Suppose that the inverse market demand function for widgets is p (q) = V 400 qP = and the inverse market supply function for widgets is pS (98) 1 60 q8 +5. = Equilibrium in the market for widgets requires that qP = qs at an economically relevant point (p*,q*). A point (p*,q*) is economically relevant if both p* > 0 and q* > 0. 1. Find the equilibrium price (p*) and equilibrium quantity (q*) for this market for widgets. (9 marks.) 2. Find the aggregate consumer surplus from the market for widgets when it is in equilibrium. (A hint is provided below.) (9 marks.) 3. Find the aggregate producer surplus from the market for widgets when it is in equilibrium. (A hint is provided below.) (7 marks.) These are some hints related to this question. - Hint 1: Suppose that is the price per widget paid by consumers and is the quantity of widgets purchased by consumers. Since p(q) > 0 for all q (0,400), we know that if p > 0 and (0,400), then the aggregate consumer surplus from the widget market can be calculated as CS (7,0) = 5 *p (6) dq - 0) 0. Hint 2: Suppose that p is the price per widget sold that is received by pro- ducers and is the quantity of widgets produced and sold by producers. Since ps (q) > 0 for all q> 0, we know that if p > 0 and > 0, then the aggregate producer surplus from the widget market can be calculated as PS (8,0) = p) (6) 1 * 38 () dq. Suppose that the inverse market demand function for widgets is p (q) = V 400 qP = and the inverse market supply function for widgets is pS (98) 1 60 q8 +5. = Equilibrium in the market for widgets requires that qP = qs at an economically relevant point (p*,q*). A point (p*,q*) is economically relevant if both p* > 0 and q* > 0. 1. Find the equilibrium price (p*) and equilibrium quantity (q*) for this market for widgets. (9 marks.) 2. Find the aggregate consumer surplus from the market for widgets when it is in equilibrium. (A hint is provided below.) (9 marks.) 3. Find the aggregate producer surplus from the market for widgets when it is in equilibrium. (A hint is provided below.) (7 marks.) These are some hints related to this question. - Hint 1: Suppose that is the price per widget paid by consumers and is the quantity of widgets purchased by consumers. Since p(q) > 0 for all q (0,400), we know that if p > 0 and (0,400), then the aggregate consumer surplus from the widget market can be calculated as CS (7,0) = 5 *p (6) dq - 0) 0. Hint 2: Suppose that p is the price per widget sold that is received by pro- ducers and is the quantity of widgets produced and sold by producers. Since ps (q) > 0 for all q> 0, we know that if p > 0 and > 0, then the aggregate producer surplus from the widget market can be calculated as PS (8,0) = p) (6) 1 * 38 () d
