Answer to Question #164072 in Microeconomics for Wynn___

Question

2. Qd= 7.000- 0.05Pd

Qs = 0.05Ps + 2.000

a. If the government collected tax = 10000/unit, what will be the equilibrium price and quantity after tax?

b. Draw a diagram that shows the effect of the tax

c. If a subsidy 5000/unit is given, what will be the equilibrium price and quantity after subsidy?

d. Draw a diagram that shows the effect of the subsidy

Answer 1

(a) (i) Let's first find the initial equilibrium price and quantity before the tax was imposed:

$$Q_d=Q_s,$$ $$7000-0.05P_{E1}=0.05P_{E1}+2000,$$ $$5000=0.1P_{E1},$$ $$P_{E1}=\$50000.$$ $$Q_{E1}=7000-0.05\cdot\$50000=4500.$$

(ii) After the tax of $10000 per unit was imposed, the price the producers get is equal to the price consumers pay minus the amount of tax:

$$P_s=P_d-10000.$$

Then, substituting $P_s$ into the supply function and equating, we get:

$$7000-0.05P_{E2}=0.05(P_{E2}-10000)+2000,$$ $$5500=0.1P_{E2},$$ $$P_{E2}=\$55000.$$ $$Q_{E2}=7000-0.05\cdot\$55000=4250.$$

(b) Let's draw the diagram:

Here, blue curve is the demand function, orange curve is the supply function before the government impose the tax, gray curve is the supply function after the government impose the tax. As we can see from the diagram, after the imposition of the tax the supply curve shifts to the left, the equilibrium price rises and the equilibrium quantity decreases.

(c) After the subsidy of $5000 per unit was given, the price the producers get is equal to the price consumers pay plus the amount of subsidy:

$$P_s=P_d+5000$$

Then, substituting $P_s$ into the supply function and equating, we get:

$$7000-0.05P_{E2}=0.05(P_{E2}+5000)+2000,$$ $$4750=0.1P_{E2},$$ $$P_{E2}=\$47500.$$ $$Q_{E2}=7000-0.05\cdot\$47500=4625.$$

(d) Let's draw the diagram:

Here, blue curve is the demand function, orange curve is the supply function before the government impose the subsidy, gray curve is the supply function after the government impose the subsidy. As we can see from the diagram, after the imposition of the subsidy the supply curve shifts to the right, the equilibrium price decreases and the equilibrium quantity increases.