12. Prove, using Eq. (4-42), that the long-run supply curve of a competitive firm is more elastic than the supply curve in which one factor is held fixed at a previously profit- maximizing level. Differentiating with respect to p, -歌。()(等) ay* əy Əy (4-42) ap ap əx. ap
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- 2. A refrigerator manufacturer is planning capacity expansions. They have determined that their capacity cost follows the equation below, where f(y) = kya, is the cost of a plant that can produce y units annually. f(y) = 0.0107y⁰.62 They have determined that when a = 0.62, using a = u/(e" - 1) gives a value u = 0.89. Their demand for refrigerators is growing at a rate of 5000 units annually, and they use a 16% interest rate for discounting. At the optimal capacity addition level, what does each capacity installation cost?10) If marginal revenue equals marginal cost, the firm is maximizing profits as long as A) the average cost curve lies above the demand curve. B) the resulting profits are positive. C) marginal cost exceeds marginal revenue for greater levels of output. D) All of the above are required. $1q 15 1110 40 MC AC AVC q I= H 11) The above figure shows the cost curves for a competitive firm. If the firm is to earn economic8. siuppose that the manager of a firm operating in a competitive market has estimated the firm's average variable cost function to be: AVC= 18-0.3Q Total fixed cost is $60 and the forecasted price of the firm's product is $12. 79 a. What is the corresponding marginal cost function? b. At what output is AVC at its minimum? C. How much outputs should the firm produce? d. How much profit or loss will the firm earn?,
- 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 ?. An electricity producer has a constant marginal cost of production equal to $40 per megawatt. The residual demand for its electricity is given by P (q) = a−bq, where P is the price and q is the quantity of power generated by this producer. The producer knows the slope, b, but he vertical intercept of the residual demand curve, a is unknown. Assume A and B are greater than zero. If you get stuck, you may answer any of the following questions for special case where a = 80 And b = 0.5 for partial credit. (a) What is the marginal revenue, M R(q), for this producer? b) What is the optimal q for this producer? (c) What is the electricity producer’s optimal price? (d) What is the electricity producer’s optimal bid in a uniform price Auction? e) Suppose b is equal to zero. Would the producer have an incentive to submit a bid above its marginal cost? Explain.Suppose you are the economic advisor of Jackie Brown Company, a perfectly competitivecompany that is suffering economic losses due to unforeseen continuous drop in the market price.Jackie Brown is a price taker; hence it cannot influence the market price, nor could it changeproduction technology in the short run. You are asked to decide whether the company should shutdown its operations or to continue to operate at a loss. Jackie Brown is selling 50 units of outputper day, at a price of $20 per unit. The cost of raw material, direct labor, energy, and othervariable inputs is about $24000 monthly. Unfortunately, an estimate of Jackie Brown fixed costs iscurrently unavailable. So, what is your decision?
- 7. Assume that the marginal cost curve is given by mc(q) = 100 + 2q. (a) If the price is $160, what is the optimal production for the firm? What if the price is $120? (ignore the shut-down decision for this part) (b) Assuming that the market is cleared at $160 (no shortage/surplus). If the market demand is equal to 10,000 units of the product. How many firms are currently operating (n) in the market? (Hint: if the market clears qª = n x q°) (c) If the total cost curve is TC 256 + 100g + q², what's the average total cost curve? %3| what's the break-even price? (d) If the demand curve is given by qd = 8, 452 – p, what's the long-run equilibrium price, the equilibrium quantity and the long-run total number of firms (n) in the industry?Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10 – 0.03Q + 0.00005Q2, TFC = 60. The optimum profit is a. 348 b. -245 c. 1,200 d. -15.2 e. 255 f. None of the above13. Suppose the total cost of producing x units of a certain commodity is given by C(x) = 100x + 15,000. The revenue function R is given by R(x) =-0.02x +300x a). Find the profit function. b). Find the marginal profit function. c). Find the actual (marginal) profit from the sale of the 1001st product. %3D %3D
- 20) - Google Chrome "mod/quiz/attempt.php?attempt%3=1579003&cmid%3812962&page%3D2 em (Academic 20- MC ATC AVC 16 4. 5 10 15 20 25 30 35 40 45 50 Quantity (units per day) The above figure shows the cost curves for a perfectly competitive firm. If all firms in the market have th same cost curves and the price equals $16 per unit Select one: O a. over time, the price will fall as new firms enter the market. O b. over time, firms will leave this market. O c. the market is in its long-run equilibrium. O d. the firm is making zero economic profit. o search hp Price and cost (dollars per unit)1. Consider the perfectly competitive market for guitar tuners. The mar- ket price for a guitar tuner is $20 and the cost functions are: TC (q) = .01q² + .2q + 4950 %3D MC (q) = .02g +.2 (a) Find the profit-maximizing quantity of guitar tuners produced by a firm in this market. (b) Calculate the profit each firm will earn in this market (c) Graphically depict the firm's profit-maximization problem. (note: this doesn't need to be to scale but should accurately reflect the sign of the profit) (d) Will firms enter into this market in the long run? (e) Graphically show how the price will change as the market pro- gresses towards a long-run equilibrium. (There's no need to find the exact long-run equilibrium price. Just follow similar steps to what we did in class)2. Suppose that a perfectly competitive firm uses two inputs to produce one output. The conditional factor demand functions for this firm are as follows: x1(W1, W2, y) = (2w2/w;)/3y*/3 x2(W1, W2, y) = (w1/2w2)²/3y4/3 a) Find the cost function. b) Using the cost function, setup the firm's profit maximization problem and find the supply function. c) Using the supply function, derive the factor demand functions.