1. (26 points) In a competitive market, consumer demand is q (p) = 10 - ap and supply 4s (p) = bp, where a, b are positive constants. a) (2 points) Compute the equilibrium price p* and quantity q*. b) (2 points) The government imposes a unit tax t. Find the new after-tax equilibrium quantity qt. Find how much do consumers pay after tax pe, how much do producers receive after tax Pp? c) (2 points) Compute the dead weight loss from the tax (as function of t). d) (2 points) Compute the government revenue from the tax (T as function of t). e) (4 points) If the government wants to maximize the tax revenue, what t will it choose? f) (4 points) What burden of the tax (tax incidence) (in proportion) is paid by consumers (note it be)? By producers (note it bp)? g) (2 points) What is the point price elasticity of demand at market equilibrium Ed? What is the point price elasticity of supply at market equilibrium ,? (use derivatives) h) (4 points) Compare the relative elasticities of demand and supply you just computed (in absolute values) ( ) with the relative tax incidence on consumers and producers ("). What do you deduce about the link between elasticity and tax incidence? i) (4 points) If a = 1, b = 3, t = 5, represent on a graph the supply, the demand, the market equilibrium, the government's tax revenue and the dead weight loss. As usual, indicate appropriate values and Always label your axes