Answer to Question #233703 in Microeconomics for Richard Chinyama

Question

1.     Assume a market has the following demand and supply functions:

Q_D = 28-3P

Q_S = 2P-12

Where P is the price

a)     Determine algebraically the equilibrium price and quantity.

b)     Plot the demand and supply curves and confirm your answer.

c)     Suppose supply shifts to Q_s =2P – 2 with no change no change in demand. Determine the new equilibrium price and quantity.

d)    Although the supply curve shifts to the right by 10, the quantity exchanged does not rise by 10, explain why the increase in quantity is smaller.

Answer 1

demand function

QD = 28-3P

supply function

Qs = 2P-12 

(a). At equilibrium, the quantity demanded is equal to the quantity supplied.

Q_d=Q_s

28−3P=2P−12

28+12=2P+3P

40=5P

P=40/5

P=8

Substitute P=8 in either demand or supply equation for the quantity.

Note: at equilibrium price, both equations will give the same quantity

Q=28−3×8

Q=28−24

Q=4

The equilibrium price is 8 and the equilibrium quantity is 4.

(b). Graphical presentation

According to the above graph, the equilibrium occurs at point E. The corresponding equilibrium price is 8 and the quantity is 4. The equilibrium price and quantity are the same as calculated in part (a)

(c). New supply equation is given below:

Q_s=2P−2

At equilibrium,

Q_D=Q_S

28−3P=2P−2

28+2=2P+3P

30=5P

P=30/5

P=6

Substitute P=6 in the supply equation for equilibrium quantity

Q=2×6−2

Q=12−2

Q=10

The equilibrium price in the case of the new supply curve is 6 and the quantity is 10.

Graphical presentation:

According to the above figure, the new equilibrium occurs at point E1. The new equilibrium price is 6 and the quantity is 10.

(d). Although the supply curve shifts to the right by 10, the quantity exchanged has only increased by 6 (10-4=6). It is because the increase in supply has taken place but the demand is the same. So the quantity exchanged (equilibrium quantity) has not increased by 10. If the demand has also increased by 10, then the quantity exchanged has gone up by 10.