please help me with the question 8 9 10 thank you so muchSol

please help me with the question 8 9 10 thank you so much!!

Solution

(8) Total cost (C) = 2 + (q/4) + (q² / 8)

Marginal cost (MC) = dC/dq = (1/4) + (2q/8) = (1/4) + (q/4)

Average cost (AC) = C/q = (2/q) + (1/4) + (q/8)

In long run equilibrium, Price = AC = MC

Equating MC & AC,

(2/q) + (1/4) + (q/8) = (1/4) + (q/4)

2/q = q/8

q² = 16

q = 4 (Long run equilibrium quantity)

Long run price = MC = (1/4) + (4/4) = (1/4) + 1 = 5/4 = 1.25

(9) Long run equilibrium price = 5/4 = 1.25 (Computed in part 8)

(10) Given demand function: Q = 2,500 - 100P

When long run P = 1.25, Q = 2,500 - (100 x 1.25) = 2,500 - 125 = 2,375

Number of firms in long run = Q / q = 2,375 / 4 = 593.75 ~ 593 (Taking lower integer value for number of firms)