Chapter 2, Problem 1P

To determine

The price at which the amount demanded equals 15 billion bushels per year and shows the demand curve for corn.

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)

Substitute the respective values in Equation (1) to calculate Y axis value or the price of corn.

$\begin{array}{c}{\text{Q}}^{\text{d}}=\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left({\text{Price}}_{\text{potatoes}}\right)-\text{0}\text{.25}\left({\text{Price}}_{\text{butter}}\right)+\text{0}\text{.0003}\left(\text{Average income}\right)\\ =\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left(\text{0}\text{.75}\right)-\text{0}\text{.25}\left(4\right)+\text{0}\text{.0003}\left(\text{40,000}\right)\\ =5-\text{2}\left({\text{Price}}_{\text{corn}}\right)+3-1+12\\ \text{2}\left({\text{Price}}_{\text{corn}}\right)=19\\ {\text{Price}}_{\text{corn}}=\frac{19}{2}\\ {\text{Price}}_{\text{corn}}=9.5\end{array}$

The price of corn is $9.5.

The X axis value or quantity demanded for corn is calculated as follows using Equation (1):

$\begin{array}{c}{\text{Q}}^{\text{d}}=\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left({\text{Price}}_{\text{potatoes}}\right)-\text{0}\text{.25}\left({\text{Price}}_{\text{butter}}\right)+\text{0}\text{.0003}\left(\text{Average income}\right)\\ =\text{5}-\text{2}\left(0\right)+\text{4}\left(\text{0}\text{.75}\right)-\text{0}\text{.25}\left(4\right)+\text{0}\text{.0003}\left(\text{40,000}\right)\\ =5-0+3-1+12\\ {\text{Q}}^{\text{d}}=19\end{array}$

The quantity demanded for corn is 19 units.

To calculate the price at which the amount demanded equals 15 billion bushels per year, substitute the quantity demanded as 15 in Equation (1).

$\begin{array}{c}{\text{Q}}^{\text{d}}=\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left({\text{Price}}_{\text{potatoes}}\right)-\text{0}\text{.25}\left({\text{Price}}_{\text{butter}}\right)+\text{0}\text{.0003}\left(\text{Average income}\right)\\ 15=\text{5}-\text{2}\left({\text{Price}}_{\text{corn}}\right)+\text{4}\left(\text{0}\text{.75}\right)-\text{0}\text{.25}\left(4\right)+\text{0}\text{.0003}\left(\text{40,000}\right)\\ 15=5-\text{2}\left({\text{Price}}_{\text{corn}}\right)+3-1+12\\ 15=19-\text{2}\left({\text{Price}}_{\text{corn}}\right)\\ {\text{2Price}}_{\text{corn}}=19-15\\ {\text{2Price}}_{\text{corn}}=4\\ {\text{Price}}_{\text{corn}}=\frac{4}{2}\\ {\text{Price}}_{\text{corn}}=2\end{array}$

The price of corn when the demand is equal to 15 billion bushels is $2.

The demand curve for corn is shown below:

In Figure 1, the vertical axis measures the price of corn and horizontal axis measures the quantity demanded. The downward sloping curve is the demand curve for corn. From this figure, it is clear that the price of corn for 19 units of corn is $9.6.

Economics Concept Introduction

Demand: Demand refers to the total value of goods and services that are demanded at a particular price in a given period of time.

Demand curve: The demand curve shows the quantity demanded at different price levels. There is a negative relationship between the price and quantity demanded and the demand curve slopes downward.