For the next 3 questions, consider the demand curve

Q = 10000 - 200 p

where Q is the market quantity and p is the good's price. At what price is elasticity of demand exactly equal to 1?

To find the price where the elasticity of demand is exactly equal to 1, we need to use the formula for the price elasticity of demand (PED):

\[
\text{Elasticity of demand (E)} = \left( \frac{dQ}{dp} \right) \cdot \frac{p}{Q}
\]

### Step 1: Differentiate \( Q = 10000 - 200p \)
To get \( \frac{dQ}{dp} \), take the derivative of the demand function with respect to \( p \):

\[
\frac{dQ}{dp} = -200
\]

### Step 2: Set up the elasticity equation
Substitute \( \frac{dQ}{dp} = -200 \), \( Q = 10000 - 200p \), and the elasticity equal to 1 into the formula:

\[
1 = (-200) \cdot \frac{p}{10000 - 200p}
\]

### Step 3: Solve for \( p \)
Now, solve the equation for \( p \).

\[
1 = -200 \cdot \frac{p}{10000 - 200p}
\]

Multiply both sides by \( 10000 - 200p \) to eliminate the denominator:

\[
10000 - 200p = -200p
\]

Simplify the equation:

\[
10000 = 0
\]

\[
10000 - 200
\ calcul work

For the next 3 questions, consider the demand curve Q = 10000 - 200p, where Q is the market quantity and p is the good's price. At what price is elasticity of demand exactly equal to 1?

This guide explains how to find the price at which the elasticity of demand equals 1 for the demand curve Q = 10000 - 200p. It covers key concepts like price elasticity of demand, the demand curve, and differentiation, making it ideal for economics students at the high school or undergraduate level.

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