Equilibrium Price: Skateboards   The demand for your hand-made skateboards, in weekly sales, is
q = −5p + 700
if the selling price is $p. You are prepared to supply
q = 5p − 400
per week at the price $p. What price should you sell your skateboards for so that there is neither a shortage nor a surplus?
$
per skateboard

To find the equilibrium price where there is neither a shortage nor a surplus, we need to set the demand equal to the supply. This means solving the equation:

\[
-5p + 700 = 5p - 400
\]

### Step-by-Step Solution

1. **Set up the equation:**

   \[
   -5p + 700 = 5p - 400
   \]

2. **Add $5p$ to both sides to get all the $p$ terms on one side:**

   \[
   700 = 10p - 400
   \]

3. **Add 400 to both sides to isolate the $10p$ term:**

   \[
   1100 = 10p
   \]

4. **Divide both sides by 10 to solve for $p$:**

   \[
   p = 110
   \]

### Conclusion

The equilibrium price is **$110** per skateboard.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What would be the equilibrium quantity of skateboards sold at this price?
2. How does a change in supply affect the equilibrium price?
3. What happens to the equilibrium price if the demand function changes?
4. How would setting a price above the equilibrium affect supply and demand?
5. What impact would an increase in production costs have on the supply equation?

**Tip:** Understanding how to derive the equilibrium in supply and demand models is key to grasping more complex economic scenarios.

Equilibrium Price: Skateboards. The demand for your hand-made skateboards, in weekly sales, is q = −5p + 700 if the selling price is $p. You are prepared to supply q = 5p − 400 per week at the price $p. What price should you sell your skateboards for so that there is neither a shortage nor a surplus? $ per skateboard

Learn how to find the equilibrium price for skateboards using linear equations for supply and demand. This problem involves solving a linear equation to determine the price where supply equals demand. Suitable for students in Grades 10-12.

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