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3) Everyone loves chocolate cake. Suppose that the market for chocolate cake at Columbia University is perfectly competitive and that the supply and demand are described by the equations below: Demand: Q!) = 75 \"P Supply: Q5 = 25 + 4;) where Q is the quantity of chocolate cakes, and the p is the price of one chocolate cake. a) Determine the equilibrium price and quantity. Graph the supply and demand curves. b) The administration is worried about sugar consumption amongst students and decides to tax cake consumption with a tax of $1 on each cake. The quantity supplied equation stays the same, but consumers now face a new price of$(p + r) and the new demand equation is QB = 75 (p + r). If the tax is set to t = 5, determine the new equilibrium price and quantity. Why is the price and equilibrium quantity different? Illustrate the impact of the tax on the supply and demand curves. 0) Calculate the amount of tax collected and the deadweight loss. How is the tax burden shared between buyers and sellers? How does the answer relate to the elasticity of supply and demand