Question

1. Assume a market of a specific good. The demand and supply equation is as shown below:

PD=70-3QD

PS=5+2QS

a. Find the demand price elasticities at the equilibrium and find the supply price elasticities at the equilibrium.

2. Let say that there is an advancement in technology that causes the input cost of the good to decrease. What do you expect to happen to:

a. Equilibrium price & Equilibrium quantity

b. Consumer surplus & Producer surplus

c. Demand price elasticities at the new equilibrium Supply price elasticities at the new equilibrium

Answer 1

1. The equilibrium occurs at the point where,

Demand = Supply

70 - 3Q = 5 + 2Q

5Q = 70 - 5 = 65

Q = 65 / 5 = 13

P = 70 - 3Q = 70 - 3(13) = $31

Thus, the equilibrium price is $31 and equilibrium quantity is 13 units.

The inverse demand function is

P = 70 - 3Q

3Q = 70 - P

Q = (70/3) - (1/3)P             [This is direct demand function]

Price elasticity of demand = (∆Q / ∆P) * (P / Q) [Where, ∆Q/∆P is the price coefficient in the direct demand function]

                                          = -(1 / 3) * (31 / 13)

                                          = -31 / 39

                                          = -0.79

The absolute value of Price elasticity of demand is 0.79.

The inverse supply function is

P = 5 + 2Q

2Q = 5 + P

Q = (5/2) + (1/2)P             [This is direct supply function]

Price elasticity of supply = (∆Q / ∆P) * (P / Q) [Where, ∆Q/∆P is the price coefficient in the direct supply function]

                                          = (1 / 2) * (31 / 13)

                                          = 31 / 26

                                          = 1.19

The Price elasticity of supply is 1.19.