Demand for widgets is Qd = 900 – 200(P) + 0.01(I) and supply is Qs = 200(P) – 200. We need to find equilibrium P and Q when I = $10,000Solution:a) At equilibrium, Qd = QsQd = Qs900 – 200(P) + 0.01(I) = 200(P) – 200On substituting I = $10,000900 – 200P + 0.01(10,000) = 200P – 200900 – 200P + 100 = 200P – 200300 = 400P or P = 0.75When P = 0.75, Qs = Qd = 200(0.75) – 200 = –50So, equilibrium price is $0.75 and equilibrium quantity is 50 units.Consumer Surplus = Area between the demand curve and equilibrium priceConsumer Surplus = (900 – 200(0.75)) * 50 / 2Consumer Surplus = $16,875Producer Surplus = Area between the supply curve and equilibrium priceProducer Surplus = (200(0.75) – 200) * 50 / 2Producer Surplus = $3,125b) If a tax of $1 per widget is imposed, then the new supply curve will shift upwards by $1.Tax-inclusive supply = 200(P) – 200 + 1Tax-inclusive supply = 200P – 199Equating the new supply curve with the demand curve, we get900 – 200(P) + 0.01(10,000) = 200P – 199900 – 200P + 100 = 200P – 199800 = 400P or P = 2When P = 2, the quantity demanded is 500 units and the quantity supplied is 300 units.The price paid by buyers = $2Price received by sellers = $1. Therefore, Producer Surplus = (300 * 1) / 2 = $150Consumer Surplus = (900 – 200 * 2) * 500 / 2 = $400d) When I = $50,000, then900 – 200P + 0.01(50,000) = 200PP = 1.5The new equilibrium quantity is Q = 200(1.5) – 200 = 100 units.Consumer Surplus = (900 – 200 * 1.5) * 100 / 2 = $12,500Producer Surplus = (200 * 1.5 – 200) * 100 / 2 = $5,000e) The economic efficiency effects of the tax depend on whether the tax is levied on the buyers or the sellers and the price elasticities of the demand and supply curves. If the income of the consumers is lower, then the burden of the tax will fall more heavily on the producers as consumers will not be able to afford the higher prices, which would lead to a larger deadweight loss.