1. (32 points) The market demand function is D(P) = 160_2P and the market supply function is S(P.) = P, _ 14, where P. and P, are the prices paid by the consumers and received by the producers respectively. Also, D(P.) and S(P,) give the quantities demanded and supplied, respectively. a. Find the market equilibrium (no-tax policy). (6 points) b. Suppose that the supplier is required to pay a per unit tax of t = $6. Draw a graph to show this change in policy compared to the no-tax policy. Find the equilibrium quantity and prices P. and P, How much of the tax is passed on to the consumers? (8 points) c. Suppose now that the demander is required to pay a per unit tax of t = $6 instead of the supplier. Draw a graph to show this change in policy compared to the no- tax policy. Find the equilibrium quantity and prices P, and P . Compare your answers with part (6). (8 points) d. Calculate the change in consumer surplus, the change in producer surplus, the tax revenue, and the deadweight loss (DWI) as a result of the tax policy. (10 points) 2. (36 points) A firm produces a product y using the production technology y = / (21, ; ) = 2ovo, where @ and 2, are the inputs used for the production. Suppose that the firm is using @, = 9 units of input 2 and is unable to vary this quantity in the short- run. In the short-run, the only thing that is left for the firm to choose is the amount of input 1. Let the input prices be w, = $6 and w, = $2, and the output price be p = $2. a. Write the firm's short-run profit-maximization problem and find the amount of input 1 used to maximize its short-run profit. (8 points) b. Suppose that the price of input 2 changes to wy = $4. How does your answer to part (@) change? What if the new output price is P = $4? How does your answer to part (@) change? (8 points) c. Keep the prices at w, = $6 and w, = $2. What is the minimum short-run cost of producing 12 units of output? (10 points) d. In the long-run, what are the inputs , and ,, and the long-run cost of producing 12 units of output? (round your answers to two decimal places). (10 points)