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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- 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?Bitcom, a manufacturer of electronics, estimates the following relation between marginal cost of production and monthly output: MC= $150+ 0.005Q What does this function imply about the effect of the law of diminishing returns on Bitcom’s short-run cost function? Calculate the marginal cost of production at 1,500, 2,000, and 3,500 units of output. Assume Bitcom operates as a price taker in a competitive market. What is this firm’s profit-maximizing level of output if the market price is $175? Compute Bitcom’s short-run supply curve for its product. Provide a 100 word summary of how this can be applied to the current economy. Show Calculations and can it be done in Excel?Assume the following short-run total cost function and its associated average total cost function corresponds to the minimum point on the long-run average total cost curve and this is a constant cost indsutry. TC = 5,000 + 4q + 0.0002q2 where TC is the firm's total cost in dollars and q is the quantity of output produced by the firm. Also assume the market demand is: Qd = 10,000,000 - 1,000,000P where Qd is the market quantity demanded and P is the commodity's price in dollars. a. What would the long-run equilibrium price equal? b. Assuming the firm and market are in long-run equilibrium, what quantity of output would the firm produce? c. Assuming all firms are identical, how many firms will there be in this market when it is in a long-run equilibrium?
- A firm has a linear demand function for it's product.When the price for the product is Sh.220,the quantity demanded is 40 units.When the price increases to Sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is given by; MC = 40Q-2Q^2+2 Fixed cost = Sh. 5 million Where Q= quantity demanded, Mc= marginal cost(cost in Sh. Million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at a maximum profitSergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.Suppose a firm has the following total cost function TC = 100 + 2q2. If price equals $20, what is the firm’s output decision? What are its short-run profits?
- A firm has a linear demand function for it's product.When the price of the product is sh.20,the quantity demanded is 40 units.When the price increases to sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is giving by: Mc = 40q- 2q^2+2 Fixed cost = 5 million Where q= quantity demanded,Mc = marginal cost(sh.million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at the maximum profitConsider a firm with a total cost function TC = q^2 + 20q + 225. a) In a diagram, measuring quantity along the horizontal axis, draw the firm’s Marginal Cost and Average Cost curves. Suppose that the government introduces a $10 per unit seller tax. b) What is the firm’s new total cost function? In the same diagram as above, illustrate how the tax affects the firm’s MC and AC curves. Does the tax affect the firm’s MC? Does it affect the firm’s minimum efficient scale? Suppose instead that the government introduces a new licensing fee that raises the firm’s recurring fixed cost to 400. C) In a new diagram draw the firm’s MC and AC before and after the introduction of the licensing fee. Does the fee affects’ the firm’s MC? Does it affect the firm’s minimum efficient scale?A competitive firm has the following short run cost function TC= q3 + 2q2 - 20q + 700. What is the value of the firm's average fixed cost (AFC)of producing 10 units of output? What is the value of the firm's average variable cost (AVC)of producing 10 units of output? What is the value of the firm's average total cost (ATC)of producing 10 units of output? What is the value of the firm's marginal cost (MC)of producing 10 units of output?
- The total cost function of a perfectly competitive firm is TC=100+10*Q+5*0^2 For what time period does the function apply? What is the equation of the marginal cost function? If the market price is 50, what is the optimal production quantity of the firm? What is the value of total revenue at the profit maximum? What is the value of total cost at the profit maximum? Will be negative or positive value of the profit at the profit maximum? In the short run, does the company decide to produce (at profit max level)? Which minimum value indicates the shutdown point? Use the following set of options to answer the above questions: long run 100 short run AVCmin ACmin maybe 4 220 positive yes MCmin no 100 years 10+5*Q 200 10+10*Q QminA firm has the following information on production and costs from past data: Output (Y) 0 6 12 18 Total Cost (TC) 9 2775 5361 8199 If the total cost function is known to be TC=aY3+bY2+kY+f, and the demand for the product of the firm is Y=320-(1/2)P. answer the following: Determine the coefficient of the cubic cost function. Derive all cost and revenue curves and the profit function. Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points.Assume that a competitive firm has the total cost function: TC=1q3−40q2+820q+1900 T C = 1 q 3 - 40 q 2 + 820 q + 1900 Suppose the price of the firm's output (sold in integer units) is $600 per unit. How many units should the firm produce to maximize profit? What is the total profit at the optimal output level? Please specify your answers as integers.
