What are the long-run market equilibrium price and quantity of hibiscus plants? How many firms operate? **Problem 11:**For parts (1)-(3), suppose the market for hibiscus plants is perfectly competitive and the long-run cost for hibiscus plants for any firm in this market is described by the cost function:\[ C(q) = 70q - 20q^2 + 2q^3 \]The market demand for hibiscus plants is represented by the demand function:\[ D(p) = 30 - \frac{1}{2}p \]---In this problem, we are analyzing a perfectly competitive market for hibiscus plants. The two key functions involved are:1. **Cost Function \( C(q) \):** Describes the total cost associated with producing q units of hibiscus plants. The equation \( C(q) = 70q - 20q^2 + 2q^3 \) is a cubic function showing how costs change with different output levels.2. **Demand Function \( D(p) \):** Relates the quantity of hibiscus plants demanded to the price level, with \( D(p) = 30 - \frac{1}{2}p \). This linear function indicates that as the price increases, the quantity demanded decreases, reflecting the typical demand relationship. These functions can be used to explore conditions of equilibrium, changes in supply and demand, or to analyze the cost structures in this competitive market.

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Answered: What are the long-run market…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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What are the long-run market equilibrium price and quantity of hibiscus plants? How many firms operate?

**Problem 11:**

For parts (1)-(3), suppose the market for hibiscus plants is perfectly competitive and the long-run cost for hibiscus plants for any firm in this market is described by the cost function:

\[ C(q) = 70q - 20q^2 + 2q^3 \]

The market demand for hibiscus plants is represented by the demand function:

\[ D(p) = 30 - \frac{1}{2}p \]

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In this problem, we are analyzing a perfectly competitive market for hibiscus plants. The two key functions involved are:

1. **Cost Function \( C(q) \):** Describes the total cost associated with producing q units of hibiscus plants. The equation \( C(q) = 70q - 20q^2 + 2q^3 \) is a cubic function showing how costs change with different output levels.

2. **Demand Function \( D(p) \):** Relates the quantity of hibiscus plants demanded to the price level, with \( D(p) = 30 - \frac{1}{2}p \). This linear function indicates that as the price increases, the quantity demanded decreases, reflecting the typical demand relationship.

These functions can be used to explore conditions of equilibrium, changes in supply and demand, or to analyze the cost structures in this competitive market.

Definition Video Definition Point where the demand and supply curves intersect. At the equilibrium price the quantity supplied of a good is equal to the quantity demanded. When the market is not in equilibrium, market surplus or market shortage occurs. The region that is above the price equilibrium indicates market surplus and the region below the price equilibrium indicates market shortage. Video

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