A competitive firm has the following short-run cost function: c(y) = y3/3 - 10y2 +11y + 12. What is its marginal cost function? Oy2-20y + 11 O 3y2-20y + 11 +12/y Oy-20y2 + 11y2 + 12 O y2-30y + 11 +12/y
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- Given the following profit function: T=-2Q^2+260Q-4500, Answer the following questions.(a) The marginal cost of two firms are given by the following | cost Firm 1: C'(Q) = 300e® 1Q+2 TC= 3000 when Q = 0 Firm 2: C'(Q) = 41 +30Q -5Q² TC =400 when Q = 0 (ii, (iii) avee (iv) Find the total cost for producing up to 100 unitsQUESTION 7 Consider a firm running a business in the pure competition setting. This firm's cost function is as follows c(y) c(y) = y² - 4y² + question are consistent with the notations used in class. What is the short-run supply function for this cost structure? OA-s(y) = y²-8y + 2 y 23 Otherwise, (y) -0 OB.s (y) = y²-8y + 2ify 26 Otherwise, s (y) = 0. Os(y)=³-4y + 2 y 23. Otherwise, a(y) = 0 OD₁(y)=³-4y + 2 fy 26. Otherwise, x(x) = 0 Note that the notations in thes
- Consider a firm running a business in the pure competition setting. This firm's cost function is as follows: c(y) = 4y2 + 3y + 10 consistent with the notations used in class %3D What is the long-run supply function and the range of output level that makes the firm stay in the business? O A. S(y) = 8y + 3, y24 O B. SG) = 8y + 3, y25 OCso) = 4y + 3 + 100 ,y24 OD s(y) = 4y + 3 + =, y25 100 OUESTION 13A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. ) If production increases continuously, what is likely to be the average cost per sink? How many laundry sinks will the company need to produce in order to maximise it′s profits? What is the maximum profit?Attempt all questions. Q1. a) A local Pepsi company has total costs of production given by the equation TC-500+10q+Sq2. This implies that the firm's marginal cost is given by the equation MC 10+10q. The market demand for cold drink is given by the equation QD-105 (1/2)*P. Write the equations showing the company's average total cost and average variable cost and average fixed cost, each as a function of q. Show the firm's MC, ATC and AVC on one graph. What is the breakeven price and breakeven quantity for this firm in the short run? What is the shutdown price and shutdown quantity for this firm in the short run? If the market price of the output is $50, how many units will this firm produce? iv) Assuming the cold drink industry is perfectly competitive, what output would be produced by the firm in long-run equilibrium? What would be the long-run equilibrium price? i) ii)
- Should a firm shut firm if its revenue is R = $1,500 per week and: a. Its variable cost is VC = $1,100 and its sunk fixed cost is F = $800? b. Its variable cost is VC = $1,600 and its fixed cost is F = $600? c. Its variable cost is VC = $1,100 and its fixed cost is F = $1000 ($800 of which is avoidable if it shuts down)?7. An analyst has found that Tom's Transmissions Company cost function is: C(x) = 40,000 + 500x – 0.55x² for, where x is the number of transmissions. a) Determine the marginal Cost function C'(x). b) Determine when the Cost function is maximized. c) Determine the marginal cost function at the 100th item proe Explain significance of the marginal cost at this point. ed and sold. d) Determine the cost difference between 101st and 100th boat ( C(101) - C(100)). Is this value the same or different from the marginal cost from part c? Explain.he total revenue curve of a firm is R(q)=40q−12q and its average cost A(q)=130q−12.85q+20 +400q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?
- A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…The following is a table of the total cost (TC) of producing output Q for a particular firm. Based on this information, which of the following statements is correct? Q Y TC (X) 10 140 20 210 30 265 40 310 50 360 60 420 O a. The marginal cost is higher than the average cost at Q = 50. Ob. The marginal cost at Q80 is £9.50. Oc The average cost at Q-40 is £7. Od. The marginal cost curve intersects the average cost curve at Q = 60. 490 8 60 570 8 90 660 100 760Break-Even The total revenue function for Frenchdoor refrigerators is given by R = 550x dollars, andthe total cost function for this same product is givenby C = 10,000 + 30x + x2, where C is measured indollars. For both functions, the input x is the numberof refrigerators produced and sold.a. Form the profit function for the refrigerators fromthe two given functions. b. What is the profit when 18 refrigerators areproduced and sold?c. What is the profit when 32 refrigerators areproduced and sold?d. How many refrigerators must be sold to breakeven on this product?