The residents of Seltzer Springs, Michigan consume bottles of mineral water according to the demand function D(p) = 1,000 -p. Here D(p) is the demand per year for bottles of mineral water if the price per bottle isp. The only distributor of mineral water in Seltzer Springs, Bubble Up, purchases mineral water atcper bottle from their supplier Perry Air. Perry Air is the only supplier of mineral water in the area and behaves as a profit-maximizing monopolist. For simplicity, we suppose that it has zero costs of production.

R = (1000-q)q = 1000q-q²

MR = 1000 - 2q

Therefore

1000-2q = c

results in

q* = 1000- c / 2

Where p* is attained with the inverse of the demand

p* = 1000 - q

= 1000 - 1000 - c

2

= 1000+c/2

Proceeding to set MR=MC with the substitution method:

1000 - 2 (1000 - c / 2) = c

This is supposed to result in c* = 500 or a price of $500 but I can't get the calculation to that number.