The demand for a certain company's e-reader can be approximated by*q* = 

780

*p*

 − 1 million units per year (60 ≤ *p* ≤ 400),

where *p* is the price charged by the company. Assume that the company is prepared to supply

*q* = 0.0195*p* − 1 million units per year (60 ≤ *p* ≤ 400)

at a price of $*p* per unit.

Given the demand and supply equations for the e-reader, we can analyze them as follows:

### Demand Equation:
The demand for the e-reader can be represented by the equation:
\[
q_d = \frac{780}{p} - 1 \quad \text{(in million units per year)},
\]
where $ p $ is the price charged per unit.

### Supply Equation:
The supply of the e-reader is given by:
\[
q_s = 0.0195p - 1 \quad \text{(in million units per year)},
\]
where $ p $ is the price per unit.

### Equilibrium Price and Quantity:
To find the equilibrium price ($ p^* $) and quantity ($ q^* $), we set the demand equal to the supply:
\[
q_d = q_s.
\]
So, 
\[
\frac{780}{p} - 1 = 0.0195p - 1.
\]

We can simplify and solve this equation to find the equilibrium price:

1. Remove the $-1$ from both sides:
\[
\frac{780}{p} = 0.0195p.
\]

2. Multiply both sides by $ p $ to eliminate the fraction:
\[
780 = 0.0195p^2.
\]

3. Divide both sides by 0.0195 to solve for $ p^2 $:
\[
p^2 = \frac{780}{0.0195}.
\]

4. Calculate the right side:
\[
p^2 = 40000.
\]

5. Take the square root of both sides to solve for $ p $:
\[
p^* = 200.
\]

Thus, the equilibrium price $ p^* $ is $200.

### Equilibrium Quantity:
Substitute $ p^* = 200 $ back into either the demand or supply equation to find the equilibrium quantity $ q^* $.

Using the supply equation:
\[
q^* = 0.0195 \times 200 - 1 = 3.9 - 1 = 2.9 \text{ million units per year}.
\]

### Summary:
- **Equilibrium Price ($ p^* $)**: $200 per unit.
- **Equilibrium Quantity ($ q^* $)**: 2.9 million units per year.

Would you like further details or have any questions? Here are some related questions that might interest you:

1. How would the equilibrium change if the demand function shifts?
2. What would happen to the equilibrium price and quantity if the supply function changes?
3. Can we find the consumer surplus at the equilibrium price?
4. How does elasticity affect the demand and supply in this scenario?
5. What external factors could shift the demand or supply curves for this e-reader?

**Tip:** Understanding how to calculate equilibrium helps in analyzing real-world market situations and the impacts of different price levels on supply and demand.

Understand how to determine equilibrium price and quantity in the e-reader market. Explore the demand and supply functions, and learn how to calculate equilibrium using these functions. Detailed solution with step-by-step calculations.

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