A Firm Sells Two Goods (X and Y)that Are Related

question 6

Multiple Choice

A firm sells two goods (X and Y) that are related in consumption.The estimated inverse demand and cost functions are: $$\begin{array} { l } P _ { X } = 105 - 0.5 Q _ { X } - 0.75 Q _ { Y } \\P _ { Y } = 120 - Q _ { Y } - 0.5 Q _ { X } \\M C _ { X } = 10 + 0.25 Q _ { X } \\M C _ { Y } = 16 + 0.5 Q _ { Y }\end{array}$$
What are the profit-maximizing levels of output for the two goods?

• A) \(Q _ { x }\) = 6, \(Q _ { Y }\) = 3
• B) \(Q _ { x }\) = 40, \(Q _ { Y }\) = 40
• C) \(Q _ { x }\) = 58, \(Q _ { Y }\) = 30
• D) \(Q _ { x }\) = 240, \(Q _ { Y }\) = 270
• E)none of the above

---

Definitions:

Percentage Change

A mathematical calculation that indicates how much a number has increased or decreased in percentage terms relative to its previous value.

Price Elastic

Describes how sensitive demand for a product or service is to changes in its price; high elasticity indicates significant demand change with price fluctuations.

Nondiscretionary

Pertaining to expenses that are essential and not subject to personal choice, such as food, housing, and utilities.

Demand Curve

A graph showing the relationship between the price of a product and the quantity of the product that consumers are willing and able to purchase at different prices.