Question #68011

Supply Function Q= 15.000+350P
Demand Function Q=35.000-150P
Cost Function=TC=40+2Q
a)Find the Marginal Revenue of this firm
b)Find the Marginal Cost of this firm
c)Find the optimal output for this firm
d)Find the optimal total revenue and profit for this firm
e)In a perfectly competitive market, firms earn zero profit in the long run. Why do firms stay in business if profit is zero ?

Expert's answer

Qs = 15,000 + 350P, Qd = 35,000 - 150P, TC = 40 + 2Q.

a) Marginal Revenue of this firm is MR = P. In equilibrium Qd = Qs, so:

15,000 + 350P = 35,000 - 150P,

500P = 20,000,

Pe = $40,

So, MR = P = $40.

b) The Marginal Cost of this firm is MC = TC' = 2.

c) The optimal output for this firm is Qe = 15,000 + 350*40 = 29,000 units.

d) The optimal total revenue and profit for this firm are:

TR = P*Q = 40*29,000 = $1,170,000,

TP = TR - TC = 1,170,000 - (40 + 2*29,000) = $1,111,960.

e) As in a perfectly competitive market firms earn zero profit in the long run, the firms continue to stay in business if profit is zero.

a) Marginal Revenue of this firm is MR = P. In equilibrium Qd = Qs, so:

15,000 + 350P = 35,000 - 150P,

500P = 20,000,

Pe = $40,

So, MR = P = $40.

b) The Marginal Cost of this firm is MC = TC' = 2.

c) The optimal output for this firm is Qe = 15,000 + 350*40 = 29,000 units.

d) The optimal total revenue and profit for this firm are:

TR = P*Q = 40*29,000 = $1,170,000,

TP = TR - TC = 1,170,000 - (40 + 2*29,000) = $1,111,960.

e) As in a perfectly competitive market firms earn zero profit in the long run, the firms continue to stay in business if profit is zero.

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