Question

Demand Equation: QD = 250 − 5P

Supply Equation: QS = 10 + 3P

1. When P = 5, the elasticity of supply is

A. 3

B. 0.6

C. 1

D. 30

E. 15

2. Suppose the government imposes a tax of of $8 per unit sold of the good. How much of the tax does the consumer pay (per unit)?

A. $8

B. $3

C. $5

D. $6

E. $4

Answer 1

Q_D = 250 - 5P

Q_S = 10 + 3P

First of all determine the equilibrium quantity

250 - 5P = 10 + 3P

5P + 3P = 250 - 10

8P = 240

Equilibrium price, P = $ 30 per unit

Equilibrium quantity, Q = 100 units

When P = $ 5

Q_D = 250 - 5*5 = 250 -25 = 225

Q_s = 10 + 3*5 = 10 + 15 = 25

Q_s = 10 + 3P

Differentiating Supply function wrt P we get

The elasticity of supply can be determined using the following formula

Plug in the values in the above equation we get

Elasticity of supply is 0.6.

Option B.

2. With a tax of $ 8 per unit. The buyers price will be $8 greater than the price received by suppliers

P_s = P_b - 8

Now demand function is

The supply function is

Equate Qd and Qs

Plug in Ps = Pb - 8

Price paid by buyers = $ 33

Price received by sellers = $ 25

Tax burden on consumer = Price buyer paid after tax - equilibrium price

Tax paid by buyer = $ 33 - 30 = $ 3 per unit

Option B is correct.

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