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# Suppose a perfectly competitive firm's cost function is C(q)=4q^2+16. Marginal cost for the firm is given by MC=8q.

Suppose a perfectly competitive firm’s cost function is C(q)=4q^2+16. Marginal cost for the firm is given by MC=8q.
Find equations for variable cost, fixed cost, average total cost, average variable cost and average fixed cost for this firm. Illustrate on a graph the firm’s average variable cost curve, average total cost curve, and marginal cost curve.
Find the outputs that minimize average total cost, average variable cost and average fixed cost.
What is the shutdown price for this firm?
What is the breakeven price for this firm?
If the price of the output is \$32, how many units will this firm produce? What is the firm’s profit?
Suppose market demand for this good is given as P=300-Q and all firms in the market are identical. How many firms are active in the market in the long run?

A representative firm has an average total cost curve that is described by the equation:

The firm’s marginal costs equation is:

Market demand is given by:

a) Sketch ATC, MC, MR (you need to derive this), and the market demand curve. Hint: to draw ATC you may want to plot points then connect the dots. Assume that the firm perceives that the market demand curve is the demand curve for the product they are producing.
b) Suppose the representative firm is an unregulated monopolist. What quantity will they produce and what price will they charge?
c) Is the monopolist’s chosen level of output allocatively efficient? Explain your answer.
d) Is there any way to regulate the firm to achieve allocative efficiency in the long run without government intervention beyond price regulation? Why or why not?
Now suppose the government decides that 18 units of the good sold be produced.
e) Suppose two firms meet this level of output by each producing 9 units. What is the total cost of production?
f) What would be the optimal number of firms if we wanted to produce 18 units at minimum cost per unit? Hint: look carefully at the shape of the ATC function.
g) How would we describe this market?

The market for olive oil in New York City is controlled by two families, the Sopranos and the Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter the New York City olive oil market. The marginal cost of producing olive oil is constant and equal to \$40 per gallon. There is no fixed cost. The accompanying table gives the market demand schedule for olive oil.

Price of olive oil
(per gallon)
Quantity of olive oil
Demanded (gallons)
Total Revenue

Marginal Revenue

\$100 1,000

90 1,500

80 2,000

70 2,500

60 3,000

50 3,500

40 4,000

30 4,500

20 5,000

10 5,500

a. [2 points] Suppose the Sopranos and the Contraltos form a cartel. For each of the quantities given in the table,
(i) calculate the total revenue for their cartel, and
(ii) the marginal revenue for each additional gallon.
How many gallons of olive oil would the cartel sell in total and at what price? The two families share the market equally (each produces half of the total output of the cartel). How much profit does each family make?
b. [1 point] Uncle Junior, the head of the Sopranos family, breaks the agreement and sells 500 more gallons of olive oil than under the cartel agreement. Assuming the Contraltos maintain the agreement, how does this affect the price for olive oil and the profits earned by each family?

c. [1 point] Anthony Contralto, the head of the Contralto family, decides to punish Uncle Junior by
increasing his sales by 500 gallons as well. How much profit does each family earn now?

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