**Problem Statement:**The demand and supply of apartments in Vancouver are described by the following equations:- **Demand:** $ P = 1200 - 2Q $- **Supply:** $ P = 2Q $**Task:**(a) Find the equilibrium price $ P^* $ and quantity $ Q^* $. Compute the consumer surplus and producer surplus.**Solution:**To find the equilibrium, set the demand equation equal to the supply equation:\[ 1200 - 2Q = 2Q \]Solve for $ Q $:\[ 1200 = 4Q \]\[ Q^* = 300 \]Substitute $ Q^* $ back into either the demand or supply equation to find $ P^* $:Using the supply equation:\[ P^* = 2(300) = 600 \]**Equilibrium Price and Quantity:**- Equilibrium Price, $ P^* = 600 $- Equilibrium Quantity, $ Q^* = 300 $**Surpluses:**- *Consumer Surplus* is the area of the triangle above the price level and below the demand curve up to the equilibrium quantity. \[ \text{Consumer Surplus} = \frac{1}{2} \times (1200 - 600) \times 300 = \frac{1}{2} \times 600 \times 300 = 90,000 \]- *Producer Surplus* is the area of the triangle below the price level and above the supply curve up to the equilibrium quantity. \[ \text{Producer Surplus} = \frac{1}{2} \times (600 - 0) \times 300 = \frac{1}{2} \times 600 \times 300 = 90,000 \]**Conclusion:**- Consumer Surplus = 90,000- Producer Surplus = 90,000These calculations assume all apartments are sold and the entire demand and supply meets perfectly at the equilibrium. This analysis provides insights into market efficiency and welfare distribution between consumers and producers.

The equilibrium price is the only price where the plans of consumers and the plans of producers agree means, where the amount consumers want to buy of the product, quantity demanded, is equal to the amount producers want to sell, quantity supplied. This common quantity is called the equilibrium quantity

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1. The demand and supply of apartments in /ancouver are given by (Demand) P = 1200 – 2Q and (Supply) P = 2Q. a) Find the equilibrium price P * and quantity Q* . Compute the consumer surplus and producer urplus

1. The demand and supply of apartments in /ancouver are given by (Demand) P = 1200 – 2Q and (Supply) P = 2Q. a) Find the equilibrium price P * and quantity Q* . Compute the consumer surplus and producer urplus

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

**Problem Statement:**

The demand and supply of apartments in Vancouver are described by the following equations:

- **Demand:** $ P = 1200 - 2Q $
- **Supply:** $ P = 2Q $

**Task:**

(a) Find the equilibrium price $ P^* $ and quantity $ Q^* $. Compute the consumer surplus and producer surplus.

**Solution:**

To find the equilibrium, set the demand equation equal to the supply equation:

\[ 1200 - 2Q = 2Q \]

Solve for $ Q $:

\[ 1200 = 4Q \]

\[ Q^* = 300 \]

Substitute $ Q^* $ back into either the demand or supply equation to find $ P^* $:

Using the supply equation:

\[ P^* = 2(300) = 600 \]

**Equilibrium Price and Quantity:**

- Equilibrium Price, $ P^* = 600 $
- Equilibrium Quantity, $ Q^* = 300 $

**Surpluses:**

- *Consumer Surplus* is the area of the triangle above the price level and below the demand curve up to the equilibrium quantity.

\[
\text{Consumer Surplus} = \frac{1}{2} \times (1200 - 600) \times 300 = \frac{1}{2} \times 600 \times 300 = 90,000
\]

- *Producer Surplus* is the area of the triangle below the price level and above the supply curve up to the equilibrium quantity.

\[
\text{Producer Surplus} = \frac{1}{2} \times (600 - 0) \times 300 = \frac{1}{2} \times 600 \times 300 = 90,000
\]

**Conclusion:**

- Consumer Surplus = 90,000
- Producer Surplus = 90,000

These calculations assume all apartments are sold and the entire demand and supply meets perfectly at the equilibrium. This analysis provides insights into market efficiency and welfare distribution between consumers and producers.

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