Question

3) Supply and demand for a competitive labor market for professional hockey players is described by the following equations, where quantity is measured in hundreds: P = 120 – 2Qd P = 20 + 3Qs Draw a graph of this labor market and calculate, and show, the equilibrium salary and quantity of players.

Assume there are 30 teams in a league. What is the effect of roster size per team being limited to 60? What is the effect of roster size per team being limited to 70?

Calculate the change in total surplus if roster size is changed from 60 to 50? As a whole, under which roster size limit are players better off?

Answer 1

Sol 3 :

(i) Equation given as follows :

P = 120 – 2Qd

P = 20 + 3Qs

At equilibrium point , Quantity demanded is equal to quantity supplied

   Qd = Qs

So equation the above two equation as follows :

   120 - 2Qd = 20 + 3Qs

100 = 2Qd + 3Qs ( Qd)

100 = 5Qd

100/5 = Qd

20 = Qd = Qs (Equilibrium Quantity of Players)

P = 120 - 40 = $80 (Equilibrium Price)

Graph for the labour market is as Follows :

w = Equilibrium salary

L = Equilibrium quantity of labour

(ii) If there is 30 teams , and roster size for each team is 60 players so , Demand for Players will increase by 1800 players ( i.e 30 x 60) and salary will increase due to increase in demand and less supply. Below diagram will depicts the same,

in the diagram , due to increase in demand for the players than before and remaining the supply for labours same as before, then due to higher demand , salary for the players will increase . ( from S to S1)

(iii) If there is 30 teams , and roster size for each team is 70 players so , Demand for Players will increase by 1800 players ( i.e 30 x 70 = 2100 players ) and salary will increase due to increase in demand and less supply. Below diagram will depicts the same

in the diagram , due to increase in demand for the players will shift the demand curve from d1 to d2 . this will cause the larger demand than the supply, which will increase the salary from the point S to S1 . and this time the increase in salary is higher than mentioned in case 1 .

(iv)In this case , roster size decreases from 60 to 50 , so , demand for players will decrease by 300 players ( 30 x 50 = 1500 players) . So, in this case demand curve will shifts backward and salary for the hockey players will decrease from case mentioned in (iii) . Below diagram depicts the same.

in this Diagram, due to decrease in demand for the players , Demand curve shifts backward from D1 to D2 . Due to more supply of labour and less demand , price for the players will decrease equal to the SS2.

(v)When the roster size is 70 , the hockey players are better off because at this point of time they are getting large salary than any other case . Let us see :

Case 1 ( ii) = P = 20 + 3 ( 1800)

                  = P = 20 + 5400

                    = P = 5420

Case 2 (iii) = P = 20 + 3 (2100)

                    = P = 20 + 6300

                      = P = 6320

Case 3 (iv) = P 20 + 3 ( 1500)

                  = P = 20 + 4500

                  = P = 4520

According to the calculation we have found that players are better off in case 2 .