Assuming an interior solution, consumer i's demand for the gizmos is zi(p) = 75p 2 when p < 75 0. when p 75 So the short-run aggregate demand curve is D(p) = K i=1 zi(p) = K(75p) 2 when p 75 0. when p > 75 b) Firm j solves the following PMP. max qj pqj (100 5qj q2 j ) So, firm j's supply function is qj (p) = p5 2 when p 5 0. when p < 5 (1) Then the short-run aggregate supply curve is S(p) = N j=1 qj (p) = N (p5) 2 when p 5 0. when p < 5 c) By the market clearing condition, when the market comprises 300 consumers and 30 firms, 300(75 p) 2 = 30(p 5) 2 10(75 p) = p 5 11p = 755 p = 755 11 68.64 Since qj (p) = p5 2 = 350 11 , each firm's profit is pqj (p) (100 5qj (p) q2 j (p)) 912.40 3