This is my question

Problem 2 (25 pts) Each of 100 identical consumers in the competitive market for widgets has a demand function 3:: (p) = 3 '23 where p is the price of a widget. The market supply function for widgets is (15(1)) 2 50p. (a) Find the market demand function for widgets, qD (p). Plot the market demand curve and the market supply curve on a graph with p on the vertical axis. Label your axes and intercepts clearly. (b) Find the equilibrium amount of widgets sold, q* and the equilibrium price, 30*. How much is the consumer's surplus? How much is the producer's surplus? Suppose now the government introduces a 50% tax on widgets, so that the price p3 that producers obtain per widget equals p5 = 0.5pD where pD is the price consumers pay per widget. (c) Find the new equilibrium quantity, qT after the tax and nd the price pD paid by consumers and the price 195 received by producers at the aftertax equilibrium. Explain how pD , p5 and qT compare to the equilibrium price and quantity in part (b). ((1) Find the tax revenue and the deadweight loss of the tax at the equilibrium in part (c). Explain why the deadweight loss arises