Questions: Suppose that corn currently costs 4 per bushel and wheat currently costs 3 per bushel. Also assume that the price elasticity of corn is 0.10, while the price elasticity of wheat is 0.15. For the following questions about elasticities, simply use the percentage changes that are provided rather than attempting to calculate those percentage changes yourself using the midpoint formula. Instructions: In part a, round your answers 701 decimal place. In parts b and c, enter your answers as a whole number. a. If the price of corn falls by 25 percent to 3 per bushel, by what percentage will the quantity demanded of corn increase? percent What will happen if the price of corn falls by 50 percent to 2 per bushel? percent b. To what value would the price of wheat have to fall to induce consumers to increase their purchases of wheat by 5 percent? per bushel c. If the government imposes a 0.40 per bushel tax on corn so that the price of corn rises by 10 percent to 4.40 per bushel, by what percentage will the quantity demanded of corn decrease? percent If the initial quantity demanded is 10 billion bushels per year, by how many bushels will the quantity demanded decrease in response to this tax? million bushels

To solve the given problems, we will use the concept of price elasticity of demand, which measures how much the quantity demanded of a good responds to a change in the price of that good. The formula for price elasticity of demand is:

\[ \text{Elasticity} = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}} \]

1. If the price of corn falls by 25 percent to \$3 per bushel, by what percentage will the quantity demanded of corn increase?

   Given:

   • Price elasticity of corn = 0.10
   • Percentage change in price = -25%

   Using the elasticity formula: \[ 0.10 = \frac{\%\text{ change in quantity demanded}}{-25} \]

   Solving for the percentage change in quantity demanded: \[ \%\text{ change in quantity demanded} = 0.10 \times (-25) = -2.5\% \]

   Since the price decrease is negative, the quantity demanded will increase by 2.5%.

2. What will happen if the price of corn falls by 50 percent to \$2 per bushel?

   Given:

   • Percentage change in price = -50%

   Using the elasticity formula: \[ 0.10 = \frac{\%\text{ change in quantity demanded}}{-50} \]

   Solving for the percentage change in quantity demanded: \[ \%\text{ change in quantity demanded} = 0.10 \times (-50) = -5\% \]

   The quantity demanded will increase by 5%.

To what value would the price of wheat have to fall to induce consumers to increase their purchases of wheat by 5 percent?

Given:

• Price elasticity of wheat = 0.15
• Percentage change in quantity demanded = 5%

Using the elasticity formula: \[ 0.15 = \frac{5}{\%\text{ change in price}} \]

Solving for the percentage change in price: \[ \%\text{ change in price} = \frac{5}{0.15} \approx 33.33\% \]

The price must decrease by approximately 33.33%. The current price of wheat is \$3 per bushel, so the new price is: \[ \text{New price} = 3 \times (1 - 0.3333) = 3 \times 0.6667 \approx 2 \]

The price of wheat would have to fall to approximately \$2 per bushel.

1. If the government imposes a \$0.40 per bushel tax on corn so that the price of corn rises by 10 percent to \$4.40 per bushel, by what percentage will the quantity demanded of corn decrease?

   Given:

   • Price elasticity of corn = 0.10
   • Percentage change in price = 10%

   Using the elasticity formula: \[ 0.10 = \frac{\%\text{ change in quantity demanded}}{10} \]

   Solving for the percentage change in quantity demanded: \[ \%\text{ change in quantity demanded} = 0.10 \times 10 = 1\% \]

   The quantity demanded will decrease by 1%.

2. If the initial quantity demanded is 10 billion bushels per year, by how many bushels will the quantity demanded decrease in response to this tax?

   Initial quantity demanded = 10 billion bushels Percentage decrease in quantity demanded = 1%

   Decrease in quantity demanded: \[ \text{Decrease} = 10 \times 0.01 = 0.1 \text{ billion bushels} = 100 \text{ million bushels} \]

In summary:

• The quantity demanded of corn will increase by 2.5% if the price falls by 25% and by 5% if the price falls by 50%.
• The price of wheat would need to fall to approximately \$2 per bushel to increase purchases by 5%.
• The quantity demanded of corn will decrease by 1% if the price rises by 10%, resulting in a decrease of 100 million bushels.