Question

The demand equation for good A is: Q_d = 1396 - 8P

The supply equation for good A is: Q_s = 824 + 3P

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 $68. Indicate whether there would be excess demand or excess supply and calculate the value of the excess demand or excess supply.

Answer 1

(a) At free market equilibrium point; Qd = Qs =Q

=> Qd = Qs

=> 1396 - 8P = 824 + 3P

=> 1396 - 824 = 3P + 8P

=> 572 = 11P

=> P = $52

the free-market equilibrium price (P*) of good A is $52

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(b)  the free-market equilibrium price (P*) of good A is $52

At equilibrium, Qd = Qs = Q

=> Q = 824 + 3P

Put P = 52

=>Q = 824 + 3(52)

=>Q = 824 + 156

=> Q = 980

the free-market equilibrium quantity (Q*) of good A is 980 units.

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(c) Regulated price is $68

Quantity demand at a price of $68 is 852 units.

i.e., Qd = 1396 - 8P

=>Qd = 1396 - 8(68)

=> Qd = 852

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Quantity supplied at a price of $68 is 1028 units

i.e., Qs = 824 + 3P

=>Qs = 824 + 3(68)

=>Qs = 1028

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The quantity supplied is higher than quantity demand at a regulated price of $68. It means there is excess supply at regulated price.

Excess supply = Qs - Qd

=> Excess supply = 1028 - 852

=>Excess supply = 176

There is excess supply of 176 units at a regulated price of $68

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