Chapter 2, Problem 3P

To determine

Equilibrium price.

Explanation of Solution

The demand function for corn is given below:

${\text{Q}}^{\text{d}}=\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left({\text{Price}}_{\text{potatoes}}\right)-\text{0}\text{.25}\left({\text{Price}}_{\text{butter}}\right)+\text{0}\text{.0003}\left(\text{Average income}\right)$        (1)

The supply function of corn is shown below:

${\text{Q}}^{\text{s}}=9+5\left({\text{Price}}_{\text{corn}}\right)-2\left({\text{Price}}_{\text{fuel}}\right)-1.\text{25}\left({\text{Price}}_{\text{soybeans}}\right)$        (2)

To calculate the equilibrium price, equate the supply and demand function.

$\begin{array}{c}\left(\begin{array}{l}9+5\left({\text{Price}}_{\text{corn}}\right)-2\left({\text{Price}}_{\text{fuel}}\right)\\ -1.\text{25}\left({\text{Price}}_{\text{soybeans}}\right)\end{array}\right)=\left(\begin{array}{l}\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left({\text{Price}}_{\text{potatoes}}\right)\\ -\text{0}\text{.25}\left({\text{Price}}_{\text{butter}}\right)+\text{0}\text{.0003}\left(\text{Average income}\right)\end{array}\right)\\ \left(\begin{array}{l}9+5\left({\text{Price}}_{\text{corn}}\right)-2\left(2.75\right)\\ -1.\text{25}\left(10\right)\end{array}\right)=\left(\begin{array}{l}\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left(0.75\right)\\ -\text{0}\text{.25}\left(\text{4}\right)+\text{0}\text{.0003}\left(40,000\right)\end{array}\right)\\ \left(9+5\left({\text{Price}}_{\text{corn}}\right)-5.5-12.5\right)=\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+3-1+12\\ -7{\text{Price}}_{\text{corn}}=-28\\ {\text{Price}}_{\text{corn}}=\frac{28}{7}\\ {\text{Price}}_{\text{corn}}=4\end{array}$

The equilibrium price is $4.

Substitute the price ($4) in supply function to calculate the quantity of corn that can be bought and sold.

$\begin{array}{l}{\text{Q}}^{\text{s}}=9+5\left(\text{4}\right)-2\left(2.75\right)-1.\text{25}\left(10\right)\\ {\text{Q}}^{\text{s}}=9+20-5.5-12.5\\ {\text{Q}}^{\text{s}}=11\end{array}$

The quantity of corn that can be bought and sold is 11 units.

If the fuel price increases to $4.50 per gallon, the price corn will increase to $4.50. The quantity supply of corn is calculated as follows:

$\begin{array}{c}{\text{Q}}^{\text{s}}=9+5\left({\text{Price}}_{\text{Corn}}\right)-9-12.5=5-5\left({\text{Price}}_{\text{Corn}}\right)+3-1+12\\ -31.50=-7{\text{Price}}_{\text{Corn}}\\ {\text{Price}}_{\text{Corn}}=\frac{31}{7}\\ {\text{Price}}_{\text{Corn}}=4.5\end{array}$

Price is $4.5.

Substitute this $4.5 to quantity supply.

$\begin{array}{c}{\text{Q}}^{\text{s}}=9+5\left(\text{4}\text{.5}\right)-2\left(4.5\right)-1.\text{25}\left(10\right)\\ {\text{Q}}^{\text{s}}=9+22.5-9-12.5\\ {\text{Q}}^{\text{s}}=10\end{array}$

The quantity supplied is 10 units.

Economics Concept Introduction

Demand: Demand refers to the total value of goods and services produced in an economy during a period of time at particular price.

Supply: Supply is defined as the quantity of a commodity offered for sale at particular price during a period of time.

Equilibrium price and quantity: The intersecting point of demand and supply curve is the equilibrium point. The corresponding price and quantity of equilibrium points are the equilibrium price and equilibrium quantity, respectively.