Question

The competitive widget market currently has 3 identical producers with production costs c(q) = 100+10q+q^2, where q is the number of widgets each individual produces.

(a) What is each firm’s marginal cost?
(b) Find the short run aggregate supply function in this market.

(c) If demand for widgets is Qd = 100 − P , what is the long run market price?

(d) How many producers are there in the long run equilibrium?

Answer 1

Answer
a)
marginal cost is the change in total cost and a change in function found by differentiation
MC=dc/dq=10+2q
MC=10+2q

b)
A short run supply function is the marginal cost function
MC=10+2q
P=10+2q ........ inverse supply curve
converting to a normal form
2q=P-10
q=0.5P-5

c)
long run price is the minimum average total cost
ATC=c/q=100/q+10+q

the minimum at first differentiation equal zero
dATC/dq=-100/q^2+1=0
q^2=100
q=10 ........... one firm quantity
the price is
P=min(ATC)=100/10+10+10
=$30
Qd=100-30=70 .......... market quantity

d)
number of producer =market quantity/one firm quantity
=70/10
=7
there will be 7 producers