To solve this, we calculate the elasticity of demand using the given price-demand equation and determine the approximate percentage change in demand due to a 2% price decrease.

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Part 1: Elasticity of Demand

The elasticity of demand is calculated using the formula:

$E(p) = \left| \frac{p}{x} \cdot \frac{dx}{dp} \right|$

Step 1: Express $x$ in terms of $p$:

The given price-demand equation is: $p + 0.002x = 28$

Solve for $x$: $0.002x = 28 - p$ $x = \frac{28 - p}{0.002} = 14,000 - 500p$

Step 2: Differentiate $x$ with respect to $p$:

$\frac{dx}{dp} = -500$

Step 3: Calculate $E(p)$ at $p = 21$:

Substitute $p = 21$ into the equation for $x$: $x = 14,000 - 500(21) = 14,000 - 10,500 = 3,500$

Now calculate $E(p)$: $E(p) = \left| \frac{p}{x} \cdot \frac{dx}{dp} \right|$ $E(21) = \left| \frac{21}{3,500} \cdot (-500) \right|$ $E(21) = \left| \frac{21 \cdot -500}{3,500} \right| = \left| \frac{-10,500}{3,500} \right| = 3$

Thus, the elasticity of demand at $p = 21$ is 3.

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Part 2: Approximate Percentage Change in Demand

If the price decreases by 2%, the approximate percentage change in demand can be calculated as:

$\%\Delta x \approx E(p) \cdot \%\Delta p$

Here: $E(p) = 3 \quad \text{and} \quad \%\Delta p = -2\% = -0.02$

Substitute into the formula: $\%\Delta x \approx 3 \cdot (-0.02) = -0.06$

Convert to percentage: $\%\Delta x = -6\%$

Thus, the approximate percentage change in demand is an increase of 6%.

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Final Answers:

1. Elasticity of demand at $p = 21$: 3.
2. Approximate percentage change in demand: 6% increase.

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Do you want further details or clarifications?
Here are 5 related questions:

1. What happens to elasticity as the price approaches 28 in this equation?
2. How is total revenue affected when price decreases in this scenario?
3. What is the significance of unit elasticity (i.e., when $E(p) = 1$)?
4. How can elasticity help determine optimal pricing for maximizing revenue?
5. How does elasticity change if the slope of the demand curve changes?

Tip: Elasticity greater than 1 (elastic demand) implies demand is sensitive to price changes, so lowering prices can increase total revenue.