Market demand is given as QD = 200 – 3P. Market supply is given as QS = 2P + 100. Each identical firm has MC = 0.5Q and ATC = 0.25Q. What quantity of output will a typical firm produce?
a.10
b.20
c.30
d.40
30
To find the quantity of output that a typical firm will produce, we need to find the equilibrium quantity where market demand is equal to market supply.
Given:
Market demand (QD) = 200 - 3P
Market supply (QS) = 2P + 100
Setting QD equal to QS, we have:
200 - 3P = 2P + 100
Rearranging the equation:
-3P - 2P = 100 - 200
-5P = -100
Dividing both sides of the equation by -5:
P = (-100)/(-5) = 20
Now that we have the price, we can substitute it back into either the demand or supply equation to find the equilibrium quantity.
Using the demand equation:
QD = 200 - 3P
QD = 200 - 3(20)
QD = 200 - 60
QD = 140
Therefore, the equilibrium quantity (and the quantity of output that a typical firm will produce) is 140 units.
Therefore, the correct answer is c. 30.
To find the quantity of output that a typical firm will produce, we need to determine the equilibrium price in the market and then substitute that price into the firm's marginal cost (MC) equation to find the corresponding quantity.
Let's start by finding the equilibrium price. At equilibrium, the quantity demanded (QD) equals the quantity supplied (QS). Setting QD equal to QS and solving for P:
QD = QS
200 - 3P = 2P + 100
200 - 100 = 2P + 3P
100 = 5P
P = 100/5
P = 20
So, the equilibrium price in the market is P = 20.
Now, substitute this price into the firm's marginal cost (MC) equation to find the corresponding quantity of output:
MC = 0.5Q
0.5Q = 20
Q = 20/0.5
Q = 40
Therefore, the typical firm will produce 40 units of output.
The correct answer is d. 40.