Demand function: P = 20 – 0.75Q
Supply function : 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).
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 $11 per hour. Ho w many drivers will be employed under this new minimum wage? Also, what is the amount of unemployment at $11 per hour ? Depict your answers in the above diagram.
To determine the number of drivers that will be employed under the new minimum wage law of $11 per hour, we need to find the quantity of drivers at which the wage provided by the supply function equals the minimum wage.
The supply function is given by:
P = 2 + 0.25Q
Setting this equal to $11, we have:
11 = 2 + 0.25Q
Solving for Q, we subtract 2 from both sides:
9 = 0.25Q
Then, dividing both sides by 0.25, we get:
Q = 36
So, at the minimum wage of $11 per hour, 36,000 drivers will be employed.
To determine the amount of unemployment at $11 per hour, we need to compare the quantity demanded with the quantity supplied at that wage level.
The demand function is given by:
P = 20 - 0.75Q
Setting this equal to $11, we have:
11 = 20 - 0.75Q
Rearranging the equation, we get:
0.75Q = 20 - 11
Simplifying further:
0.75Q = 9
Dividing both sides by 0.75, we find:
Q = 12
So, at the minimum wage of $11 per hour, the quantity demanded is 12,000 drivers.
To find out the amount of unemployment, we subtract the quantity demanded from the quantity supplied:
Unemployment = Quantity supplied - Quantity demanded
Unemployment = 36,000 - 12,000
Unemployment = 24,000
Therefore, at the minimum wage of $11 per hour, there will be 24,000 drivers unemployed.
To depict this information in the diagram, you can plot the supply and demand curves using the given functions. The vertical axis represents the wage per hour (P), and the horizontal axis represents the number of bus drivers hired (Q). Plot the demand curve with a negative slope, starting at P = 20 when Q = 0, and plot the supply curve with a positive slope, starting at P = 2 when Q = 0. Then, add a horizontal line at the price of $11, intersecting the demand and supply curves. The intersection point will represent the equilibrium quantity of drivers employed under the new minimum wage, and the difference between the supply curve and the demand curve at that price will represent the amount of unemployment.