Given: (q is number of items) Demand function: d(q) = 743.6 – 0.6q² Supply function: s(q) = 0.5q² Find the equilibrium quantity: Find the equilibrium price: $ items
Given: (q is number of items) Demand function: d(q) = 743.6 – 0.6q² Supply function: s(q) = 0.5q² Find the equilibrium quantity: Find the equilibrium price: $ items
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Equilibrium Quantity and Price Calculation
Given the equations:
- **Demand function**: \( d(q) = 743.6 - 0.6q^2 \)
- **Supply function**: \( s(q) = 0.5q^2 \)
Where \( q \) is the number of items, you are required to find the equilibrium quantity and price where demand equals supply.
#### Equilibrium Quantity:
To find the equilibrium quantity, set the demand function equal to the supply function:
\[ 743.6 - 0.6q^2 = 0.5q^2 \]
Simplify and solve for \( q \):
\[ 743.6 = 0.6q^2 + 0.5q^2 \]
\[ 743.6 = 1.1q^2 \]
\[ q^2 = \frac{743.6}{1.1} \]
\[ q = \sqrt{\frac{743.6}{1.1}} \]
#### Equilibrium Price:
Once you have found the equilibrium quantity \( q \), substitute it back into either the demand or supply function to find the equilibrium price.
```html
<form id="equilibrium-form">
<label for="equilibrium-quantity">Find the equilibrium quantity:</label>
<input type="text" id="equilibrium-quantity" name="equilibrium-quantity"> items<br><br>
<label for="equilibrium-price">Find the equilibrium price:</label>
<input type="text" id="equilibrium-price" name="equilibrium-price"> $<br><br>
<button type="submit">Submit Question</button>
</form>
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa39fb107-3a22-4843-8482-67ca4b18789f%2F57cb9d82-c967-488b-9542-f56e60b90296%2Fkib5qlf_processed.png&w=3840&q=75)
Transcribed Image Text:### Equilibrium Quantity and Price Calculation
Given the equations:
- **Demand function**: \( d(q) = 743.6 - 0.6q^2 \)
- **Supply function**: \( s(q) = 0.5q^2 \)
Where \( q \) is the number of items, you are required to find the equilibrium quantity and price where demand equals supply.
#### Equilibrium Quantity:
To find the equilibrium quantity, set the demand function equal to the supply function:
\[ 743.6 - 0.6q^2 = 0.5q^2 \]
Simplify and solve for \( q \):
\[ 743.6 = 0.6q^2 + 0.5q^2 \]
\[ 743.6 = 1.1q^2 \]
\[ q^2 = \frac{743.6}{1.1} \]
\[ q = \sqrt{\frac{743.6}{1.1}} \]
#### Equilibrium Price:
Once you have found the equilibrium quantity \( q \), substitute it back into either the demand or supply function to find the equilibrium price.
```html
<form id="equilibrium-form">
<label for="equilibrium-quantity">Find the equilibrium quantity:</label>
<input type="text" id="equilibrium-quantity" name="equilibrium-quantity"> items<br><br>
<label for="equilibrium-price">Find the equilibrium price:</label>
<input type="text" id="equilibrium-price" name="equilibrium-price"> $<br><br>
<button type="submit">Submit Question</button>
</form>
```
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