• Suppose that there are one consumer of type "A" and another consumer of type "B".
• A's inverse demand function: p = 4-x and B's inverse demand function : p = 2-2/3x
• There is one firm with cost function c(x)=tx^2 + 1 (where t>0)

Derive the aggregate demand function.

Derive the firm's supply curve, assuming that the firm is a price taker in a competitive market (again, useful to draw it in a scratch paper)

Calculate market equilibrium for each t. As t changes, how does equilibrium change? Any economic intuition behind this change?