Suppose You Are a Monopolist Operating Two Plants at Different $C _ { 1 } = 25 + 2 Q _ { 1 } ^ { 2 }$

question 46

Essay

Suppose you are a monopolist operating two plants at different locations.Both plants produce the same product; Q₁ is the quantity produced at plant 1,and Q₂ is the quantity produced at plant 2.You face the following inverse demand function:
P = 500 - 2Q,where Q = Q₁ + Q₂.The cost functions for the two plants are
$C _ { 1 } = 25 + 2 Q _ { 1 } ^ { 2 }$ ; $C _ { 2 } = 20 + Q _ { 2 } ^ { 2 }$ .
a.What are your marginal revenue and marginal cost functions?
b.To maximize profits,how much should you produce at plant 1?
At plant 2?
c.What is the price that maximizes profits?
d.What are the maximum profits?

---

Definitions:

Working-Class Background

Refers to a socioeconomic status or background characterized by families whose members are primarily engaged in manual labour with lower income and educational levels.

Appalachian Accent

A regional dialect found in the Appalachian region of the United States, marked by distinctive phonological features.

Blue-Collar Worker

An employee who performs manual labor, often in industries like manufacturing, construction, and maintenance, usually paid hourly.

Highly Paid CEO

An executive officer of a company who receives compensation significantly above the average for their role, often reflecting the size, profitability, and complexity of the organization.