Answer to Question #83296 in Economics of Enterprise for Cláudia Matos

Question

1. Assume that the equations of Demand and Supply of a specific good X in 2018 are as follows: Qd = 20,000 - 500P; Qs = -8,000 + 3000P
Assume that in the 2019 Budget proposal, the Government plans to introduce a tax on the producers of good X. The tax will be equal to one euro per unitof good X produced. Assuming that all other exogenous variables remain constant in 2018 and 2019:

a. Solve for the equilibrium price and quantity for good X in 2018.
b. Solve for the equilibrium price and quantity for good X in 2019.
c. Draw an adequate graph describing both equilibria.
d. What is the change in net revenues (from 2018 to 2019) for the producers of good X?
e. How is the tax burden divided between producers and consumers? Explain your results.

Answer 1

1. Qd = 20,000 - 500P; Qs = -8,000 + 3000P

The tax will be equal to one euro per unit of good X produced.

a. The equilibrium price and quantity for good X in 2018 were:

Qd = Qs,

20,000 - 500P = -8,000 + 3,000P,

3,500P = 28,000,

P = 8 euro,

Q = 20,000 - 500*8 = 16,000 units.

b. The equilibrium price and quantity for good X in 2019 is:

Qd = Q's,

20,000 - 500P = -8,000 + 3,000(P - 1),

3,500P = 31,000,

P' = 8.86 euro,

Q' = 20,000 - 500*8.86 = 15,571 units.

c. The supply curve will shift leftwards, so the equilibrium price will rise and equilibrium quantity will decrease.

d. The change in net revenues (from 2018 to 2019) for the producers of good X is:

P'Q' - PQ = 8.86*15,571 - 8*16,000 = $9,959, so the net revenues will increase.

e. Producers will pay less of the tax burden and consumers will pay more, because the demand is inelastic, as the total revenue will increase as a result of increase in price.