Suppose the market demand for milk is [Math Processing Error]Qd=40−4P, where [Math Processing Error]Qd is millions of gallons demanded and [Math Processing Error]P is the price per gallon. Suppose the market supply for milk is [Math Processing Error]Qs=−40/3+20/3P

a. What is the equilibrium price?

b. Suppose a tax of $1 per gallon of milk is imposed in this market. What is the new price paid by consumers?

a. What is the equilibrium price?

To get the equilibrium values, we set the market demand and supply equal, D = S,

Qd = Qs

40 - 4P = -40/3 + 20/3P

P = $5

Substituting P to get Q to either function,

Qd = 40 - 4P

Qd = 40 - 4 (5)

Q = 20

b. Suppose a tax of $1 per gallon of milk is imposed in this market. What is the new price paid by consumers?

The demand and supply functions can be written as their inverses, such as,

Pd = 10 - 1/4Qd

Ps = 2 + 3/20 Qs + tax = 2 + 3/20 Qs + 1

Solving for the new equilibrium, we set the inverse demand function and the inverse supply function equal,

10 - 1/4Qd = 2 + 3/20Qs + 1

Q = 17.5

Substituting Q to get P,

Pd = 10 - 1/4Qd = 10 - 1/4 (17.5) = $5.63

Ps = 2 + 3/20 Qs = 2 + 3/20 (17.5) = $4.63

After-tax, consumers will pay $5.6 and producers will receive $4.63