Smith is the owner of a sole mineral water spring in an isolated economy. It costs Smith $2 per gallon to get his water bottled. The inverse demand curve for Smith's water is p = 20 - q / 5 , where p is the price per gallon and q is the number of gallon sold.
a. Write down an expression π(q ) for profits as a function of q. Find the profit-maximizing choice of q for Smith, and the corresponding price and profit.
b. Suppose now Henry, Smith's neighbor, finds also a mineral spring that produces mineral water just as good as Smith's, but it costs Henry $6 a bottle. The total market demand remains as before. Determine the Cournot duopoly equilibrium.