To find the equilibrium price and quantity, we need to set the supply equal to the demand and solve the system of equations defined by the supply and demand models.
The supply model is given by:
\[ p = 0.004x \]
The demand model is given by:
\[ p = -0.006x + 200 \]
(a) Solve the system of equations.
We can find the equilibrium by setting the two equations for \( p \) equal to each other:
\[ 0.004x = -0.006x + 200 \]
Now, we'll combine like terms by adding \( 0.006x \) to both sides:
\[ 0.004x + 0.006x = 200 \]
This simplifies to:
\[ 0.010x = 200 \]
Now, we can solve for \( x \):
\[ x = \frac{200}{0.010} = 20000 \]
So, the equilibrium quantity \( x \) is \( 20000 \).
(b) What is the equilibrium price?
Now that we have the equilibrium quantity, we can plug it back into either the supply or demand equation to find the equilibrium price \( p \). We'll use the supply equation:
\[ p = 0.004x = 0.004(20000) = 80 \]
(c) What is the equilibrium quantity?
We already found the equilibrium quantity \( x \) in part (a), which is:
\[ \text{Equilibrium quantity} = 20000 \]
Summary
- (a) The equilibrium quantity is \( 20000 \).
- (b) The equilibrium price is \( 80 \) S.
- (c) The equilibrium quantity is \( 20000 \).