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3. Consider a perfectly competitive market in which a tax of to 2 0 is collected from sellers for each unit sold. Price and quantity are determined by the following supply and demand functions: Qd = 1000 - 20P QS = -200 + 100(P - to) a. Write down the matrix equation Ax = b that describes the equilibrium combination of price and quantity when x is defined as x = To-. In particular, what are A and b? b. Use Cramer's rule to find the function that relates the equilibrium quantity (Q") to the per- unit tax (to). c. Write down the equation that describes total tax revenue as a univariate function of to. Hint: by definition, TTR = Q' x to. d. Find the first and second derivatives of the total tax revenue function. e. How large would the tax need to be in order to maximize total tax revenue