Canola Oil Producing Industry Assignment Help
1.The canola oil industry is perfectly competitive. Every producer has the following long-run total cost function: LTC = 2Q3 – 15Q2 + 40Q, where Q is measured in tons of canola oil. The corresponding marginal cost function is given by LMC = 6 Q2 – 30Q + 40.
a. Calculate and graph the long-run average total cost of producing canola oil that each firm faces for values of Q from 1 to 10.
b. What will the long-run equilibrium price of canola oil be?
c. How many units of canola oil will each firm produce in the long run?
d. Suppose that the market demand for canola oil is given by Q = 999 – 0.25P. At the long-run equilibrium price, how many tons of canola oil will consumers demand? e. Given your answer to (d), how many firms will exist when the industry is in long-run equilibrium?
2.Assume that the ice cream industry is perfectly competitive. Each firm producing ice cream must hire an operations manager. There are only 50 operations managers that display extraordinary talent for producing ice cream; there is a potentially unlimited supply of operations managers with average talent. Operations managers are all paid $200,000 per year.
• The long-run total cost (in thousands of dollars) faced by firms that hire operations managers with exceptional talent is given by LTCE = 200 + Q2 , where Q is measured in thousands of 5-gallon tubs of ice cream. The corresponding marginal cost function is given by LMCE = 2Q, and the corresponding longrun average total cost is LATCE = 200/Q + Q.
• The long-run total cost faced by firms that hire operations managers with average talent is given by LT CA = 200 + 2Q2 . The associated marginal cost function is given by LMCA = 4Q, and the corresponding long-run average total cost is LATCA = 200/Q + 2Q.
a. Derive the firm supply curve for ice cream producers with extraordinary operations managers.
b. Derive the firm supply curve for ice cream producers with average operations managers.
c. The minimum LAT C A (for firms with average operations managers) is $40, achieved when those firms produce 10 units of output. The minimum LATCE (for firms with exceptional operations managers) is $28.28, achieved when those firms produce 14 units of output. Explain why, given only that information, it is not possible to determine the long-run equilibrium price of 5-gallon tubs of ice cream.
d. Referring to part (c), suppose that you know that the market demand for ice cream is given by Qd = 8,000 – 100P. Explain why, in the long run, that demand will not be filled solely by firms with extraordinary managers. (Hint: Derive the industry supply of extraordinary producers and then use the demand curve to determine the equilibrium price. Can that price persist in the long run?)
e. In part (d), you explained why the supply side of the market will consist of both firms with extraordinary managers and firms with average managers. What will the long-run equilibrium price of ice cream be?
f. At the price you determined in part (e), all 50 firms with extraordinary managers will find remaining in the industry worthwhile. How many firms with average managers will also remain in the industry?
g. At the price you determined in part (e), how much profit will a firm with an average manager earn?
h. At the price you determined in part (e), how much profit will a firm with an extraordinary manager earn? How much economic rent will that talented manager generate for her firm?
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3.A homogeneous products duopoly faces a market demand function given by P = 300 – 3Q, where Q = Q1 + Q2. Both firms have a constant marginal cost MC = 100.
a) What is Firm 1’s profit-maximizing quantity, given that Firm 2 produces an output of 50 units per year? What is Firm 1’s profit-maximizing quantity when Firm 2 produces 20 units per year?
b) Derive the equation of each firm’s reaction curve and then graph these curves.
c) What is the Cournot equilibrium quantity per firm and price in this market?
d) What would the equilibrium price in this market be if it were perfectly competitive?
e) What would the equilibrium price in this market be if the two firms colluded to set the monopoly price? f )
f ) What is the Bertrand equilibrium price in this market?
g) What are the Cournot equilibrium quantities and industry price when one firm has a marginal cost of 100 but the other firm has a marginal cost of 90?
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