Microeconomics Assignment: Pricing, Production, and Demand Analysis

This microeconomics assignment delves into various pricing and production scenarios. It explores profit maximization under different cost and demand conditions, including scenarios with single and multiple markets, joint products, and interdependent demand. The assignment requires calculating optimal prices, quantities, and profits, analyzing the impact of different pricing strategies, and understanding the relationship between cost functions, demand curves, and revenue maximization. It covers topics such as marginal cost, average cost, and the application of economic principles to real-world business decisions, providing a comprehensive understanding of microeconomic concepts and their practical applications. The assignment includes mathematical solutions and graphical representations to illustrate key concepts.

1) The manufacturer of high-quality flatbed scanners is trying to decide what price to set for its
product. The costs of production and the demand for the product are assumed to be as follows:
TC = 500,000 + 0.85Q + 0.015 Q2
Q = 14.166 – 16.6P
a) Determine the short-run profit-maximizing price.
b) Plot this information on a graph showing AC, AVC, MC, P and MR
2) An amusement park, whose customer set is made up of two markets, adults and children, has
developed demand schedules as follows:
Quantity
Price ($)
Adult
s
Childre
n
5 15 20
6 14 18
7 13 16
8 12 14
9 11 12
10 10 10
11 9 8
12 8 6
13 7 4
14 6 2
The marginal operating cost of each unit of quantity is $5. (Hint: Because marginal cost is a constant,
so is average cost. Ignore fixed cost). The owners of the amusement park want to maximize profits.
a) Calculate the price, quantity, and profit if
1. The amusement park charges a different price in each market
2. The amusement park charges the same price in the two markets combined
3. Explain the difference in the profit realized under the two situations
b) (Mathematical solution) The demand schedules presented in Problem 2 can be presented in
equation form as follows (where subscript A refers to the adult market, subscript C refers to
the market for children, and subscript T to the two markets combined):
QA = 20 – 1PA
QC = 30 – 2PC
QT = 50 – 3PT
Solve these equations for the maximum profit that the amusement park will attain when it
charges different prices in the two markets and when it charges a single price for the
combined market.
3) The Bramwell corporation has estimated its demand function and total cost function to be as
follows:
Q = 25 – 0.05P

TC = 700 + 200Q
Answer the following questions either by developing demand and cost schedules (Hint: use
quantities from 1 to 14) or by solving the equations.
a) What will be price and quantity if Bramwell wants to
1. Maximize profits?
2. Maximize revenue?
3. Maximize revenue but requires the profit to be a minimum of $300?
b) Now assume the cost function is TC = 780 + 200Q while the demand function remains the
same. What will be the price and quantity if Bramwell wants to :
1. Maximize profits?
2. Maximize revenue?
3. Maximize revenue but requires the profit to be a minimum of $300?
c) Why are the answers the same in a(1) and b(1) but different in a(3) and b(3)?
10) The Prime Company produces two products, X and Y. They are produced jointly so for each X
manufactured a unit of Y is produced. The joint cost function is
TC = 50 + 2Q + .5Q2
Q represents the number of joint units produced. The demand equations for the two products are
the following:
QX = 100 – PX
QY = 60 – 2PY
a) How many units should the company produce per period?
b) What price should it charge for each of the joint products?
c) What will be the company’s profit per period?
Assume the company is a profit maximizer
12) 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 = 100 – 20x + 3y
PY = 500 – 5y + x
The firm faces join fixes costs of $12000 and constant marginal cost of production in each product
segment, MCX = $200, and MCY = $100
a) What bundle of products (x*, y*) should the firm produce?
b) What prices will the firm be able to charge for each product given production at (x*, y*)?
c) What profits results in this instance?
d) At (x*, y*) what are the values ∂TRy
∂ x and ∂TRx
∂ x ? Provide a short (one or two sentence)
explanation for each value. That is, explain to your less mathematically sophisticated boss
the economic significance of each value.