Chapter 2, Problem 6P

(a)

To determine

Graph the supply curve.

Explanation of Solution

Given information:

The supply function of wheat:${\text{Q}}^{\text{S}}{}_{\text{W}}=-6+4{\text{P}}_{\text{W}}-2{\text{P}}_{\text{C}}-{\text{P}}_{\text{F}}$ (1)

In Equation (1), “Q^S_W” is the quantity of wheat supplied, “P_W” is the price of wheat per bushel, “P_C” is the price of corn per bushel, and “P_F” is the price of tractor fuel per gallon.

Price of corn (P_C): $4

Price of fuel (P_F): $2

Calculation:

The supply equation can be simplified by substituting the respective values in Equation (1). This is done because while calculating the change in supply due to the changes in the price of that good, all the other factors are considered constant.

$\begin{array}{l}{\text{Q}}^{\text{S}}{}_{\text{W}}=-6+4{\text{P}}_{\text{W}}-2{\text{P}}_{\text{C}}-{\text{P}}_{\text{F}}\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=-6+4{\text{P}}_{\text{W}}-\left(2\times 4\right)-\left(1\times 2\right)\end{array}$

${\text{Q}}^{\text{S}}{}_{\text{W}}=-16+4{\text{P}}_{\text{W}}$ (2)

The supply equation when other things remain the same is ${\text{Q}}^{\text{S}}{}_{\text{W}}=-16+4{\text{P}}_{\text{W}}$.

Rearrange Equation (2) in terms of price of those goods to derive the invers supply equation.

$\begin{array}{c}{\text{Q}}^{\text{S}}{}_{\text{W}}=-16+4{\text{P}}_{\text{W}}\\ 4{\text{P}}_{\text{W}}=16+{\text{Q}}^{\text{S}}{}_{\text{W}}\\ {\text{P}}_{\text{W}}=\frac{16}{4}+\frac{{\text{Q}}^{\text{S}}{}_{\text{W}}}{4}\end{array}$

${\text{P}}_{\text{W}}=4+0.25{\text{Q}}^{\text{S}}{}_{\text{W}}$ (3)

Substitute the quantity as zero in Equation (3) to calculate the price of wheat (minimum willing price).

$\begin{array}{l}{\text{P}}_{\text{W}}=4+0.25{\text{Q}}^{\text{S}}{}_{\text{W}}\\ {\text{P}}_{\text{W}}=4+\left(0.25\times 0\right)\\ {\text{P}}_{\text{W}}=4\end{array}$

The minimum wiling price of wheat is $4. The slope indicates that increasing 4 units of quantity leads to increase the price by $1(increasing 1 unit increases the price by $0.25).

By using these information, the supply curve of wheat is illustrated in Figure 1 as follows:

In Figure 1, the vertical axis measures the price of wheat and the horizontal axis measures the quantity of wheat. The upward sloping curve “S” is the supply curve of wheat.

Economics Concept Introduction

Supply curve: A supply curve is a graph which shows the quantities of commodity that the producers are willing to sell at different price levels.

(b)

To determine

The calculation of quantity supply.

Explanation of Solution

At price $4, the quantity supply of wheat (Q^S_W ) is calculated by substituting the respective values in Equation (2) as follows:

$\begin{array}{l}{\text{Q}}^{\text{S}}{}_{\text{W}}=-16+4{\text{P}}_{\text{W}}\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=-16+\left(4\times 4\right)\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=0\end{array}$

The quantity supplied of wheat at price $4 is 0 unit.

At price $8, the quantity supply of wheat (Q^S_W ) is calculated by substituting the respective values in Equation (2) as follows:

$\begin{array}{l}{\text{Q}}^{\text{S}}{}_{\text{W}}=-16+4{\text{P}}_{\text{W}}\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=-16+\left(4\times 8\right)\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=-16+32\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=16\end{array}$

The quantity of wheat supplied at price $8 is 16 units.

(c)

To determine

The changes in the supply of wheat.

Explanation of Solution

Given information:

Price of corn (P_C) is $6.

Calculation:

The supply equation can be simplified by substituting the respective values in Equation (1). This is done because while calculating the change in supply due to the changes in the price of that good, all the other factors are considered constant.

$\begin{array}{l}{\text{Q}}^{\text{S}}{}_{\text{W}}=-6+4{\text{P}}_{\text{W}}-2{\text{P}}_{\text{C}}-{\text{P}}_{\text{F}}\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=-6+4{\text{P}}_{\text{W}}-\left(2\times 6\right)-2\end{array}$

${\text{Q}}^{\text{S}}{}_{\text{W}}=-20+4{\text{P}}_{\text{W}}$ (4)

The new supply equation when other things remain the same is ${\text{Q}}^{\text{S}}{}_{\text{W}}=-20+4{\text{P}}_{\text{W}}$.

Rearrange Equation (4) in terms of price of those goods to derive the invers supply equation as follows:

$\begin{array}{c}{\text{Q}}^{\text{S}}{}_{\text{W}}=-20+4{\text{P}}_{\text{W}}\\ 4{\text{P}}_{\text{W}}=20+{\text{Q}}^{\text{S}}{}_{\text{W}}\\ {\text{P}}_{\text{W}}=\frac{20}{4}+\frac{{\text{Q}}^{\text{S}}{}_{\text{W}}}{4}\end{array}$

${\text{P}}_{\text{W}}=5+0.25{\text{Q}}^{\text{S}}{}_{\text{W}}$ (5)

Substitute the quantity as zero in Equation (5) to calculate the price of wheat (minimum willing price).

$\begin{array}{l}{\text{P}}_{\text{W}}=5+0.25{\text{Q}}^{\text{S}}{}_{\text{W}}\\ {\text{P}}_{\text{W}}=5+\left(0.25\times 0\right)\\ {\text{P}}_{\text{W}}=5\end{array}$

The price of wheat is $5. The slope indicates that increasing 4 units of quantity leads to increase the price by $1(increasing 1 unit increases the price by $0.25).

By using this information, the change in supply curve of wheat is shown  in Figure 2 as follows:

In Figure 2, the vertical axis measures the price of wheat and the horizontal axis measures the quantity of wheat demanded. S1 is the initial supply curve of the wheat. The increase in quantity supply of wheat shifts the supply curve from S1 to S2. It leads to increase the choke price from $4 to $5.

Economics Concept Introduction

Supply curve: A supply curve is a graph which shows the quantities of commodity that the producers are willing to sell at different price levels.

(d)

To determine

The changes in the supply of wheat.

Explanation of Solution

Given information:

The price of fuel (P_F) is $1 and the price of corn remains at $4.

Calculation:

The supply equation can be simplified by substituting the respective values in Equation (1). This is done because while calculating the change in supply due to the changes in the price of that good, all the other factors are considered constant.

$\begin{array}{l}{\text{Q}}^{\text{S}}{}_{\text{W}}=-6+4{\text{P}}_{\text{W}}-2{\text{P}}_{\text{C}}-{\text{P}}_{\text{F}}\\ {\text{Q}}^{\text{S}}{}_{\text{W}}=-6+4{\text{P}}_{\text{W}}-\left(2\times 4\right)-1\end{array}$

${\text{Q}}^{\text{S}}{}_{\text{W}}=-15+4{\text{P}}_{\text{W}}$ (6)

The new supply equation when other things remain the same is ${\text{Q}}^{\text{S}}{}_{\text{W}}=-15+4{\text{P}}_{\text{W}}$.

Rearrange Equation (6) in terms of price of those goods to derive the invers supply equation.

$\begin{array}{c}{\text{Q}}^{\text{S}}{}_{\text{W}}=-15+4{\text{P}}_{\text{W}}\\ 4{\text{P}}_{\text{W}}=15+{\text{Q}}^{\text{S}}{}_{\text{W}}\\ {\text{P}}_{\text{W}}=\frac{15}{4}+\frac{{\text{Q}}^{\text{S}}{}_{\text{W}}}{4}\end{array}$

${\text{P}}_{\text{W}}=3.75+0.25{\text{Q}}^{\text{S}}{}_{\text{W}}$ (7)

Substitute the quantity as zero in Equation (7) to calculate the price of wheat (minimum willing price).

$\begin{array}{l}{\text{P}}_{\text{W}}=3.75+0.25{\text{Q}}^{\text{S}}{}_{\text{W}}\\ {\text{P}}_{\text{W}}=3.75+\left(0.25\times 0\right)\\ {\text{P}}_{\text{W}}=3.75\end{array}$

The price of wheat is $3.75. The slope indicates that increasing 4 units of quantity leads to increase the price by $1(increasing 1 unit increases the price by $0.25)..

By using this information, the change in the supply curve of wheat is shown below Figure 3:

In Figure 3, the vertical axis measures the price of wheat and the horizontal axis measures the quantity of wheat demanded. S1 is the initial supply curve of the wheat. The reduction in the quantity supply of wheat shifts the supply curve from S1 to S2. It leads to decrease the choke price from $4 to $3.75.

Economics Concept Introduction

Supply curve: A supply curve is a graph which shows the quantities of commodity that the producers are willing to sell at different price levels.