Question

Let the demand and supply functions for widgets be given by the following:

P = 200-4.5Qd

P = 100+20Qs

a) Solve the market equilibrium price and quantity for widgets

b) Calculate the supply and own-price demand elasticities for widgets

c) Interpret the elasticities in your own work

d) If the price of widgets went up by 20%, what will happen to the quantity demanded and supplied in the market? Is this an equilibrium? Why or Why not?

Thank you

Answer 1

4.5Qd = 200 - P

Qd = 200/4.5 - 1/4.5P so dQd/dP = -1/4.5

20Qs = P - 100

Qs = 1/20P - 5 so dQs/dP = 1/20

Equilibrium at a point where the price is same and one, so

200 - 4.5Q = 100 + 20Q

24.5Q = 100

Q = 4.081633

P = 200-4.5*4.081633 = 181.6327

Elasticities

Supply = dQs/dP*P/Q = 1/20*(181.6327/4.081633) = 2.225

Demand = dQd/dP*P/Q = -1/4.5*(181.6327/4.081633) = -9.89

The demand elasticity is on the higher side which means that the demand is highly sensitive to the price, demand is more than unitary elastic and a 1% change in price will lead to change in quantity demanded by more than 1 percent. Similarly supply is also more than unitary elastic and a 1% change in price will lead to change in quantity supplied by more than 1 percent.

If price increases by 20 percent, new price will be = 181.6327*1.20 = 217.9562

Qd = 200/4.5 - 1/4.5P = -3.99

Qs = 5-1/20*217.9562 = 5.89781

Quantitites are not equal so it is not equilibrium al also the demand has become negative which is not possible.