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
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 is each firm’s profit?
a.$0
b.$200
c.$400
d.$800
10
1. 40
2. 400
20
To determine the quantity of output that a typical firm will produce, we need to find the equilibrium point where the quantity demanded (QD) equals the quantity supplied (QS).
Given:
Market demand: QD = 200 - 3P
Market supply: QS = 2P + 100
Setting QD equal to QS, we have:
200 - 3P = 2P + 100
Simplifying the equation:
200 - 100 = 2P + 3P
100 = 5P
P = 20
Now that we have the equilibrium price (P = 20), we can substitute it back into either QD or QS to find the quantity:
QD = 200 - 3(20)
QD = 140
QS = 2(20) + 100
QS = 140
Since QD and QS are both equal to 140, a typical firm will produce a quantity of 140.
Therefore, the answer to the first question is b. 20.
To determine each firm's profit, we need to calculate their total revenue (TR) and total cost (TC).
Total revenue (TR) is given by the equation:
TR = P × Q
For each firm, total cost (TC) is the sum of the marginal cost (MC) and average total cost (ATC):
TC = MC × Q + ATC × Q
Substituting the given values into the equations:
TR = 20 × 140
TR = 2800
TC = 0.5Q × Q + 0.25Q × Q
TC = 0.75Q^2
For a typical firm, profit (π) is given by the equation:
π = TR - TC
Substituting the values we found:
π = 2800 - 0.75(140)^2
π = 2800 - 14700
π = -11900
Since the profit (π) is negative, it means the firm is making a loss.
Therefore, the answer to the second question is a. $0.