ECO101: Introduction to Microeconomics
Problem Set 02| Summer 2024
1.
MC
Price, Costs
ATC
25 AVC
20
15
8
D
Quantity
10 18
20
MR
Answer the following question using the graph provided above.
a) What type of competition is the firm facing?
b) What is its profit maximizing level of output and price?
c) Is the firm earning a profit or making a loss? Calculate the profit/loss.
d) If this firm is operating in a competitive market, what will be the price and output?
e) Calculate the amount of loss/profit if this firm is operating in a competitive market.
f) How does a monopoly cause a deadweight loss?
g) Calculate the deadweight loss.
2. In a perfectly competitive industry, all firms are identical with identical cost curves.
Suppose that a representative firm’s total cost is given by the equation: 𝑻𝑪=𝟐𝒒𝟐+𝟓𝒒+𝟓𝟎,
where q is the quantity of output produced by an individual firm.
Additionally, the market demand for this product is given by the equation P=1000−2Q and
the market supply is given by 𝑷=𝟏𝟎𝟎+𝑸, where Q is the overall market output.
a) Find the equilibrium price and quantity in the market.
b) The firm’s MC equation based upon its TC equation is 𝑴𝑪=𝟒𝒒+𝟓. Given this
information and your answer in part (a), what is an individual firm’s profit-maximizing
level of production in the short-run?
c) Calculate the firm’s total revenue, total cost, and profit at this profit-maximizing level of
production.
d) Find the equation for a representative firm’s average total cost (ATC) curve. What should
be the relationship between price and ATC in the long run?
3. Recently, there has been much concerning news on the consumption of soft drinks “MaxCola”
and its impact on health. Reports found sugar as the main ingredient of this soft drink. Given that
the price of sugar is 20TK per kg.
Now, consider the soft drinks “MaxCola” market:
Demand function:
𝑃 = 100 − 2𝑄𝑑 where 𝑃 is the price per unit of “MaxCola” and 𝑄𝑑 is the Quantity
demanded.
Supply function:
0.25𝑃 = 5 + 2𝑄𝑠 + 0.25𝑃0 where 𝑃 is the price per unit of “MaxCola”, 𝑃0 is the price per
kg of sugar and 𝑄𝑠 is the Quantity supplied
Answer the following:
a) Find the market price and quantity at the equilibrium.
b) Calculate the Producer Surplus.
4. The information about the costs of a firm is given below.
Output AFC, $ AVC, $
1 50.00 100.00
2 25.00 80.00
3 16.67 66.67
4 12.50 65.00
5 10.00 68.00
6 8.37 73.33
7 7.14 80.00
a) What is the firm's fixed cost?
b) If the firm produces five units, what is the average total cost?
c) What is the total cost of producing four units?
d) If the firm closes down and produces no output, what will be its total cost?
5. What is the firm’s profit/loss in the graph shown below?
6. The health ministry is evaluating the data of the soft beverages market.
Demand function: Qd = 290 – 5P
Supply function: Qs = 5P – 60
a) Find CS and PS.
b) Find the total surplus.
Answers
1.a) Monopoly/ Single-price monopoly/ Imperfect competition
1.b) Qm = 10, Pm = 20.
1.c) Loss. Profit/loss = TR – TC = 20x10 – 25x10 = -50 (loss).
1.d) Qpc = 18, Ppc = 15.
1.e) Profit/loss = TR – TC = 15x18 – 20x18 = -90 (loss).
1.f) Monopolies make less than the socially efficient quantity and charge
higher price, which creates the deadweight loss.
1.g) DWL = ½ x (18 – 10) x (20 – 8) = 48
2.a) Q* = 300, P* = 400.
2.b) P = MR
MR = 400
MR = MC
400 = 4q + 5
Qpc = 98.75
2.c) TR = 400 x 98.75 = 39500
TC = 2(98.75)^2 + 5(98.75) + 50 = 20046.88
Profit = 39500 – 20046.88 = 19453.12
2.d) ATC = 2q + 5 + 50/q
In the long run, the relationship between price and ATC should be such that firms in the market
earn zero economic profit. This implies that price should equal average total cost (P = ATC) for
firms to cover all costs, including normal profit.
3.a) Q* = 6, P* = 88.
3.b) PS = 144
4.a) FC = AFC x Q, and it doesn't matter which row of the table we take data from.
For instance, $50 x 1 = $50, and $6.25 x 8 = $50.
4.b) ATC = AFC + AVC. For 5 units of output, ATC =$10 + $68 = $78.
4.c) TC = ATC x Q = (AFC+AVC) x Q. For 4 units of output, TC = ($12.50 + $65) x 4 =
$310. Another way would be to calculate VC = $65 x 4 = $260 and it to FC = $50 obtained in
part a to get TC = $310.
4.d) No output means no variable cost. The firm's cost will then be limited to its fixed cost, TC =
FC = $50.
5. Profit/loss = TR – TC
= PxQ – ATCxQ
= 20x6 – 29.50x6 (from the graph)
= 120 – 177
= -57 (loss)
6.a) At equilibrium,
Qd = Qs
290 – 5P = 5P – 60
10P = 350
P* = 35
Q = 5(35) – 60
Q* = 115
When Qd = 0,
290 – 5P = 0
Pd = 58
When Qs = 0,
5P – 60 = 0
Ps = 12
CS = 1/2 x 115 x (58 – 35) = 1322.5
PS = 1/2 x 115 x (35 – 12) = 1322.5
6.b) Total surplus = CS + PS = 2645
Solutions to Assignment 02
1.a)
Quantity TR ($) TC ($) VC AVC ATC MC AR MR
0 0 10 0 - - - 0 0
1 9 14 4 4 14 4 9 9
2 18 19 9 4.5 9.5 5 9 9
3 27 25 15 5 8.33 6 9 9
4 36 32 22 5.5 8 7 9 9
5 45 40 30 6 8 8 9 9
6 54 49 39 6.5 8.16 9 9 9
7 63 59 49 7 8.42 10 9 9
8 72 70 60 7.5 8.75 11 9 9
9 81 82 72 8 9.11 12 9 9
1.b) As discussed in class. 2.a) continued,
1.c) Q* = 6 at MR=MC=9 Q* = -2 + 14
1.d) Min ATC = 8 (breakeven) and min Q* = 12
AVC = 4 (shutdown)
2.b) When Qd = 0,
40 – 2P = 0
2.a) Given,
Pb = 20
Qd = 40 – 2P
When Qs = 0,
Qs = -2 + P
-2 + P = 0
At equilibrium, Qs = Qd
Ps = 2
-2+P = 40 – 2P
CS = ½ x 12 x 6 = 36
3P = 42
PS = ½ x 12 x 12 = 72
P* = 14
TS = 36 + 72 = 108
2.c) As discussed in class.
