$2.$ Let $\backslash ($ c$\_\{$i$\}\backslash )$ be the constant marginal and average cost for firm $\backslash ($ i $\backslash )($so that firms may have different marginal costs$).$ Suppose demand is given by $\backslash ($ P$=1-\backslash$mathrm$\{$Q$\}\backslash ).$

a$.$ Calculate the Nash equilibrium quantities assuming there are two firms in a Cournot market. Also compute market output, market price, firm profits, industry profits, consumer surplus, and total welfare.