In class we mathematically derived the equilibrium effects of a per unit sales tax. We also showed the effects graphically, and identified the tax revenue. For this question, suppose you're an economic advisor in charge of trying to raise a maximum level of tax revenue for the government. You consider taxing the suppliers in the market for corn, a major agricultural product in the United States. Suppose consumer demand for corn is:

qd = 200 - 50pd

and supply is

qs = 50ps

Your ultimate goal is to solve for $&tau, the per unit tax that maximizes revenue.

a) Solve for the equilibrium quantity and price, after the tax has been imposed. (Hint: Remember in equilibrium, qd = qs. However, ps = pd - τ when a tax exists. Substitute for ps, then solve for the equilibrium. You answers will be a function of &tau.

b) Noting that tax revenue is T, we know T = τQ. Using your answer from (a), substitute for Q and write the resulting expression.

c) Set up your optimization problem. Include all parts as we have done in lecture.

d) Finally, solve for τ*, the optimal per unit tax.

Although it is not required, a diagram illustrating the effects of a tax is helpful.