# Managerial Econ- 3 Problems

• YOU MUST SHOW YOUR WORK. No credit will be given for answers, right or wrong, if you do not show how you obtained them.
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1. Find the equilibrium price and quantity with QD = 90 -16P and QS = 14P. (10 points)
2. Increase the supply function in problem 1 by 18 and calculate the new equilibrium price and quantity. (10 points)
3. Starting with QD = 150 – 2.5P and QS = 30 + 5P and supposing that the government imposes an excise tax of \$2.25 per unit collected from producers, find (a) the new equilibrium price and quantity and (b) how much of the tax is actually paid by consumers and how much falls on producers (20 points)

Note that the new supply curve should show that the QS is 18 units greater at every price.Reference pages 65-66 of the text.

To work problem 3 you must do the following.

1. Find the pre-tax equilibrium. The amount of the tax paid by consumers is the amount by which the price of the product goes up. You the pre-tax equilibrium to compare to the post-tax equilibrium
2. Find the reverse supply function. A normal supply equation tells you what the quantity supplied is for any given price. You, however, need to add the excise tax, measured in dollars, to the cost, measured in dollars. So you need to rewrite the supply equation algebraically so that is shows dollars (i.e., price) at each possible quantity supplied. This is called a reverse supply function.
3. Add the excise tax to the constant to get the reverse supply function with the tax included.
4. Algebraically convert the reverse to the standard supply function (i.e., reverse the reverse supply function)
5. Find the new equilibrium. The change in the price is the amount paid by the consumers. Any remaining amount of the tax is paid by the producer.

Reference the calculations on pp. 67-68