Question

1.Suppose the demand and supply for milk is described by the following equations: Qd= 600-100P and Qs= -150 + 150P, where P is the price of a gallon of milk.a.What is the equilibrium price and quantity?b.Suppose the US government imposes a $1 per gallon milk tax on dairy farmers. What is the new equilibrium price and quantity? How much do consumers now pay? How much do producers now receive? How much tax revenue is raised by the milk tax?c.Based on your answer to part b, is supply or demand more elastic? Explain.

Answer 1

Qd = 600 - 100P  

Qs = - 150 + 150P

Qd = Qs  

600 - 100P = - 150 + 150P  

600 + 150 = 150P + 100P

750 = 250P  

P = 3  

Q = 600 - 100(3)  

Q = 600 - 300

Q = 300  

b)  

US government imposes a $1 per gallon milk tax on dairy farmers so supply curve after tax is

Qs = - 150 + 150(P - T)

Qs = - 150 + 150(P - 1)

Qs = - 150 + 150P - 150

Qs = - 300 + 150P

Qs = Qd

- 300 + 150P = 600 - 100P

150P + 100 = 600 + 300

250 = 900

P = 3.6  

Price paid by consumers Pc = 3.6

Price received by producers = 3.6 - 1 = 2.6

Equilibrium quantity after tax is Q = 600 - 100(3.6) = 600 - 360 = 240

Tax revenue = (3.6 - 2.6)240 = 240  

Qd = 600 - 10P  

dQ/dP = - 10  

Ed = (dQ/dP)(P/Q)

= (- 10)(3/300)

= - 30/300

= - 0.1

|Ed| =  | -0.1| = 0.1 < 1 (inelastic)

Qs = - 150 + 150P  

dQ/dP = 150  

Es = (dQ/dP)(P/Q)  

= 150(3/300)  

= 450/300

= 1.5 > 1 (elastic)

supply curve is more elastic