Question

4 (10pl Assume you are gven the following equations for demend and supply o-13-2P P-2 a Calculate the equabrium price and quantity. :5-2 3 13-2P- P-2 53 Q-3 P5 b) Draw a diagram and show the producer and consumer surplus 13-2P 2P Go 13 G5 P-13-4p er Srp 55T 2 P 4.5+ sepl Calculate the consumer and producer surplus c 2 PS-153) CSSG.S-4) 12.5 PS=3 praducer urplus4 Consumer surpluG.25 d) Calculate the (own) price elasticity of demand and the (own) price elasticity of supply at the equilibrium. Are they elastic or inelastic? -2 2-동 3.33 clastic

Answer 1

Solution:

4. We are given the demand function as: Qd = 13 - 2P

And supply function as: Qs = P - 2

a) At equilibrium, since quantity demanded equals the quantity supplied, so

Qd = Qs

13 - 2P* = P* - 2

2P* + P* = 13 + 2

So, P* = 15/3 = $5

And equilibrium quantity is Q* = 5 - 2 = 3 units

b) To draw the required graph of Quantity Price plane (XY-plane), we simply find the required intercepts:

Then for demand curve:

If P = 0, Qd = 13 and if Qd = 0, P = 13/2 = 6.5

So, required intercepts are: (13, 0) and (6.5, 0). Joining these two, we simply get the demand curve. (Your vertical intercept is correct, however horizontal intercept is nearly 5, instead of 13)

Similarly, for the supply curve:

If P = 0, Qs = -2 and if Qs = 0, P = 2. Ignoring the negative quantity side, we also know that another point on supply curve is the equilibrium point itself. So, joining vertical intercept (0, 2) and (3, 5), we get the required supply curve. (So, supply curve does not start from origin, unlike the graph you drew).

c) Consumer surplus = Area above price and below demand curve (as correctly presented by you in the graph). Then using the area of a triangle, we know that

CS = (1/2)*equilibrium quantity*(maximum willingness to pay possible - price actually paid(or equilibrium price))

CS = (1/2)*3*(6.5 - 5) = $2.25

Producer surplus = area below the price and above the supply curve (again correctly marked on the graph by you)

So, again using the area of a right angled triangle

PS = (1/2)*equilibrium quantity*(price received(or equilibrium price) - minimum willingness to accept)

PS = (1/2)*3*(5 - 2) = $4.5

d) Price elasticity of demand, ed = (dQd/dP)*(P/Qd)

Given that Qd = 13 - 2P, dQd/dP = -2

At equilibrium then, ed = (-2)*(5/3) = -3.33

Since this value, |-3.33|, is greater than 1 in absolute terms, demand is elastic.

Price elasticity of supply, es = (dQs/dP)*(P/Qs)

Given the supply curve as Qs = P - 2, dQs/dP = 1

So, at equilibrium, es = 1*(5/3) = 1.667

Again this value is also greater than 1 in absolute terms (1.667 > 1), so supply curve is also elastic (however, relatively less elastic as compared to the demand curve).