Question

Suppose demand and supply are given by Qd = 60 - P and Qs = 1.0P - 20.

Answer 1

Answer:

a.  Equilibrium quantity: 40 units;  Equilibrium price: $40.

b. Quantity demanded: 10 units; Quantity supplied: 30 units;  Surplus: 20 units.

c.  Quantity demanded: 9 units; Quantity supplied: 31 units;  Shortage: 22 units.

Explanation:

a. The equilibrium quantity occurs when the demanded and supplied quantity are the same, the price for which this situation happens is:

$60 - P = 1.0P - 20.\\2P=80\\P=\ 40$

At an equilibrium price of $40, the equilibrium quantity is:

$Q = 40 -20 = 40\ units$

b. At a price of $50, the quantity demanded, the quantity supplied, and the magnitude of the surplus are, respectively:

$Q_d = 60 - P =60-50 =10\ units\\Q_s = 1.0P - 20=50-20 = 30\ units\\Surp = Q_s - Q_d = 30 -10 = 20\ units$

c. At a price of $29, the quantity demanded, the quantity supplied, and the magnitude of the shortage are, respectively:

$Q_d = 60 - P =60-29 =31\ units\\Q_s = 1.0P - 20=29-20 = 9\ units\\Short = Q_d - Q_s = 31 -9 = 22\ units$