Equilibrium Price: Skateboards   The demand for your hand-made skateboards, in weekly sales, is
q = −6p + 600
if the selling price is $p. You are prepared to supply
q = 4p − 300
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, we need to set the quantity demanded $ q_d $ equal to the quantity supplied $ q_s $, as at equilibrium, the quantity demanded is equal to the quantity supplied.

Given:
- Demand function: $ q_d = -6p + 600 $
- Supply function: $ q_s = 4p - 300 $

At equilibrium:
\[
q_d = q_s
\]
\[
-6p + 600 = 4p - 300
\]

Now, solve for $ p $:

1. Add $ 6p $ to both sides:
\[
600 = 10p - 300
\]

2. Add $ 300 $ to both sides:
\[
900 = 10p
\]

3. Divide by 10:
\[
p = 90
\]

Therefore, the equilibrium price is **$90 per skateboard**.

Would you like further details on how equilibrium works, or do you have any questions?

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Here are 5 related questions to explore:
1. How would a change in the supply function affect the equilibrium price?
2. What happens to the equilibrium quantity if the demand increases?
3. How do you calculate the equilibrium quantity once you know the price?
4. How does a price above the equilibrium affect the market?
5. What is the role of elasticity in determining the equilibrium price?

**Tip**: Always double-check your functions when setting them equal at equilibrium, as small algebraic errors can lead to incorrect solutions.

The demand for your hand-made skateboards, in weekly sales, is q = −6p + 600 if the selling price is $p. You are prepared to supply q = 4p − 300 per week at the price $p. What price should you sell your skateboards for so that there is neither a shortage nor a surplus?

Discover how to find the equilibrium price for skateboards using supply and demand functions. This problem involves solving linear equations, key concepts in algebra, and the equilibrium price theorem, suitable for Grades 10-12 students.

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