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To find the **elasticity coefficient (E)** for the demand function $ p = \frac{4400}{q + 3} $ at $ p = 220 $, we need to use the **price elasticity of demand formula**:

\[
E = \left| \frac{d q}{d p} \times \frac{p}{q} \right|
\]

### Step 1: Express $ q $ as a function of $ p $
The given demand function is:

\[
p = \frac{4400}{q + 3}
\]

Solve for $ q $ in terms of $ p $:

\[
q + 3 = \frac{4400}{p} \quad \Rightarrow \quad q = \frac{4400}{p} - 3
\]

### Step 2: Differentiate $ q $ with respect to $ p $
The function $ q = \frac{4400}{p} - 3 $ can be differentiated as:

\[
\frac{d q}{d p} = -\frac{4400}{p^2}
\]

### Step 3: Find the value of $ q $ when $ p = 220 $
Substitute $ p = 220 $ into the expression $ q = \frac{4400}{p} - 3 $:

\[
q = \frac{4400}{220} - 3 = 20 - 3 = 17
\]

So, when $ p = 220 $, $ q = 17 $.

### Step 4: Calculate the elasticity coefficient
Using the formula $ E = \left| \frac{d q}{d p} \times \frac{p}{q} \right| $, substitute the known values:

\[
\frac{d q}{d p} = -\frac{4400}{220^2} = -\frac{4400}{48400} = -0.0909
\]

Now multiply by $ \frac{p}{q} = \frac{220}{17} $:

\[
E = \left| -0.0909 \times \frac{220}{17} \right| = \left| -0.0909 \times 12.94 \right| = \left| -1.176 \right| = 1.18
\]

### Final Answer
The elasticity coefficient when $ p = 220 $ is:

\[
E = 1.18
\]

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Would you like a breakdown of any step, or do you have any further questions?

### 5 Related Questions:
1. How do we interpret the value of the elasticity coefficient?
2. What does it mean if the elasticity coefficient is greater than 1?
3. How would the elasticity change if the demand function was different?
4. What is the significance of the negative sign in elasticity calculations?
5. How do you find elasticity at different points on a non-linear demand curve?

### Tip:
Price elasticity tells you how sensitive the quantity demanded is to a change in price. An elasticity coefficient of 1.18 means the product is **elastic**—a 1% change in price leads to a 1.18% change in quantity demanded.

If the demand function for a product is given by p = 4400 / (q + 3), find the elasticity coefficient for this demand function when p = $220. Round your answer off to 2 decimal places.

Learn how to find the elasticity coefficient for the demand function p = 4400 / (q + 3) when the price is $220. This involves using the price elasticity of demand formula, differentiation, and algebra to calculate the coefficient to 2 decimal places. Suitable for advanced high school or college-level economics and calculus students.

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