Question

1.Suppose the market demand for good X is given by the equation Qd = 1000 – 20p ; and market supply is given by the equation Qs = 500 +30p

a.find quantity demanded and quantity supplied when the price of good X is $ 12. Is there a surplus or shortage in the prodsuction of good X? What should happen to the price of good X ?

b.Find the equilibrium price for good X by equating Qd and Qs ?

c. Is this the equilibrium price ?​

Answer 1

Answer:

1.Suppose the market demand for good X is given by the equation Qd = 1000 – 20p ; and market supply is given by the equation Qs = 500 +30p

a) Quantity demanded =760

  Quantity supplied = 860

The supply of commodity X is surplus.

Price should be lowered

b) Equilibrium price = $10

c) The equilibrium price is $10

Explanation:

a) If the demand of the good X is given by the equation Qd = 100 - 20p, we can substitute the price p to calculate the quantity demanded (Qd)

Qd = 1000 - 20p, If price p is $12

Qd = 1000 - 20(12)

Qd = 1000 - 240

Qd = 760

Therefore the quantity demanded is 760 of commodity X

Find the quantity of commodity X supplied  if price is $12, in the equation Qs = 500 +30p

Qs = 500 + 30p

Qs = 500 + 30(12)

Qs = 500 + 360

Qs = 860

Since the quantity demanded is 760 of commodity X and the amount supplied is 860, therefore there is a surplus in the supply.

Since the supply is in surplus, the price should be lowered to increase the demand.

b) Find the equilibrium price by equating Qd and Qs

Qd = 1000 - 20p

Qs = 500 + 30p

Equating the two equation gives:

If Qd = Qs

Then, 1000 - 20p = 500 + 30p

1000 - 20p = 500 + 30p

1000 - 500 = 30p + 20p

500 = 50p

50p = 500

p = 500/50

p = 10

Therefore the equilibrium price is $10.

c. Is this the equilibrium price?

The equilibrium price is indeed $10 because it is at this price that the quantity of X demanded is exactly equal to the quantity supplied of X.

Qd =1000 - 20p ⇒ Qd = 1000 - 20(10) = 1000 - 200 = 800

Qs = 500 + 30p ⇒ Qs = 500 +30(10) = 500 + 300 = 800