### Supply and Demand Analysis**Problem Statement:**Let $ D(x) $ represent the price, in dollars per unit, that consumers are willing to pay for $ x $ units of an item. Similarly, $ S(x) $ signifies the price, in dollars per unit, that producers are willing to accept for $ x $ units. Your tasks are to determine:- (a) The equilibrium point.- (b) The consumer surplus at the equilibrium point.- (c) The producer surplus at the equilibrium point.**Given Functions:**- Demand function: $ D(x) = (x - 9)^2 $- Supply function: $ S(x) = x^2 + 2x + 21 $**Steps to Solve:**1. **Equilibrium Point:** - Set $ D(x) = S(x) $ and solve for $ x $.2. **Consumer Surplus:** - Calculate the area between the demand curve and the equilibrium price up to the equilibrium quantity.3. **Producer Surplus:** - Calculate the area between the supply curve and the equilibrium price up to the equilibrium quantity.By solving these equations and calculations, you will understand how consumer and producer behaviors balance in a market to reach an equilibrium point, and how surpluses are quantified at that point.

(a) Given that, the demand function is Dx=x-92 and the supply function is Sx=x2+2x+21. In order to…

D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point. D(x) = (x - 9)?, S(x) = x² + 2x + 21

D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point. D(x) = (x - 9)?, S(x) = x² + 2x + 21

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

### Supply and Demand Analysis

**Problem Statement:**

Let $ D(x) $ represent the price, in dollars per unit, that consumers are willing to pay for $ x $ units of an item. Similarly, $ S(x) $ signifies the price, in dollars per unit, that producers are willing to accept for $ x $ units. Your tasks are to determine:
- (a) The equilibrium point.
- (b) The consumer surplus at the equilibrium point.
- (c) The producer surplus at the equilibrium point.

**Given Functions:**
- Demand function: $ D(x) = (x - 9)^2 $
- Supply function: $ S(x) = x^2 + 2x + 21 $

**Steps to Solve:**

1. **Equilibrium Point:**
- Set $ D(x) = S(x) $ and solve for $ x $.

2. **Consumer Surplus:**
- Calculate the area between the demand curve and the equilibrium price up to the equilibrium quantity.

3. **Producer Surplus:**
- Calculate the area between the supply curve and the equilibrium price up to the equilibrium quantity.

By solving these equations and calculations, you will understand how consumer and producer behaviors balance in a market to reach an equilibrium point, and how surpluses are quantified at that point.

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