Consider a competitive market in which the market demand for the product is expressed as P = 65 -0

Firstly, we find the market supply.
Individual supply is given by P = MC
MC = d(TC)/dq = 2(6q) - 3 = 12q - 3
So, P = MC gives,
P = 12q - 3
So, 12q = P + 3
So, q = (P/12) + (3/12)
Market supply, Q = 1000q = 1000[(P/12) + (3/12)]
So, Q = (1000P + 3000)/12
So, 1000P + 3000 = 12Q
So, 1000P = 12Q - 3000
So, P = 12Q/1000 - 3000/1000
So, P = 0.012Q - 3

At equilibrium, market demand = market supply
So, 65 - 0.005Q = 0.012Q - 3
So, 0.012Q + 0.005Q = 65 + 3
So, 0.017Q = 68
So, Q = 68/0.017
So, Q = 4000

P = 0.012(4000) - 3 = 48 - 3 = 45
So, P = 45

b. q = Q/1000 = 4000/1000 = 4
So, q = 4

c. Now, market demand = market supply gives
99 - 0.005Q = 0.012Q - 3
So, 0.012Q + 0.005Q = 99 + 3
So, 0.017Q = 102
So, Q = 102/0.017
So, Q = 6000

P = 0.012(6000) - 3 = 72 - 3 = 69
So, P = 69

q = Q/1000 = 6000/1000 = 6
So, q = 6

d. No, if the original situation represented a long run equlibrium then the new situation would not represent a long run equilibrium because in the new situation, demand has increased which creates positive economic profits which can only occur in the shirt run in a competitive market because in long run, more firms will enter so supply will also increase.