Review for Midterm 2

Short-Answer Questions

ARSC 1432 Microeconomics Co-Seminar

SPRING 2009

1.  Willingness to Pay and Surplus:

  1. In the following table calculate marginal benefit for each quantity. From the following table, graph the Demand curve. If the market price of the good is $4, what is the consumer surplus?

Quantity / WTP / MB
1 / 9
2 / 15
3 / 20
4 / 23
  1. The Demand equation for Rolos is P= 5 – 2Q, and the Supply equation for Rolos is P=1 +Q. Calculate the equilibrium price and quantity. Calculate the Consumer and Producer surplus at the equilibrium.
  2. From part b. suppose that the government imposes a $1 tax on Rolos which shifts the Supply curve to P = 2 + Q. What is the new consumer and producer surplus at the new equilibrium? What is the tax revenue to the government and the dead weight loss to society?

Answer: a.

Quantity / WTP / MB
1 / 9 / 9
2 / 15 / 6
3 / 20 / 5
4 / 23 / 3

If the market price of the good is $4, then this consumer will buy the first, second and third unit of the good, but not the fourth since her Marginal Benefit for the fourth unit is less than $4.

Quantity / MB – P / Consumer surplus
1 / 9 – 4 / 5
2 / 6 – 4 / 2
3 / 5 – 4 / 1
Total surplus = / 8

b. The Demand equation for Rolos is P= 5 – 2Q, and the Supply equation for Rolos is P=1 +Q. The equilibrium price is 7/3 and the equilibrium quantity is 4/3. The consumer surplus at equilibrium, calculated by solving for the area of the triangle under the demand curve and above the price is: CS = ½*(4/3)*(8/3) = 16/9. The producer surplus at equilibrium, calculated by solving for the area of the triangle above the supply curve and below the price is: PS = ½*(4/3)*(4/3) = 8/9 .

c. From part b. suppose that the government imposes a $1 tax on Rolos which shifts the Supply curve to P = 2 + Q. What is the new consumer and producer surplus at the new equilibrium? What is the tax revenue to the government and the dead weight loss to society?

Now consumer surplus is lower: CS = ½*(1)*(2) = 1 . New Producer surplus is also lower: PS = ½*(1)*(1) = ½ . The government collects $1 on each unit sold after the imposition of the tax, so tax rev = $1 * 1 unit = $1. The dead weight loss to society is the triangle at the old equilibrium to the new quantity between the demand and new supply curves. DWL = ½*( 1/3)*(1) = 1/6. Though this seems like a small number, relative to both the tax revenue and the total surplus under original market equilibrium, this number is quite large.