Answer to Question #205895 in Macroeconomics for Joel

Question

Suppose one thousand (1000) units of products A are produced by XYZ limited and the quantity demanded for the product is two thousand (2000) units. All other things remaining constant a Ghc 24 Change in the price of product A results in a change in quantity demanded and supplied and 6 and 4 units respectively.

 XYZ limited has a workforce of people who pay income tax of Ghc200 each to the government.

A.  

Calculate the equilibrium price (In Ghc) and equilibrium quantity

B.

Suppose government introduces a Subsidy of Ghc10 on each unit of product A produced, calculate the new equilibrium price and que equilibrium quantity.

C.

Graphically indicate how much of the Subsidy will be received by the producer and consumer respectively. 

 

D.

How much revenue is the government going to forgo in the form of subsidy?

Answer 1

Equilibrium price and quantity is obtained when market demand is equal to market supply. 

Quantity Demand = a + bP

Quantity supplied = a - bP

Given:

1000 units of good A produced

2000 units of good A demanded.

Change in price of good A = Ghc 24

Change in quantity demanded = 6 

Change in quantity supplied = 4

Using the demand and supply formula:

Q_d = 2000 - (6/24)P

Qs = 1000 + (4/24)P

Market is in equilibrium when demand = supply

2000 - (1/4)P = 1000 + (1/6)P

1000 = (1/4 + 1/6) P

1000 = (5/12) P

P = 12000 / 5

P = Ghc 2400

For Q substitute P value in the demand and supply equation.

Q_d = 2000 - (1/4) 2400

Q_d = 1400 units

Q_s = 1000 + (1/6) 2400

Q_s  = 1400 units.

The equilibrium price is Ghc 2400 and the quantity at equilibrium is 1400 units.

B

If the government introduces a subsidy of Ghc 10, the change in price decreases to 14

Therefore equilibrium price and quantity will be obtained by;

Making P the subject of the the equations

$Pd=8000-4Q$

$Ps=6Q-6000$

With subsidy

$Pd+10=Ps$

$8000-4Q+10=6Q-6000$

$Q= 1401$

1401 units is the quantity at the new equilibrium.

The price at equilibrium is ;

$6(1401)-6000=Ghc 2406$

C.Graphically indicate how much of the Subsidy will be received by the producer and consumer respectively

How much revenue is the government going to forgo in the form of subsidy?

Revenue foregone is;

$1401×10= Ghc 14010$

This is obtained by multiplying the quantity demanded by the subsidy.