ECON 101: Principles of Microeconomics – Discussion Section Week 8 – Spring 2015
Content for Today
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Cost curves
Profit maximization
Questions
1. Black Swan Clothing is a firm producing costumes for residents in Econ
Town. Assume Black Swan Clothing takes prices as given when choosing
the quantity it will produce (perfectly competitive market). If q is the
number of costumes made my Black Swan Clothing, their costs are given
by
TC = 0.5q2 + q + 2
MC = q + 1
a. What are Black Swan’s fixed costs? What are their variable costs?
Fixed costs are the costs when the firm produces no output, so FC =
2. Variable costs are those that do depend on output, so VC = 0.5q2
+ q.
b. Give equations for Black Swan’s AFC, ATC and AVC. AFC = FC/q
= 2/q. AVC = VC/q = 0.5q + 1. ATC = TC/q = AFC + AVC = 0.5q +
1 + 2/q.
c. Find the quantity where ATC = MC (we need this to plot the cost
curves). Solving 0.5q + 1 + 2/q = 1 + q gives q2 = 4, so q = 2. At this
quantity ATC = MC = 3.
d. Draw a graph that represents Black Swan Clothing’s MC, AVC, and
ATC curves. See graph below.
e. How many costumes will the firm produce when price, P, is given
as P = $2? The firm sets MR = MC to maximize profits. Since MR =
P (the firm is a price taker since it is in perfect competition), 2 = 1 +
q gives q = 1.
f. More generally, if the price is some unknown amount P, how many
costumes will the firm produce? P = MC, so P = q + 1 gives q = P –
1. The firm’s marginal cost curve is their supply curve! There is a
subtlety here to do with the “shutdown point” we will talk about at
some point.
g. Suppose there are 10 firms in the market, including Black Swan
Clothing, which all have the same cost curves. Assume that this
market is perfectly competitive. What is the market supply curve
given this information? Since there are 10 firms, Q = 10q. Hence the
market supply curve is given by Q = 10(P – 10) = 10P – 10. It is
important to get your axes the right way around here!
h. Suppose demand is given by the equation Qd = 50 - 10P. Calculate
the equilibrium price and quantity. How much quantity does each
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ECON 101: Principles of Microeconomics – Discussion Section Week 8 – Spring 2015
firm produce in this equilibrium, and what are their profits? Setting
supply equal to demand gives P = 3 and Q = 20. Since there are 10
firms, each firm produces 2 units (or you could plug P = 3 into the
firm supply curve). Note that we are at the point where P = MC =
ATC, so firms make zero profit.
i. Calculate the producer surplus in equilibrium. What is the
difference between profit and producer surplus? PS = 0.5*(3-1)*20 =
$20. This is the same as the sum of the fixed costs of all the firms,
who are making zero profit. More generally, producer surplus is
the same as profit, except it does not take into account fixed costs
(so it is total revenue minus total variable costs).
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ECON 101: Principles of Microeconomics – Discussion Section Week 8 – Spring 2015
2. Examine the following graph which shows the cost curves of an individual firm
in the market for widgets, which is perfectly competitive:
a. What are the fixed costs of this firm? To find this, calculate total costs at a
certain quantity and subtract total variable costs (by taking ATC and
AVC and multiplying by quantity). You could also do it in the opposite
order by finding AFC = ATC-AVC and then multiplying by quantity. For
instance, at q=4, the AVC=10 and the ATC=20. Thus AFC=ATCAVC=$10, so FC=q*AFC=4*10=$40.
b. How many widgets will the firm produce if the price is $10? Using the
firm’s optimality rule MR = MC and the fact that the market is perfectly
competitive, so P = MR, the firm will produce where 10 = MC, i.e. at a
quantity of 4.
c. What will be this firm’s profit if the price is $10? At q=4, TR=4*10=$40.
When the firm produces 4 units, its is ATC=$20, so TC=4*20=$80. Thus
the profit is TR-TC=$40-$80=-$40. Note that the firm could also produce
zero units, which would give a loss of the fixed costs of $40.
d. Find the profit and the total variable cost of the firm when the widget
price is $15. Give an argument that the firm should not produce a
quantity of 0 at this price. TR=5*15=$75. TC=5*19=$95. Thus profit = $75 $95 = -$20. However, if the firm produced a quantity of 0 it would still
lose the fixed costs of $40, so it is better off producing 5 units than 0.
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ECON 101: Principles of Microeconomics – Discussion Section Week 8 – Spring 2015
e. What is the firm's profit when the price is $18? From looking at the
diagram, when P = 18, q = 6. At this quantity ATC is also equal to 18, so
the firm makes zero profit.
f. What is the firm's profit when the price is $40? TR=8*40=$320.
TC=8*20=$160. Thus profit is TR-TC=$160.
3. (More practice at discrete cost curve calculations) Dunkin Donuts operates with a
weekly fixed cost $1000 and hires workers, paying each worker $500 a week.
They only need workers and the bakery to make delicious donuts. Fill in the
table below for Dunkin Donuts’ weekly costs. Also find the break-even price and
quantity.
Output
0
1
2
3
4
Workers
0
1
2
4
8
FC
$1,000
$1,000
$1,000
$1,000
$1,000
VC
$0
$500
$1,000
$2,000
$4,000
TC
$1,000
$1,500
$2,000
$3,000
$5,000
AFC
$1,000
$500
333.33
$250
AVC
$500
$500
666.67
$1,000
ATC
$1,500
$1,000
$1,000
$1,250
MC
$500
$500
$1,000
$2,000
The break-even point is the point at which MC = P = ATC. This happens at a price of
$1,000, where output is 3.
4. (Kelly Fall 2013 midterm 2 question) Given the following total cost function, derive
the fixed cost.
5
𝑇𝐶 =
+ 5 + 5𝑞 + 𝑞 2
𝑞+1
a. $4
b. $5
c. $8
d. $10
Answer: Fixed costs are when q = 0, so TC = 5/1 + 5 + 0 + 0 = 10.
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