Question #50716

In a given market, demand is described by the equation
Qd = 1800 -10P
and supply is described by
Qs = 200 + 10P
a) determine the equilibrium price and quantity
b) graphically illustrate the equilibrium price and quantity
c) Determine the price elasticity of demand at the equilibrium level
d) determine the surplus of shortage that would exist if the price where $60

Expert's answer

Qd = 1800 -10P

Qs = 200 + 10P

a) The equilibrium price and quantity is determined in the point, where Qd = Qs.

1800 - 10P = 200 + 10P

P = $80, Q = 200 + 10*80 = 1000 units.

b) The equilibrium price and quantity is depicted as intersection of

demand and supply curves (lines in our case) in the point E(1000;80).

c) The price elasticity of demand at the equilibrium level can be determined from the coefficient b, if P = a + b*Q.

In our case, P = 180 - 0.1Q, so Ed = -0.1 and demand is inelastic.

d) If the price is $60, then Qd = 1800 - 10*60 = 1200 and Qs = 200 +

10*60 = 800, so there will be a shortage of 1200 - 800 = 400 units.

Qs = 200 + 10P

a) The equilibrium price and quantity is determined in the point, where Qd = Qs.

1800 - 10P = 200 + 10P

P = $80, Q = 200 + 10*80 = 1000 units.

b) The equilibrium price and quantity is depicted as intersection of

demand and supply curves (lines in our case) in the point E(1000;80).

c) The price elasticity of demand at the equilibrium level can be determined from the coefficient b, if P = a + b*Q.

In our case, P = 180 - 0.1Q, so Ed = -0.1 and demand is inelastic.

d) If the price is $60, then Qd = 1800 - 10*60 = 1200 and Qs = 200 +

10*60 = 800, so there will be a shortage of 1200 - 800 = 400 units.

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