Question

Understanding Minimum Wage Policy

Minimum wage is one of the most classic price floor policies that governments use in practice. Suppose the following demand and supply curves describe the labor market for bus drivers in Endor.

Demand: P = 20 – 0.75Q

Supply:   P = 2 + 0.25Q

where P is the wage per hour, and Q represents the number of bus drivers hired, in thousands

(e.g. Q = 1 means that 1,000 drivers have been hired).

a) Calculate the equilibrium wage and the number of drivers hired. Illustrate on a graph.

b) After a brief rebellion, bus drivers in Endor successfully argue for a minimum wage

law. The minimum wage law requires that all bus drivers earn at least $8 per hour.

How many drivers will be employed under this new minimum wage? Illustrate on a

graph.

c) Using your graphs from (a), calculate the consumer surplus and producer surplus at the

initial equilibrium price and quantity from part (a).

d) Calculate the new consumer surplus and producer surplus with the minimum wage of

$8 (part b).

e) How does the total consumer and producer surplus in part (c) compare to the total

consumer and producer surplus in part (d)? What explains the difference in these two

figures? Please explain intuitively.

Answer 1

a) Calculate the equilibrium wage and the number of drivers hired. Illustrate on a graph.

Graph is shown below. Demand must equal supply at equilibrium which implies

D = S

20 - 0.75Q = 2 + 0.25Q

18 = Q

Hence Q* = 18 ('1000 units) and market clearing wage is 20 - 0.75*18 = $6.5 per hour

b)The minimum wage law requires that all bus drivers earn at least $8 per hour. How many drivers will be employed under this new minimum wage?

At a wage of $8 per hour, quantity demanded of labor is 8 = 20 - 0.75*Q or Qd = 16 ('000 units) and at this level, the quantity supplied is 8 = 2 + 0.25Q or Qs = 24 ('000 units). Hence a total of  16000 bus drivers are employed. There is a total surplus of 24000 - 16000 = 8000 workers that are unemployed due to minimum wage.

c) Using your graphs from (a), calculate the consumer surplus and producer surplus at the initial equilibrium price and quantity from part (a).

Here consumer is the employer and producer is the worker. Consumer surplus = 0.5*(max wage - current wage)* current eq level of workers employed = 0.5*(20 - 6.5)*18000 = $121,500

Producer surplus = 0.5*(current wage - minimum wage)* current eq level of workers employed = 0.5*(6.5 - 2)*18000 = $40,500

d) Calculate the new consumer surplus and producer surplus with the minimum wage of $8 (part b).

New wage is $8. At this level. CS is 0.5*(20 - 8)*16000 = $96,000 and PS = 0.5*(6 - 2)*16000 + (8 - 6)*16000 = $64,000.

e) How does the total consumer and producer surplus in part (c) compare to the total consumer and producer surplus in part (d)? What explains the difference in these two figures?

Note that total surplus (consumer and producer) is  $121,500 + $40,500 = $162,000 before the change and now it has reduced to $96,000 + $64,000 = $160,000. Hence there is a loss in total surplus which is due to the deadweight loss created as a result of minimum wage.