Problem Set #2 - Noor - Fall 2019
Problem Set #2 – UN 1105 – Noor – Fall 2019 1
UN 1105: Principles of Economics
Problem Set #2 – October 3
Fall 2019
Waseem Noor (section 3)
Problem Set Guidelines
• You will receive 4 assigned problem sets through the semester and together they account for 15% of
your grade. This problem set is due at the beginning of lecture on Thursday, October 10. No late
assignments will be accepted.
• A physical copy of the problem set should be handed in at the beginning of class. Please staple the
physical copy if there are multiple pages and put your name and UNI on all the pages.
• In addition, a scanned PDF copy of the problem set should be uploaded by 10a on Thursday, October 10
efore the lecture. Be sure to scan all the pages, not just the first page. The system will close at
10am and will not accept submissions after that time. Problem sets will be returned during your
ecitation session.
• Students can work on problem sets in groups of maximum three people, but each student should write up
his/her own solution, and list all the names of the people in a group.
• TA’s will read and grade all the problems sets, so please write legibly. All graphs should have units and
axes clearly labelled. If they cannot read the answers they will not be able to give you credit.
• It goes without saying that copying your solutions from others is considered cheating and will be
sanctioned. (please read Columbia’s policy on academic integrity at
https:
www.college.columbia.edu/academics/academicintegrity ). Solutions to the problem sets will be
discussed during recitations.
Problem Set #2 – UN 1105 – Noor – Fall 2019 2
1) Silvio runs a pastry shop. The following table shows the total number of cupcakes produced as a
function of the number of workers put into making them.
Number of Workers Cupcakes
0 0
1 10
2 25
3 35
4 44
5 52
6 58
7 62
8 63
9 62
a) Graph Silvio’s cupcake production function against number of workers.
) What happens to the marginal product of labor as the amount of labor input increases?
c) What happens to the marginal product of labor after 8 workers are hired? Why does this happen?
2) Chengzhi is running a firm in a competitive market. The firm always makes the choice to maximize its
profit. The figure below shows cost curves for the firm. The x-axis is quantity of output.
a) If the market price is $3.25, how much does Chengzhi choose to produce? What are her total
evenues, total costs and profits? Draw the total revenue, total cost and profit on a separate graph.
) If the market price of the product is $3.25, what is her fixed cost? Indicate how you calculate the
amount. Would the fixed cost change if the market price changes to $1.75?
c) If the market price is $1.50 how much would she produce? If the price drops further should she
continue to produce? If the price increases to $1.75 should she continue to produce?
d) Draw out the short run supply curve for Chengzhi’s firm.
Problem Set #2 – UN 1105 – Noor – Fall 2019 3
3) Omer is running a firm in a competitive market. The firm always makes the choice to maximize profits.
The figure below shows the marginal cost (circles) and the average variable cost (crosses) of his firm.
At a price of $1700, the AVC and MC are the same.
a) Draw out the short run supply curve for Omer’s firm.
) If the market price of the product is $5,000, what is the firm's producer surplus? If the market price
of the product is $3,400, what is the firm's producer surplus? If the market price is $1,700 what is the
firm’s producer surplus?
c) Is producer surplus same as profit? Explain.
4) Raquel runs a perfectly competitive firm selling cupcakes. Her firm has the following cost functions:
Total cost: TC(q) = $10,000 + $100q + $10q2,
Marginal cost: MC(q) = $100 + $20q, where q is the number of cupcakes
a) What is the Average Total Cost, Average Fixed Costs and Average Variable Cost functions? Draw
out the three curves along with the marginal cost curve on one graph.
) If Raquel’s firm faces a market price of $900 per unit, how much will she produce at the profit
maximizing point?
c) In the short run, what are profits and producer surplus at the profit maximizing level of output?
5) Jean- Baptiste makes homemade pastries. His fixed input in the short run is the mixer. In the long run,
he can choose a spatula, hand mixer, or a stand mixer. The following table shows the short-run fixed
cost (FC) and variable cost (VC) of weekly production using each different level of the capital input.
Output of
pastries
FC ($)
spatula
mixer
VC ($)
spatula
mixer
FC ($)
hand
mixer
VC ($)
hand
mixer
FC ($)
stand
mixer
VC ($)
stand
mixer
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX25
XXXXXXXXXX 50
XXXXXXXXXX 100
XXXXXXXXXX200 250
Problem Set #2 – UN 1105 – Noor – Fall 2019 4
a) If Jean-Baptiste makes 10 pastries per week, which type of capital input (spatula mixer, hand mixer
or stand mixer) should he choose? If he wants to make 100 pastries per week, which level of capital
input should he choose? If he wants to make 500 pastries per week?
) Draw out the short-run average total cost curve for a spatula mixer. On the same graph draw out the
average total cost curve for a hand mixer and stand mixer.
c) What does the long-run average total cost curve look like for Jean-Baptiste’s firm?
6) Suppose the market for Columbia sweatshirts is competitive and has ten buyers and ten sellers. The
following table shows the reservation values for both buyers and sellers.
Buyer
Reservation Value
of Buyer ($) or
Willingness to Pay
Seller
Reservation Value
of Seller ($) or
Willingness to
Accept
Aaron 15 Kelly 1
Bob 14 Lina 2
Cain 13 Max 4
Dana 12 Newt 6
Eve 11 Oliver 8
Flora 10 Pete 10
Gordon 9 Quinn 12
Ha
y 8 Ray 14
I
ahim 7 Sue 16
Jordan 6 Tory 18
a) What is the equili
ium quantity of sweatshirts bought/ sold? At what equili
ium price? Which
individuals are indifferent between trading and not-trading?
) At the equili
ium price and quantity, what is the amount of producer surplus? What is consumer
surplus? What is social surplus?
c) Is the equili
ium outcome pareto efficient? Explain why or why not. Does it maximize social
surplus? Explain why or why not.
d) Suppose the equili
ium price in the market is $10, but the market is constrained so only 2
sweatshirts are allowed to be sold. What is social surplus in this scenario? Is this pareto efficient?
Why or why not?
e) Suppose a price floor of $12 is imposed on this market, which does not allow the price of sweatshirts
to drop below $12. How many sweatshirts will be sold and what is the new social surplus? Is this
pareto efficient? Why or why not?
7) Lupita and Nazim live in a small town. The figure on the left below shows the demand for fuel by
Lupita and Nazim during ordinary times. Assume that Lupita and Nazim are the only consumers. In the
figure on the right, D0 is the market demand, and S0 is the supply in ordinary times in the town.
Problem Set #2 – UN 1105 – Noor – Fall 2019 5
a) How is the market demand function (D0) generated?
) A hu
icane hits the town. The acute need for fuel to operate electric generators pushes the demand
for fuel to D1. Meanwhile, the supply plummets to S1 because some of the fuel storage tanks
owned by the town seller have been damaged by the storm. This occu
ence pushes the price up to
$5 per liter where only Lupita can afford some fuel. Is this a pareto efficient equili
ium? Why or
why not? Is this an equitable outcome? Why or why not?
c) Nazim complains to the town council of price gouging by the fuel sellers. In response, an anti-
price-gouging law is immediately passed that puts the price ceiling at $1.75 per liter. What will
likely happen next?
d) Suppose that fuel sellers outside the affected area have a cost of production such that MC = ATC at
$2.50 per liter, which includes the cost of transporting the fuel under hazardous conditions.
Suppose that the price-gouging law was never enacted, and the price was $5 per liter. What will
the presence of outside fuel sellers do to the price? Why? Is this equili
ium pareto efficient? Is it
equitable?
8) Assume that the market demand for slices of chocolate cake is given by QD = 650 − 25P and the
market supply of chocolate cake is given by QS = 200 + 20P.
a) What is the market equili
ium price for slices of chocolate cake?
) Marcello wants to sell chocolate cake. He has a marginal cost curve of MC(q) = 2 + ½ q where q is
the number of slices of chocolate cake produced by Marcello. What is his marginal revenue for
each slice of cake? How many slices of chocolate cake will Marcello make given the equili
ium
price?
c) Marcello’s Fixed Cost in order to set up the business is $40. His variable costs are VC(q)= 2q+ ¼
q2. Draw out