3. Suppose that the inverse demand for marching band music is given by P = $1,000 – Q. Because marching bands across the world produce music of sufficient quality at increasing marginal cost, the industry marginal cost is given by MC = 0.75Q. Unfortunately, marching band music is not produced in a vacuum: People near marching bands become increasingly aggravated the more music they hear. At the industry level, the external marginal cost is given by EMC = 0.25Q.

a. Graph the demand, marginal cost, and external marginal cost functions.

b. If marching bands do not consider the external marginal costs they impose on others, how many songs will be played?

i. Calculate the total consumer surplus.

ii. Calculate the total producer surplus.

iii. Calculate the total surplus to market participants.

iv. Calculate the total damage to those harmed. (Hint: This damage can be represented as the area under the EMC curve. It’s up to you to figure out why!)

v. Subtract the damage to those harmed from total surplus to market participants to determine the net value created for society by marching band music.

c. Determine social marginal cost.

d. Determine the quantity of marching band music that would be produced if marching bands were forced to consider the costs they imposed on others.

e. What happens to the price of marching band music if the bands were forced to consider the external marginal costs?

f. As you did in (b), calculate consumer surplus, producer surplus, and total damage. (Be sure to remember that producer surplus is the area between private marginal cost and the price!)

Compared to your answers in (b), i. What happens to the total surplus received by market participants when external marginal costs are considered?

ii. What happens to the damage created by marching band music?

iii. What happens to the net value created for society by marching band music?