Sove it plxxx

10. The market demand function for widgets is QD = 200 - 3PD (3) where Qp denotes quantity demanded and Pp denotes the after-tax price paid by the consumer. The market supply function for widgets is Qs = 100 + 5PS (4) where Qs denotes quantity supplied and Pg denotes the after-tax price received by the supplier. (a) What is the market equilibrium price and quantity in the absence of a tax? Label your solutions for the equilibrium market price and quantity P* and Q*, respectively. (b) Calculate the price elasticity of demand and price elasticity of supply at P* and Q*. Label the price elasticity of demand ED (P*), and label the price elasticity of supply es (P*). (c) In Chapter 16, we demonstrated that if r denotes the tax rate, the impact of a $1 increase in T on the equilibrium price is dp* (T) ED dT ES - ED (5) where Ep is the price elasticity of demand and es is the price elasticity of supply. Use Equation 5 and your answers to Part b to calculate how the equilibrium price of widgets will respond if the government requires that consumers pay a quantity tax of $1 per widget. (d) Now say that the government imposes a $1 quantity tax on consumers of widgets. That is PD = Ps +1 Solve for the equilibrium quantity (Q"), equilibrium demand price (PZ), equilibrium supply price (P5). (e) Compare P* from Part a with P, and Pg from Part d. What fraction of the incidence of the tax is borne by consumers in this example? What fraction of the tax's incidence is borne by the producers