ECON 101: Principles of Microeconomics – Discussion Section Week 11 TA: Kanit Kuevibulvanich

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Important Concepts: • Production and Cost • Perfectly Competitive Market

Problems 1. The graph below shows the production cost curves of a firm in a perfectly competitive

industry. Assume the equilibrium price equals $30 in the short run.

a. In the short run, what is the profit maximizing level of output for this firm? At this

quantity, what is the marginal revenue? b. In the short run, how much is the total cost for this firm at the profit maximizing level of

output? c. In the short run, will the firm make (economic) profit or suffer loss? How much? Should

the firm shut down? d. Given the information above, can you figure out the fixed cost of this firm? Can you

figure out the variable cost at the production of 35? How about the variable cost at the level of 40?

e. What is the break-even price for this firm? What is the shut down price for this firm? f. Suppose that the fixed cost increases, what impact will this have on this firm’s profit

maximizing level of output in the short run? 2. In a perfectly competitive industry, all the potential firms are identical with the following

TC = 6q2 + 2q + 96 and MC = 12q + 2 a. Find the VC, FC, AVC and ATC for each firm. What is the shutdown price? What is the

break-even price? b. What is the supply curve of each firm? c. Suppose that there are two firms in the short-run, what is the market supply? d. The market demand is P = 114 – Q. Find the equilibrium price. How many units are

consumed? How many units does each firm produce? e. What is the profit of each firm? f. Find the equilibrium in the long run, what is the price? Quantity consumed? How many

firms will there be in the long run? What is the profit of each firm? g. If the market demand has changed to P = 30 – Q, briefly explain what would happen.

ECON 101: Principles of Microeconomics – Discussion Section Week 11 TA: Kanit Kuevibulvanich

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Solutions: Question 1 a. Profit maximization: produce at P = MC, so q* = 35. Marginal revenue = $30, since we are in

perfectly competitive market. If the price you asked is higher than $30, I can walk away. Total revenue = 30 x 35 = $1050.

b. Total cost = ATC x q = 40 x 35 = $1400. c. Loss = (40 – 30) x 35 = $350, since fixed cost = $700, do not shutdown. d. Fixed cost = (40 – 20) x 35 = $700. Total variable cost = $1400 – $700 = $700. e. Breakeven is the lowest point of ATC, which MC also cuts through, so Pbreakeven = $38.

Shutdown is the lowest point of AVC, which MC also cuts through, so Pshutdown = $15 f. Fixed cost does not matter to quantity q* that maximizes profit since it is the point where P =

MC, but the short run profit decreases if fixed cost increases. However, it will affect the breakeven and shutdown price.

Question 2 a.

𝑉𝐶 = 6𝑞! + 2𝑞 𝐹𝐶 = 96

𝐴𝑇𝐶 =𝑇𝐶𝑞= 6𝑞 + 2 +

96𝑞

𝐴𝑉𝐶 =𝑉𝐶𝑞= 6𝑞 + 2

The shutdown price is equal to the minimum AVC. In this special case the AVC is a linear line with positive slop. If you draw the line you can see that the minimum is 2. So the shutdown price is 2. The break-even price is equal to the minimum ATC. We know that the MC intersect with the ATC at the minimum, so we can find the minimum of ATC by finding the point of intersection (MC = ATC):

𝑀𝐶 = 𝐴𝑇𝐶

12𝑞 + 2 = 6𝑞 + 2 +96𝑞

𝑞! = 16 𝑞 = 4

To find the minimum ATC we just need to plug 𝑞 = 4  in the ATC or MC (Check that they

are equal at this point). 𝑀𝑖𝑛  𝐴𝑇𝐶 = 6 ∙ 4 + 2 + !"!= 50

So the break-even price is 50. b. The supply curve of each firm, is the part of the MC curve that is above the AVC. In this

special case you can easily see that MC is above AVC for any quantity (they intersect at q=0). So the supply curve is 𝑃 = 12𝑞! + 2.

c. The market supply if there were two firms is 𝑄! = 𝑞!! + 𝑞!!:

𝑃 = 12𝑞!! + 2 ⇒ 𝑞!! =𝑃12

−16

𝑃 = 12𝑞!! + 2 ⇒ 𝑞!! =𝑃12

−16

ECON 101: Principles of Microeconomics – Discussion Section Week 11 TA: Kanit Kuevibulvanich

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𝑄! = 𝑞!! + 𝑞!! =𝑃6−13

⇒ 𝑃 = 6𝑄! + 2 d. Equilibrium 𝑄! = 𝑄!

6𝑄 + 2 = 114 − 𝑄 ⇒ 𝑄∗ = 16 ⇒ 𝑃∗ = 98

The firms are price takers, to find how many units each one produces, we just need plug the market price in their supply curve.

𝑞!!∗ =𝑃∗

12−16= 8

𝑞!!∗ =𝑃∗

12−16= 8

Alternatively you can argue that since the firms are identical, the market quantity will be divided equally between the two firms.

𝑞!!∗ = 𝑞!!∗ =𝑄∗

2= 8

e. The profits of the two firms are the same (why is that?): 𝜋!∗ = 𝑃∗ ∙ 𝑞!!∗ − 6 𝑞!!∗ ! − 2𝑞!!∗ − 96 𝜋!∗ = 98 ∙ 8 − 6 ∙ 8! − 2 ∙ 8 − 96 = 160

𝜋!∗ = 160 f. We know that in the long run with free entry/exit of firms to the market, the profit of each

firm is normal (profit equal 0). The price will be equal to the minimum ATC. 𝑃∗ = 𝑀𝑖𝑛  𝐴𝑇𝐶 = 50

Given the equilibrium price in the long-run, we can find the quantity demanded in the market by plugging the price in the market demand:

𝑄! = 114 − 𝑝 𝑄!∗ = 114 − 50 = 64

We know that each firm that is in the market produces 4 units of the good (Why is that? Think what quantity brings ATC to the minimum), so we can find the number of firms:

𝑛∗ =𝑄∗

𝑞!∗=644= 16

g. (d) equilibrium 𝑄! = 𝑄! 6𝑄 + 2 = 30 − 𝑄

⇒ 𝑄∗ = 4 ⇒ 𝑃∗ = 26

You can find the quantity that each firm produces (see part d above): 𝑞!∗ = 𝑞!∗ = 2

(e) 𝜋!∗ = 𝜋!∗ = −72 (f) None! Note that the break-even price for any firm (with this cost function) is 50, but the quantity demanded for this level of price is 0.