Question

1. Suppose the demand for a product is given by P = 30 – 2Q. Also, the supply is given by P = 5 + 3Q. If a $5 per-unit excise tax is levied on the buyers of a good, then after the tax sellers will receive _________ for each unit of the good.

a) $4

b) $5

c) $20

d) $22

e) $17

2. Suppose the demand for a product is given by P = 30 – 3Q. Also, the supply is given by P = 10 + Q. If a $4 per-unit excise tax is levied on the buyers of a good, producer surplus is equal to

a) $4

b) None of these

c) $8

d) $16

e) $24

Answer 1

1. e) $17
After tax price paid by buyer will increase to P + tax = P + 5. So, demand equation becomes:
P + 5 = 30 - 2Q
So, P = 30 - 2Q - 5 = 25 - 2Q
Now, new demand = supply gives,
25 - 2Q = 5 + 3Q
So, 3Q + 2Q = 25 - 5
So, 5Q = 20
So, Q = 20/5 = 4
Now, P = 5 + 3Q = 5 + 3(4) = 5 + 12 = 17

2. c) $8
After tax price paid by buyer will increase to P + tax = P + 4. So, demand equation becomes:
P + 4 = 30 - 3Q
So, P = 30 - 3Q - 4 = 26 - 3Q
Now, new demand = supply gives,
26 - 3Q = 10 + Q
So, 3Q + Q = 26 - 10
So, 4Q = 16
So, Q = 16/4 = 4
Now, P = 10 + Q = 10 + 4 = 14
Minimum price producer is willing to accept (at Q = 0) = 10 + 0 = 10
Producer surplus = area of triangle = (1/2)*(P-Minimum price)*Q = (1/2)*(14-10)*4 = (1/2)*4*4 = 8