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Please solve all the problems in this document. In part two, please answer questions with many steps do not only provide a final answer. The step need to be clear and logic. Also if problems need use graph to present those relationship please provide a simple graph to show.
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Part I
Short Answer Questions
1.(5 points) Each pair of Fancy Shoes costs Bradbury Footwear Stores $30. Bradbury’s economist has
estimated the point elasticity to be -1.8. WHat price should Bradbury charge if it wants to maximize
profits
2.(46 points) An amusement park, whose customer set is made up of two markets, adults (A) and children
(C), has identified the demand functions as follows:
QA = 20 – PA
QC = 30 – 2PC
The marginal operating cost of each unit of quantity is $5. The park is a monopolist and exercises
significant price making power in the market.
Suppose the park charges a single price from both adults and children.
(2.1)(5 points) Calculate the aggregate demand curve QT faced by the monopolist.
(2.2)(5 points) Calculate the (aggregate) marginal revenue function M RT (Q) of the monopolist.
(2.3)(3 points) What is the profit maximizing level of output Q*T produced by the monopolist?
(2.4)(2 points) What is the price charged for that level of output?
(2.5)(3 points) Assuming that fixed costs are zero, how much (aggregate) profits ? T are earned by the
monopolist at the profit maximizing level of output?
Now suppose the park decides to charge different price from its Adult(A) and Children(C) customers
(2.6)(3 points) Calculate the revenue function T RA(Q) for the adult market.
(2.7)(3 points) Calculate the marginal revenue function M RA(Q) for the adult market. (2.8)(3
points) What is the profit maximizing number of tickets sold Q*A in the adult market? (2.9)(2
points) What is the ticket price charged for the adult market.?
(2.10)(3 points) Assuming that fixed costs are zero, how much profits are earned by the amusement park
in the adult market at the profit maximizing level of output?
(2.11)(3 points) Calculate the revenue function T RC(Q) for the children market.
(2.12)(3 points) Calculate the marginal revenue function M RC(Q) for the children market. (2.13)(3
points) What is the profit maximizing number of tickets sold Q*C in the children market? (2.14)(2
points) What is the ticket price charged in the children market?
(2.15)(3 points) Assuming that fixed costs are zero, how much profits are earned by the amusement park
in the children market at the profit maximizing level of output?
1 of 2
Prof. Sharma
3.(37 points) A firm makes two products, X and Y. Inverse demand for each shows that pricing in one
market depends on sales in the other according to the equations:
PX = 1000 – 20X + 3Y
and
PY = 500 – 5Y + X
The firm faces joint fixed cost of $12000 and constant marginal cost of production in each product
segment, M CX = $200, and M CY = $100.
(3.1)(5 points) What is the firm’s total revenue function T R(X, Y )?
(3.2)(5 points) What is the firm’s marginal revenue function M RX for product X?
(3.3)(5 points) What is the firm’s marginal revenue function M RY for product Y?
(3.4)(10 points) What bundle of products ( X* , Y * ) should be produced by the firm?
(3.5)(7 points) How price should the firm charge for products X and Y ?
(3.6)(5 points) What profits result in this instance?
4.(12 points) The Jam Factory makes boutique jams that it sells in specialty stores in two different cities.
In City 1, the daily inverse demand function is
P1 = 12 – 0.5Q1
and the marginal revenue function is M R1 = 12 – Q1. In City 2, the inverse demand and marginal
revenue functions are
P2 = 20 – Q2
and M R2 = 20 – 2Q2. The firm’s cost function is
T C(Q) = 10 + 6Q
where Q = Q1 + Q2.Thus the firm’s marginal cost of production is 6 per unit.
(4.1)(4 points) Create an excel spreadsheet with columns for Q1, Q2, p1, p2, M R1, M R2 and M C. Put
the values 1 to 12 in increments of 1 in the Q1 column and put the same values in the Q2 column.
Fill in the appropriate formulas in the other cells, noting that MC column has the value 6 for each
quantity.
(4.2)(6 points) The Jam Factory price discriminates by charging a different price in each city. Find the
profit-maximizing quantities and prices. Verify that the marginal revenues are the same in each
city at the profit maximizing quantities.
(4.3)(2 points) Determine the firm’s profit.
5.(10 points (bonus)) An anonymous survey is made available on Black Board. While I can not match
individual responses to any one of you, I can see whether or not you have submitted the survey. You
will earn 10 points if you submit “Week 14 Survey” by 11.59 p.m. on 28th April 2018.
6.(5 points (bonus)) Spring 2018 course evaluations are currently open on myIIT portal. Your responses
to these evaluations are stored anonymously. They are NOT be made available to me until 14 May
2018. However, I can view the aggregate response rate for the class. You will earn 5 points if aggregate
response rate reaches 80% by 11.59 p.m. on 28th April 2018.
2 of 2
Prof. Sharma
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