Let the demand and supply functions be represented by p=D(q) and p=S(q), respectively, where p is the price per item in dollars and q is the quantity of items. D(q) = 42-.03q S(q) = .02q -20

Find the equilibrium price. Hint: you will first find the equilibrium quantity (q) and once you know this you can find the equilibrium price (p)

At equilibrium supply equals demand

42-.03q=.02q-20
.01q=20
q=2000

To find the equilibrium price, we need to find the quantity at which the demand and supply functions are equal.

Step 1: Set D(q) = S(q)

42 - 0.03q = 0.02q - 20

Step 2: Simplify the equation

0.05q = 62

Step 3: Solve for q

q = 62 / 0.05

q = 1240

The equilibrium quantity is 1240.

Step 4: Find the equilibrium price by substituting the equilibrium quantity into either the demand or the supply function.

Using the demand function:
p = D(q) = 42 - 0.03q
p = 42 - 0.03(1240)
p = 42 - 37.2
p = 4.8

The equilibrium price is $4.80 per item.

To find the equilibrium price, we need to find the quantity at which the demand and supply functions intersect. This quantity is known as the equilibrium quantity (q).

To find the equilibrium quantity, we set the demand and supply functions equal to each other and solve for q:

D(q) = S(q)
42 - 0.03q = 0.02q - 20

To solve this equation, we can first add 0.03q to both sides:
42 = 0.05q - 20

Next, we can add 20 to both sides:
62 = 0.05q

Finally, we divide both sides by 0.05 to solve for q:
q = 62 / 0.05
q = 1240

So, the equilibrium quantity (q) is 1240.

Now that we have the equilibrium quantity, we can find the equilibrium price (p) by plugging this value back into either the demand or supply function. Let's use the demand function, D(q), to find the equilibrium price:

p = D(q)
p = 42 - 0.03q
p = 42 - 0.03 * 1240
p = 42 - 37.2
p = 4.8

Therefore, the equilibrium price is $4.80 per item.