Microeconomics, Module 8: “Competition: Long Run” (Chapter 7)

Homework

(The attached PDF file has better formatting.)


Suppose a firm’s fixed costs are $80,000, and its marginal cost curve is MC = ¼ Q. The market demand curve is Q = 10,000 – 10P.

A.    What is the firm’s variable cost curve? (Integrate the marginal cost curve.)
B.    What is the firm’s total cost curve? (Add fixed and variable costs.)
C.    What is the firm’s average cost curve? (Divide total costs by quantity.)
D.    What is the firm’s minimum average cost? (Set the partial derivative with respect to quantity equal to zero.)
E.    What is the quantity at this minimum average cost? (At this point, average cost equals marginal cost; use the marginal cost curve to determine the quantity.)
F.    What is the industry demand at this price? (Use the market demand curve.)
G.    If firms are identical, how many firms compete in this industry? (Divide the market quantity by the firm’s quantity.)
H.    What is the industry short run supply curve? (Multiple each firm’s supply curve by the number of firms.)
I.    If the market demand curve changes to Q = 8,000 – 10P, what is the new short run equilibrium price and quantity? (Solve for the intersection of the supply and demand curves.)
J.    What is the quantity produced by each firm, assuming all are identical? (Divide market quantity by the number of firms.)
K.    What is the revenue for each firm? (Quantity times price.)
L.    What are the costs of each firm? (Fixed costs plus variable costs at the new production level.)
M.    What is the profit or loss to each firm in the short run? (Revenue minus costs.)
N.    If firms expect the change in market demand to be temporary, what do they do? (Would an increase or decrease in quantity supplied raise or lower profits?)
O.    If firms expect the change in market demand to be permanent, what do they do? What items determine whether a firm exits the industry?

This homework assignment follows the pattern in the discussion board practice problem postings.

Can anyone help with this homework? I think I'm OK up to "H," but then I get stuck. How do I know what the supply curve is? I know we are given the demand curve and the cost information, but I can't find how to get the supply curve from that. Any ideas?

The supply curve for each firm looks the same as the marginal cost curve. Whereas the marginal cost curve is a function of Q(quantity), the supply curve is a function of P(price). So solving for Q, the firm's supply curve is Q=4P. The industry supply curve is the sum of all firm's suppply curve and that is why you need to multiply the firm's supply curve by 10(the number of firms in the industry), making the industry supply curve Q=40P.

In part J, are they asking what is the quantity produced by each firm based on the new industry demand curve? I'm assuming they are since its the following question, and we have pretty much answered the same question for the old demand curve in part E..

I agree.  Each firm's demand is derived from the market demand obtained from the previous question.

in part N, the question paranthetically asks if an increase or decrease in quantity supplied would raise or lower profits. I don't necessarily see how that is relevant to the question of what each individual firm would do given that they expect the decrease in demand is a temporary one. It would seem to me that because they expect the demand to return to normal, they would all keep producing 640 units and simply shoulder the loss. Why would there be an increase or decrease in the quantity supplied?

The only way that the parenthetical question makes sense to me is if it is referring what would happen if an individual firm is increaseing or decreasing their quantity supplied. If a single firm decides to produce less to adjust to the demand, the leftward shift in its supply curve will raise its equilibrium price. However, the market price will remain at $160 per unit so the firm that decided to produce less and increase their price will suffer a loss in market share and therefore have a larger net loss.

Thoughts?

I think that is exactly what the question is getting at.  When it asks if the companies will increase or decrease production in order to increase profits, it wants you to realize that there is no way they can increase their profits, whether they increase or decrease production.  That is just what you have explained above.  So the question may not be worded as well as it could be, but I think you are describing the concept they want you to understand.

Jacob: How might we summarize the gist of this homework assignment?

Rachel: The chapters on competition assume perfect markets. If demand increases, new firms enter, because they expect the higher demand to continue. In practice, demand fluctuates. If higher demand seems to be temporary, firms have no incentive to enter the market. It costs money to set up a new firm, and when the higher demand ceases, many of the new entrants are forced out.

I disagree, based on Exhibit 7.10 on pg 183, a short term rise in demand results in increased output as well as price, and thus greater profit. This is logical too, many industries charge more at times of peak demand to maximize their profits...

[NEAS: Correct. Since new firms do not enter the market to take up the higher demand, the existing firms raise prices and earn higher profits.]