Question

The demand equation for good A is: Q_d = 1430 - 8P

The supply equation for good A is: Q_s = 923 + 5P

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 $61. Indicate whether there would be excess demand or excess supply and calculate the value of the excess demand or excess supply.

Answer 1

Demand is given as Qd = 1430 - 8P
Supply is given as Qs = 923 + 5P
At equilibrium, demand = supply
1430 - 8P = 923 + 5P
or, 8P + 5P = 1430 - 923
or, 13P = 507
or, P = 507 / 13
or, P = 39 (equilibrium price)

Plugging the value P = 39 in the demand function to obtain equilibrium quantity. However the same can be obtained from the supply function also.
Q = 1430 - 8P
= 1430 - 8*39
= 1430 - 312
= 1118 (equilibrium quantity)

a) At free market equilibrium price of good A, P* = $39

b) At free market equilibrium quantity of good A, Q* = 1118 units.

c) Now given that price of good A is regulated at $61.

At price $61, quantity demanded = 1430 - 3*61 = 1430 - 183 = 1247
quantity supplied = 923 + 5*61 = 923 + 305 = 1228

As we can see that quantitydemanded is greater than quantity supplied. Hence there is excess demand for good A at price $61.
After price regulation, there arises an excess demand of 1247 - 1228 = 19 units.

There is excess demand. Excess demand = 19 units.