2. Suppose the total cost function of a firm that produces hotdogs is C= 150q - 4q° + 29' where q is the output level of the firm. i. Find the average cost function of the firm. Show your workings. ii. If the firm's marginal cost function is 150 – 8q + 6q°, at what output level, the average cost is minimized? Show your workings. iii. Show your answer of part ii) in a well-labeled diagram.
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- A competitive firm has the following average cost function: AC=y2 - 8y + 30 + 5/y. The corresponding marginal cost function is MC = 3y2 - 16y + 30 a) Derive the total cost function, then find the firm’s average variable cost, average fixed cost, and fixed cost. Is this firm in the short run or the long run? How do you know? b) At what quantity is marginal cost equal to average variable cost? At what quantity is average variable cost minimized? The firm will supply zero output if the price is less than what? c) What is the smallest positive amount that the firm will ever supply at any price? At what price would the firm supply exactly 6 units of output?Given the following short run production cost schedule: Short Run Total Cost Function Quantity Produced Total Cost ($) 0 20 10 27 20 38 30 53 40 73 50 100 60 130 The table above gives the short run total cost function for a typical firm in a perfectly competitive industry. Please answer related questions below (a) What is the dollar value of the firm’s total fixed cost? (b) At what level of quantity, the average total cost is minimized? Show your work. (c) Calculate the marginal cost of producing the first 10 units of output? (d) At what level of quantity, the marginal cost is lowest? (e) Explain the average-marginal rule in cost curves? (f) What is the market price? (Assume the firm is operating in a pure competitive market.) (g) If the firm enjoys market power than the firm’s market price will be higher or lower than the competitive market price? Why? What is natural monopoly? Explain why governments…Given the following short run production cost schedule: Short Run Total Cost Function Quantity Produced Total Cost ($) 0 20 10 27 20 38 30 53 40 73 50 100 60 130 The table above gives the short run total cost function for a typical firm in a perfectly competitive industry. Please answer related questions below (a) What is the dollar value of the firm’s total fixed cost? (b) At what level of quantity, the average total cost is minimized? Show your work. (c) Calculate the marginal cost of producing the first 10 units of output? Show your work (d) At what level of quantity, the marginal cost is lowest? (e) Explain the average-marginal rule in cost curves? (f) What is the market price? (Assume the firm is operating in a pure competitive market.) (g) If the firm enjoys market power than the firm’s market price will be higher or lower than the competitive market price? Why?
- Month (m): 4 Day (d): 1 Use the two numbers above, m and d, to complete the cost function for a perfectly competitive firm: Cost (q) = m q2 + d = (30) For a cost function like yours, Marginal Cost (MC) = 2 m q . Specifically, what are the following for the cost function you wrote out above? Fixed Cost = Average Total Cost = Cost (q)/q = Variable Cost = Average Fixed Cost = FC/q = Marginal Cost = 2 m q = Average Variable Cost = VC/q = (15) Fill in the table with your values from your cost function. q Total Cost AVC AFC ATC MC 0 0 0 -- -- -- 1 2 3 4 5 6Sketch a marginal cost curve for a firm that has constant marginal costs of production up to its capacity of 500 units but which cannot increase its output beyond that capacity PLEASEE SHOW THE CURVEGiven the following short run production cost schedule: Short Run Total Cost Function Quantity Produced Total Cost ($) 0 20 10 27 20 38 30 53 40 73 50 100 60 130 The table above gives the short run total cost function for a typical firm in a perfectly competitive industry. Please answer related questions below Calculate the marginal cost of producing the first 10 units of output? Show your work
- Q)Assume that a competitive firm has the total cost function: TC=1q^3−40q^2+740q+1600 Suppose the price of the firm's output (sold in integer units) is $650 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. A. How many units should the firm produce to maximize profit? B. What is the total profit at the optimal output level? Please specify your answer as an integer.Which one of the following statements about a firm’s cost curves is true? A. The average variable cost curve only includes explicit costs. B. Increases in input prices for variable factors of production will shift the firm’s marginal cost curve up and also shift the firm’s total variable cost curve up. C. Fixed costs only include implicit costs. D. An increase in the price of a fixed factor of production will shift all of the firm’s cost curves up. E. A competitive firm’s short run supply curve is always identical at all points to its short run marginal cost curve.The total cost function of a firm producing Jeans is TC = 0.5Q3− 15Q2 + 175Q + 100, where Q is output. a.What are the total variable cost (TVC) and the total fixed cost (TFC) in this case? b.The average cost is given by AC = TC/Q, the average variable cost is AVC = TVC/Q and the average fixed cost is AFC = TFC/Q. Find the AC, AVC and AFC functions. c. If the marginal cost is MC = 3(0.5)Q2 - 2(15)Q + 175, then roughly sketch the graph of MC, AVC and AC (If you know how to use Excel, then you can get more accurate graphs). What relationship do you observe between the three cost curves?
- Marginal Analysis II Question 1 Assume that a competitive firm has the total cost function: TC=1q3−40q2+870q+1500TC=1q3-40q2+870q+1500 Suppose the price of the firm's output (sold in integer units) is $700 per unit. Using calculus and formulas to find a solution (don't just build a table in a spreadsheet as in the previous lesson), how many integer units should the firm produce to maximize profit? Please specify your answer as an integer. Hint 1: The first derivative of the total cost function, which is cumulative, is the marginal cost function, which is incremental. The narrated lecture and formula summary explain how to compute the derivative. Set the marginal cost equal to the marginal revenue (price in this case) to define an equation for the optimal quantity q. Rearrange the equation to the quadratic form aq2 + bq + c = 0, where a, b, and c are constants. Use the quadratic formula to solve for q: q=−b±b2−4ac−−−−−−−√2aq=-b±b2-4ac2a For non-integer quantity, round up and down to…Suppose an increase in the cost of land increases the firm's fixed costs, as a result, average total cost increases from ATC2 to ATC1. What is profit maximizing quantity and price after the increase in average total costs? After the increase in average total costs does the firm make economic profit, economic loss or breaks even? How do you know? explain your answer.Quantity of Output Total Cost 0 $12 1 $14 2 $18 3 $24 4 $32 5 $42 6 $54 7 $68 The table above shows the total cost function for a typical firm producing hats in a perfectly competitive market. The market price for hats is $9 per hat. (a) Calculate the average variable cost of the fifth unit. Show your work. (b) What is the firm’s profit-maximizing quantity of hats? Explain using marginal analysis. (c) Draw a correctly labeled graph showing the firm’s demand and marginal cost curves, and show the profit-maximizing quantity of hats determined in part (b). (d) If the rent of the building the firm occupies increases, what will happen to the firm’s profit-maximizing quantity of output in the short run? Explain.