Question $3,(9$ marks$)$

Suppose that Firm $1$ can choose to produce either good A$,$ good B$,$ both goods, or nothing. Firm $2,$

on the other hand, can produce only good C or nothing. Firms' profits corresponding to each

possible scenario of goods for sale are described in the following table.

$($a$)$ Set up the normal form game for when the two firms simultaneously select their production

choices. What will be the Nash equilibrium$($s$)?$

$($b$)$ What is the maximum amount that Firm $1$ should be willing to pay for the opportunity to

move first instead of moving at the same time as Firm $2?$ Explain.