Answer to Question #235452 in Economics for amanuel

Question

In a market there are 20 buyers of a leather bag each having identical demand function Qd = 10 - 2P and 40 producers each with identical supply curve given by P= 4+Qs where Qd and Qs are quantity demanded and supplied respectively. A) Calculate the market equilibrium price and quantity B) Calculate the price elasticity of supply at the market equilibrium C) Calculate the price elasticity of demand at the market equilibrium D) Compute the consumer and producer surplus at the equilibrium E) What happens in the market if the price is 2 in the market? F) Is there surplus or shortage at price 15 in the market?

Answer 1

A) The market demand is:

Qd = (10 - 2P)×20 = 200 - 40P.

The marker supply is:

Qs = (P - 4)×40 = 40P - 160.

In equilibrium Qd = Qs,

200 - 40P = 40P - 160,

80P = 360,

P = 4.5,

Q = 200 - 40×4.5 = 20 units.

B) The price elasticity of supply at the market equilibrium is:

Es = 40×4.5/20 = 9, so the supply is elastic.

C) The price elasticity of demand at the market equilibrium is:

Ed = -40×4.5/20 = -9, so the demand is elastic.

D) The consumer and producer surplus at the equilibrium are:

CS = 0.5×(5 - 4.5)×20 = 5,

PS = 0.5×(4.5 - 4)×20 = 5.

E) If the price is 2 in the market, then the shortage will occur.

F) There is a surplus at price 15 in the market.