Answer to Question #306035 in Microeconomics for katrichie

Question

The demand curve for a good is Q = 60 – p and the supply curve is Q = p. The government imposes a specific tax of t = 2 per unit of output. 

a) Find the market equilibrium output (Q) and price (p) before tax?          (4)  

b) Find the new market equilibrium output (Q) and price (p) after tax        (5).  

c) Explain the effect the tax has on consumer surplus and producer surplus.   (6) 

Answer 1

a. The market is at equilibrium when Quantity demanded (Q_d) equals Quantity supplied(Q_s)

$Q_d =Q_s$

60-P=P

2P=60

P=30

Since Q=P, then;

the market is at equilibrium when

Q=P=30.

b. New supply function=old supply function + tax

Q+2Q=P

3Q=P

$Q=\dfrac{P}{3} ​$

Equate Q_d and Q_s

$60-P=\dfrac{P}{3}$

180-3P=P

P=45

substitute for the value of P

$Q=\dfrac{45}{3}$

Q=15

c. Since tax imposition increases the amount consumers pay for a commodity, it reduces consumers surplus. Likewise, since tax imposition reduces the revenue of suppliers, it reduces producers surplus