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- A firm’s profit is given by the following function, which maps output q ≥ 0 onto profit (revenue minus cost). π(q) = 11q − (q 2 + 2q + 10) = −q 2 + 9q − 10, The firm is constrained by a quota such that output q cannot be greater than a value Q. (a) What is the domain of this profit function? 1 of 2 ECON10071/20071 - 2020/21 (b) Given this, what is (global) profit maximising output when (i) Q = 6, and when (ii) Q = 2.2. ABC Manufacturing has provided you with their demand function Qd = 2000-2p and supply function Qs = 60+5p, please answer the following questions: a. What is the company’s marginal revenue function? b. At level of output is profits maximized? c. At what price is profits maximized? d. What is total revenue at the profit maximization level of output?Consider a competitive firm with a short-run cost function C(q) = 100q−q2 + 1/5q3 +450. (a) Suppose that the market price is $205. Find the optimal output. Find the profit or loss at the optimal output. Will the firm stay or shutdown? Why? (b) Suppose that the market price is $105. Find the optimal output. Find the profit or loss at the optimal output. Will the firm stay or shutdown? Why? (c) Suppose that the market price is $205 and there is a tax of $65 per unit produced. Find the optimal output. Find the profit or loss at the optimal output. Will the firm stay or shutdown? Why?
- For a firm with market power, what is the marginal revenue gained when one more unit of output is sold? Question 19Answer a. The price at which the extra unit is sold plus the rise in revenue from selling other units at a higher price b. The price of the unit of output sold minus the production cost of that unit c. The price of the unit of output sold d. The price at which the extra unit is sold less the drop in revenue from selling other units at a lower price2. 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. Solve for the short-run equilibrium outcome: P*, Q* and q*. b. What is one firm's economic profit in this market? c. 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.A firm faces the following average revenue (demand) curve:P = 120 − 0.02Qwhere Q is weekly production and P is price, measured in cents per unit. The firm’s costfunction is given by C = 60Q + 25,000. Assume that the firm maximizes profits.i. What is the level of production, price, and total profit per week?ii. If the government decides to levy a tax of 14 cents per unit on this product, what will be thenew level of production, price, and profit?b. The United States currently imports all of its coffee. The annual demand for coffee by U.S.consumers is given by the demand curve Q = 250 – 10P, where Q is quantity (in millions ofpounds) and P is the market price per pound of coffee. World producers can harvest and shipcoffee to U.S. distributors at a constant marginal (= average) cost of $8 per pound. U.S.distributors can in turn distribute coffee for a constant $2 per pound. The U.S. coffee market iscompetitive. Congress is considering a tariff on coffee imports of $2 per pound.i. If there…
- a. A firm faces the following average revenue (demand) curve:P = 120 − 0.02Qwhere Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C = 60Q + 25,000. Assume that the firm maximizes profits. i. What is the level of production, price, and total profit per week?ii. If the government decides to levy a tax of 14 cents per unit on this product, what will be the new level of production, price, and profit?1- Suppose that the total cost function of a firm is given as follows;TC = 500 + 2Q2And the price of the firm’s product is determined by the market equilibrium at $100.a- Set the profit maximizing condition . Find the profit maximizing output level for this firm .b- What is the total revenue ?c- What is the total cost ?d- What is the profit earned by the firm ?e- Illustrate your answer by using a well-labeled graph .f- Denote the break even price level with Pb on the same graph .g- Denote the shut down price level with Ps on the same graph.h- Show the firm’s supply curve on the same graph .i- Does the firm function in short-run or long-run ? Why ?1. Imagine that there is an industry for a particular product where the demand for this product is given by P = 100-X. There are two factors of production, capital K and labor L; the price of each will be $1 throughout. The firms all have identical technology, which is given by a fixed coefficients production function: where Y is the level of output and a is some constant from (0, 1). Each firm has fixed costs of 16. (a) Suppose there are precisely six firms in this industry; they can exit if they are unprofitable, but no firms can enter. What is the long-run equilibrium in this case? (Even though there are only six firms, they all entertain competitive conjectures about their effect on various prices.) (b) Suppose there is free entry into this industry. What is the long-run equilibrium? 2. Suppose one firm in a general equilibrium economy has a technology with free disposal Prove that Walrasian equilibrium prices are nonnegative.
- 1) There are 1000 pear producers that have identical cost functions, where q is the number of crates of pear produced. The producers operate in a perfectly competitive market. The supply curve of each producer is _______ The total supply curve for the market is _______ At a price of 100, the elasticity of supply for the market is _______ , meaning that supply is _______. (see image for answer options) 2) A firm can sell its output at the price p=10 per unit. The firm’s cost function is C=16+q2 To maximize its profit, the firm chooses to produce q=___________. The profit of this firm is $_____________Suppose the demand for a product X produced by a company AAA is given by the following function: QX = 2000 - 250*PX. At what price per item of the product X (EUR) can this copmany maximize its total revenues? Fill in the Table gaps: Demand function Price function Total Revenue (EUR) Marginal Revenue (EUR) Quantity Price per product (EUR) Q = 2000 - 250P P = ? TR = Q*P MR = dTR/dQ = 0 Q = ? P = (2000 - Q)/250 250P = 2000 - Q TR = Q*(2000 - Q)/250 MR = 8 - 2*Q/250 Q/125 = 8 P = (2000 - 1000)/250 P = (2000 - Q)/250 TR = 8*Q - Q^2/250 8 - Q/125 = 0 Q = 1000 P = 4 Alternative solution Demand function Total Revenue (EUR) Marginal Revenue (EUR) Price per product (EUR) Q = 2000 - 250P TR = Q*P MR = dTR/dP = 0 2000 - 500*P = 0 TR = (2000 - 250P)*P MR = 2000 - 2*250*P 500*P = 2000 TR = 2000P - 250P^2 MR = 2000 - 500*P P = 45. Suppose that market demand is described by P = 100 – (Q+q), where P is the market price, Q is the output of the incumbent firm and q is the output of a potential entrant to the market. The incumbent firm’s total cost function is TC(Q) = 40Q, whereas the cost function of the entrant is C(q) = 100 + 40q, where 100 is a sunk cost incurred to enter the market. If the entrant observes the incumbent producing Q units of output and expects this output level to be maintained, write down the equation for the residual demand curve that the entrant firm faces. If the entrant firm maximize profit given the residual demand curve in a) what output qe will the entrant produce? [Write qe as a function of Q] How much output would the incumbent firm have to produce to just keep the entrant out of the market? [That is, solve for the limit output QL.] At what price will the incumbent sell the limit output?