Question

The demand equation for good A is: Q_d = 810 - 14P

The supply equation for good A is: Q_s = 396 + 9P

a. Calculate the value of the free-market equilibrium price (P*) of good A.

b. Calculate the value of the free-market equilibrium quantity (Q*) of good A.

c. Suppose that a law requires that the regulated price of good A be set at $28. Indicate whether there would be excess demand or excess supply and calculate the value of the excess demand or excess supply.

Answer 1

Demand equation is as follows -

Qd = 810 - 14P

Supply equation is as follows -

Qs = 396 + 9P

At equilibrium, demand equals supply

Qd = Qs

810 - 14P = 396 + 9P

-14P - 9P = 396 - 810

-23P = -414

23P = 414

P = 414/23

P = 18

Putting the value of P in either demand equation or supply equation to ascertain equilibrium quantity.

Taking demand equation,

Qd = 810 - 14P

Qd = 810 - [14 * 18]

Qd = 810 - 252

Qd = 558

(a)

The value of the free market equilibrium price (P*) of good A is 18.

(b)

The value of the free market equilibrium quantity (Q*) of good A is 558.

(c)

Now, the price of good A is fixed at $28.

Calculate quantity demanded at new price -

Qd = 810 - 14P

Qd = 810 - (14 * 28)

Qd = 810 - 392

Qd = 418

The quantity demanded at new price is 418 units.

Calculate the quantity supplied at new price -

Qs = 396 + 9P

Qs = 396 + (9 * 28)

Qs = 396 + 252

Qs = 648

The quantity supplied at new price is 648 units.

It can be seen that at new regulated price, the quantity supplied exceeds the quantity demanded.

When quantity supplied exceeds the quantity demanded, there is excess supply.

Thus,

There would be excess supply.

Calculate the value of excess supply -

Excess supply = Quantity supplied - Quantity demanded

Excess supply = 648 units - 418 units = 230 units

Thus,

The value of excess supply is 230 units.