Imagine an economy with Demand curve D and supply curve S. Demand is strictly decreasing and Supply is strictly increasing. You may assume all the conditions for equilibrium existence hold. Denote with p the market price without tax and suppose the government imposes a lump sum tax, t. Denote with p the equilibrium price that consumers pay after the lump sum tax is implemented. Show that p p < t. That is, the price increase that consumers experience after the tax is implemented is actually lower than the full amount of the tax. A roadmap on how to proceed, should you need to: Proceed by contradiction: contrary to what we want to prove, assume that p t p. Under this assumption, how does S(p t) compare to S(p)? Is it higher/lower/equal to? How does S(p) compare to D(p)? How does D(p) compare to S(p t)? These items induce a comparison between D(p) and D(p). Is this comparison consistent with our assumption that D is decreasing? Explain why or why not.