Question

3. Suppose you are the CEO of a watchmaking firm operating in a competitive market. Your cost of production is given by C=200+2q2, where q is the level of output and C is total cost.
a. What is the marginal cost?
b. What is fixed cost?
c. If the price of watches is $100, how many watches should you produce to maximize profit?
d. What will the profit level be?
e. At what minimum price will the firm produce a positive output?

Answer 1

Answer
a)
MC=dC/dq=4q ...... MC is found by the first derivative of the total cost function and the power rule is used.
b)
FC is the constant term in the total cost function and that is $200
c)
the firm produces at MC=P
equating both
4q=100
q=25

d)
profit=TR-TC
TR=P*Q=100*25
=2500
TC=200+2*25^2
=1450
profit=2500-1450=1050
-
e)
above 0
the price is above minimum AVC and that is found by first-order condition equal to zero (FOC is the derivative of the function
VC=TC-FC=200-2q^2-200=2q^2
AVC=VC/q=2q
dAVC/dq=2
and the derivative is equal to constant means the min(AVC) is equal to zero or below so the firm should have the price above zero to produce.