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. Bradburys 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 firms total revenue function T R(X, Y )?

(3.2)(5 points) What is the firms marginal revenue function M RX for product X?

(3.3)(5 points) What is the firms 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 firms cost function is

T C(Q) = 10 + 6Q

where Q = Q1 + Q2.Thus the firms 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 firms 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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