 1000b. 970c. 950d. 900e. 485In a certain perfectly competitive market, there are 150 firms, and the short-run total cost function of each is given by Short Term Total Cost (q) = 3q³ - 16q² + 40q + 432 (note that "q" is the quantity produced by the firm). Besides that, any firm (active or potential entrant) can produce according to the total cost function Short Term Total Cost (q) = 2q³ - 16q² + 148q (desconsidering the entrance or exit of firms). Furthermore, the inverse aggregate demand function of this market corresponds to Pd(Q) = 676 - 0.56Q (which "Q" is the total quantity demanded). Based on this information, please check True or False in the arguments below: 1-The profit that each producer makes in the short-run competitive equilibrium is greater than the profit that each producer makes in the long-run competitive equilibrium. True or False? 2-In the long-term competitive equilibrium, there are 200 active firms in this market. True or False? 3-The price p* = 105 and the quantity Q* = 750 composes the…Consider a perfectly competitive market with the market demand functionQd = 1000 − 10pThere are many small, identical firms in the market. Each firm has the marginal cost function:MC = 10 + 10qand the average total cost function:ATC = 45/q + 10 + 5q(a) Suppose the equilibrium price is currently 30 (in the short run). Determine the quantity sold by eachfirm, the market equilibrium quantity, and the number of firms there must be in the market. Hint: Onceyou know the market quantity and quantity per firm, you can back out the number of firms.(b) If entry and exit is possible in the long run, determine long-run equilibrium price, quantity sold by eachfirm, the market equilibrium quantity, and the number of firms there will be
- 2. Consider a market with 90 firms, each firm has a short-run total cost function as follows: TC(q) = 5q2, and a marginal cost function: MC(q) = 10q. Market demand is given by equation Qd(p) = 200 - p. a) What is the fixed cost? Solve the average variable cost function in the short-run. b) What is the supply function of each firm? c) Solve for the short-run equilibrium outcome: P*, Q* and q*. d) What is one firm's economic profit in this market?2. Consider a market with 90 firms, each firm has a short-run total cost function as follows: TC(q) = 5q2, and a marginal cost function: MC(q) = 10q. Market demand is given by equation Qd(p) = 200 - p. a. What is the fixed cost? Solve the average variable cost function in the short-run. b. What is the supply function of each firm? c. Solve for the short-run equilibrium outcome: P*, Q* and q*. d. What is one firm's economic profit in this market? e. Consider a different market structure, where there is only one firm, interpreted as a monopolist, and then critically discuss the impact on equilibrium price and quantity. Discuss total surplus for these two types of market structures.The information below applies to a competitive firm that sells its output for $45 per unit. When the firm produces and sells 100 units of output, its average total cost is $24.5.When the firm produces and sells 101 units of output, its average total cost is $24.65. Suppose the firm is currently producing and selling 100 units of output. Should the firm increase its output to 101 units? a. Yes, because the marginal revenue exceeds the marginal cost. b. Yes, because the marginal revenue exceeds the average total cost c. No, because the marginal cost exceeds the marginal revenue. d. No, because the average total cost exceeds the marginal revenue.
