Chapter 3, Problem 6P

(a)

To determine

Equilibrium wage.

Explanation of Solution

Given information:

Demand function of labor:${\text{Q}}^{\text{D }}=240-20\text{W }$ (1)

Supply function of labor:${\text{Q}}^{\text{S }}=10\text{W }$ (2)

Calculation:

Intersecting point of demand and supply curve of labor is the equilibrium point. The corresponding wage in the equilibrium point is the equilibrium wage rate. The calculation of equilibrium wage is shown below:

$\begin{array}{c}{\text{Q}}^{\text{S }}={\text{Q}}^{\text{D }}\\ 10\text{W }=240-20\text{W}\\ 20\text{W}-10\text{W}=240\\ 30\text{W}=240\\ \text{W}=\frac{240}{30}\\ \text{W}=8\end{array}$

Equilibrium wage is $8.

Substitute the wage rate in to the demand equation (Equation (1)) to calculate the equilibrium quantity of labor.

$\begin{array}{l}{\text{Q}}^{\text{D }}=240-20\text{W}\\ {\text{Q}}^{\text{D }}=240-20\left(8\right)\\ {\text{Q}}^{\text{D }}=240-160\\ {\text{Q}}^{\text{D }}=80\end{array}$

Equilibrium quantity of labor is 80 (80,000) units.

Economics Concept Introduction

Equilibrium wage and quantity: The intersecting point of demand and supply curve of labor is the equilibrium point. The corresponding wage and quantity in the equilibrium point is the equilibrium wage rate and equilibrium quantity of labor.

(b)

To determine

New equilibrium wage.

Explanation of Solution

Given information:

New equilibrium wage rate: $9.

Calculation:

Substitute the new wage rate in to the demand equation (Equation (1)) to calculate the new equilibrium quantity of labor.

$\begin{array}{l}{\text{Q}}^{\text{D }}=240-20\text{W}\\ {\text{Q}}^{\text{D }}=240-20\left(9\right)\\ {\text{Q}}^{\text{D }}=240-180\\ {\text{Q}}^{\text{D }}=60\end{array}$

New equilibrium quantity of labor is 60 (60,000) units.

Substitute the new wage rate in to the supply equation (Equation (2)) to calculate the quantity of labor supplied.

$\begin{array}{l}{\text{Q}}^{\text{S }}=10\text{W}\\ {\text{Q}}^{\text{S }}=10\left(9\right)\\ {\text{Q}}^{\text{S }}=90\\ \end{array}$

Quantity of labor supplied is 90 (90,000) units.

The excess supply of labor in the market is shown below.

$\begin{array}{c}\text{Excess supply of labor}=\text{Total supply of labor}-\text{Total }\text{demand for labor }\\ =90,000-60,000\\ =30,000\end{array}$

The excess supply of labor is 30,000.

Economics Concept Introduction

Equilibrium wage and quantity: The intersecting point of demand and supply curve of labor is the equilibrium point. The corresponding wage and quantity in the equilibrium point is the equilibrium wage rate and equilibrium quantity of labor.

(c)

To determine

Deadweight loss.

Explanation of Solution

At wage $9, the quantity demand for labor is 60,000 units (this is calculated in sub-part (b)). Even though, at wage $9 more number of labors (more than 60,000) are ready to provide their service, market quantity of 60,000 labors only. Thus, the new acceptable labor wage at quantity 60,000 (60 units) is calculated as follows:

$\begin{array}{c}{\text{Q}}^{\text{S }}=10\text{W}\\ \text{60}=10\text{W}\\ 10\text{W}=60\\ \text{W}=\frac{60}{10}\\ \text{W}=6\\ \end{array}$

Acceptable labor wage at quantity 60,000 (60 units) is $6.

Deadweight loss is calculated as follows:

$\begin{array}{c}\text{Deadweight loss}=\frac{1}{2}\times \left[\begin{array}{l}\left(\text{New minimum wage}-\text{New acceptable wage }\right)\times \\ \left(\text{Equilibrium quantity}-\text{New quantity}\right)\end{array}\right]\\ =\frac{1}{2}\times \left(9-6\right)\times \left(80,000-60,000\right)\\ =\frac{1}{2}\times 3\times 20,000\\ =30,000\end{array}$

Deadweight loss is $30,000.

Economics Concept Introduction

Deadweight loss: Deadweight loss is the loss of economic surplus because of the market economy not being in the competitive equilibrium.

(d)

To determine

Change in producer surplus.

Explanation of Solution

To find out the consumer surplus, the chock price of demand curve has to be calculated. The calculation of chock price is shown below:

Substitute the value of quantity demand as zero in Equation (1).

$\begin{array}{c}{\text{Q}}^{\text{D }}=240-20\text{W }\\ 20\text{W }=240\\ \text{W }=\frac{240}{20}\\ \text{W}=12\end{array}$

The demand chock price (maximum willing wage) is $12.

Change in consumer surplus is calculated as follows:

$\begin{array}{c}{\text{Consumer surplus}}_{\text{Change}}=\left(\begin{array}{l}\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing wage}\\ -\text{New minimum wage}\end{array}\right)\\ \times \text{New equilibrium quantity}\end{array}\right)\\ -\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing wage}\\ -\text{Equilibrium wage}\end{array}\right)\\ \times {\text{Equilibrium quantity}}_{\text{Initial}}\end{array}\right)\end{array}\right)\\ =\left(\left(\frac{1}{2}\times \left(12-9\right)\times 60,000\right)-\left(\frac{1}{2}\times \left(\text{12}-\text{8}\right)\times \text{80,000}\right)\right)\\ =90,000-160,000\\ =-70,000\end{array}$

Change (decrease) in consumer surplus is $70,000.

To find out the producer surplus, the chock price of supply curve has to be calculated. The calculation of chock price is shown below.

Substitute the value of quantity supply as zero in Equation (2).

$\begin{array}{c}{\text{Q}}^{\text{S }}=10\text{W }\\ \text{0}=10\text{W }\\ 10\text{W}=0\\ \text{W}=\frac{0}{10}\\ \text{W}=0\end{array}$

The supply chock price (minimum acceptable wage) is $0.

Change in producer surplus is calculated as follows:

$\begin{array}{c}{\text{Producer surplus}}_{\text{Change}}=\left(\begin{array}{l}\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}\text{New acceptable wage}\\ -\text{Minimum willing to accept wage}\end{array}\right)\\ \times \text{New equilibrium quantity}\end{array}\right)\\ +\left(\begin{array}{l}\text{New minimum wage}\\ -\text{New acceptable wage }\end{array}\right)\times \text{New equilibrium quantity}\\ -\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}{\text{Equilibrium wage}}_{\text{Initial}}\\ -\text{Minimum willing to accept wage}\end{array}\right)\\ \times {\text{Equilibrium quantity}}_{\text{Initial}}\end{array}\right)\end{array}\right)\\ =\left(\left(\frac{1}{2}\times \left(\text{6}-0\right)\times 60,000\right)+\left(9-6\right)\times 60,000-\left(\frac{1}{2}\times \left(\text{8}-\text{0}\right)\times \text{80,000}\right)\right)\\ =\left(\left(180,000\right)+180,000-\left(320,000\right)\right)\\ =40,000\end{array}$

Change (increase) in producer surplus is $40,000.

Economics Concept Introduction

Producer surplus: Producer surplus is the difference between the lowest willing price accepted by the producer and the actual price received by the producer.

Consumer surplus: Consumer surplus is the difference between the highest willing price of a consumer and the actual price that the consumer pays.

(e)

To determine

Change in producer surplus.

Explanation of Solution

Substitute the new wage rate in to the demand equation (Equation (1)) to calculate the new equilibrium quantity of labor.

$\begin{array}{l}{\text{Q}}^{\text{D }}=240-20\text{W}\\ {\text{Q}}^{\text{D }}=240-20\left(11\right)\\ {\text{Q}}^{\text{D }}=240-220\\ {\text{Q}}^{\text{D }}=20\end{array}$

New equilibrium quantity of labor is 20 (20,000) units.

At wage $11, the quantity demand for labor is 20,000 units. Even though, at wage $11 more number of labors (more than 20,000) are ready to provide their service, market quantity of 20,000 labor only. Thus the new acceptable labor wage at quantity 20,000 (20 units) is calculated as follows.

$\begin{array}{c}{\text{Q}}^{\text{S }}=10\text{W}\\ \text{20}=10\text{W}\\ 10\text{W}=20\\ \text{W}=\frac{20}{10}\\ \text{W}=2\\ \end{array}$

Acceptable labor wage at quantity 20,000 (20 units) is $2.

Deadweight loss is calculated as follows:

$\begin{array}{c}\text{Deadweight loss}=\frac{1}{2}\times \left[\begin{array}{l}\left(\text{New minimum wage}-\text{New acceptable wage }\right)\times \\ \left(\text{Equilibrium quantity}-\text{New quantity}\right)\end{array}\right]\\ =\frac{1}{2}\times \left(11-2\right)\times \left(80,000-20,000\right)\\ =\frac{1}{2}\times 9\times 60,000\\ =270,000\end{array}$

Deadweight loss is $270,000.

To find out the consumer surplus, the chock price of demand curve has to be calculated. The calculation of chock price is shown below:

Substitute the value of quantity demand as zero in Equation (1).

$\begin{array}{c}{\text{Q}}^{\text{D }}=240-20\text{W }\\ 20\text{W }=240\\ \text{W }=\frac{240}{20}\\ \text{W}=12\end{array}$

The demand chock price (maximum willing wage) is $12.

Change in consumer surplus is calculated as follows:

$\begin{array}{c}{\text{Consumer surplus}}_{\text{Change}}=\left(\begin{array}{l}\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing wage}\\ -\text{New minimum wage}\end{array}\right)\\ \times \text{New equilibrium quantity}\end{array}\right)\\ -\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing wage}\\ -\text{Equilibrium wage}\end{array}\right)\\ \times {\text{Equilibrium quantity}}_{\text{Initial}}\end{array}\right)\end{array}\right)\\ =\left(\left(\frac{1}{2}\times \left(12-11\right)\times 20,000\right)-\left(\frac{1}{2}\times \left(\text{12}-\text{8}\right)\times \text{80,000}\right)\right)\\ =10,000-160,000\\ =-150,000\end{array}$

Change (decrease) in consumer surplus is $150,000.

To find out the producer surplus, the chock price of supply curve has to be calculated. The calculation of chock price is shown below:

Substitute the value of quantity supply as zero in Equation (2).

$\begin{array}{c}{\text{Q}}^{\text{S }}=10\text{W }\\ \text{0}=10\text{W }\\ 10\text{W}=0\\ \text{W}=\frac{0}{10}\\ \text{W}=0\end{array}$

The supply chock price (minimum acceptable wage) is $0.

Change in producer surplus is calculated as follows:

$\begin{array}{c}{\text{Producer surplus}}_{\text{Change}}=\left(\begin{array}{l}\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}\text{New acceptable wage}\\ -\text{Minimum willing to accept wage}\end{array}\right)\\ \times \text{New equilibrium quantity}\end{array}\right)\\ +\left(\begin{array}{l}\text{New minimum wage}\\ -\text{New acceptable wage }\end{array}\right)\times \text{New equilibrium quantity}\\ -\left(\begin{array}{l}\frac{1}{2}\times \left(\begin{array}{l}{\text{Equilibrium wage}}_{\text{Initial}}\\ -\text{Minimum willing to accept wage}\end{array}\right)\\ \times {\text{Equilibrium quantity}}_{\text{Initial}}\end{array}\right)\end{array}\right)\\ =\left(\left(\frac{1}{2}\times \left(\text{2}-0\right)\times 20,000\right)+\left(11-2\right)\times 20,000-\left(\frac{1}{2}\times \left(\text{8}-\text{0}\right)\times \text{80,000}\right)\right)\\ =\left(\left(20,000\right)+180,000-\left(320,000\right)\right)\\ =-120,000\end{array}$

Change (decrease) in producer surplus is $120,000.

Economics Concept Introduction

Producer surplus: Producer surplus is the difference between the lowest willing price accepted by the producer and the actual price received by the producer.

Consumer surplus: Consumer surplus is the difference between the highest willing price of a consumer and the actual price that the consumer pays.