Suppose market for corn is in long-run equilibrium. All suppliers face same cost curve $AC=300-q+0.02q^2$. The demand curve is given by: $D(P)=642,000-36P$. How many firms are there in the market ?
I'm getting no idea how to do it. Any help would be appreciated
The long-run competitive equilibrium price equals the minimum average total cost.
We find the quantity produced by each firm at the minimum average cost by solving the first-order condition $$ \frac{\mathrm d AC(q)}{\mathrm d q}=-1+0.04q=0\quad\Longrightarrow\quad q=25 $$ Then plug this quantity into the average total cost equation to get the equilibrium price: $$ P=AC(25)=300-25+0.02\times (25)^2=287.5 $$ At this price, the quantity demanded in the market is $$ D(287.5)=642,000−36\times 287.5=631,650 $$ So, the number of firms is $$ N=\frac{\text{market output}}{\text{firm output}}=\frac{631,650}{25}=25,266 $$
