Understanding the Relationship Between Wheat Price and Consumption

In the dynamic and evolving agricultural market, the relationship between the price of wheat and its demand is a critical consideration for consumers, retailers, and policymakers. This article explores how a decrease in the price of wheat and an increase in expenditure can affect its consumption. We will use a mathematical approach to determine the precise percentage by which wheat consumption can be increased under these conditions.

Mathematical Analysis

Let's begin by defining the initial conditions:

The initial price of wheat is represented as ( P ). The initial quantity of wheat consumed is denoted by ( Q ). The initial expenditure on wheat is ( E P times Q ).

When the price of wheat decreases by 25 percent, the new price becomes:

( P_{text{new}} P - 0.25P 0.75P )

If the expenditure is increased by 5 percent, the new expenditure becomes:

( E_{text{new}} E 0.05E 1.05E 1.05PQ )

To find the new quantity consumed ( Q_{text{new}} ), we use the equation for expenditure with the new price:

( E_{text{new}} P_{text{new}} times Q_{text{new}} )

Substituting the known values:

( 1.05PQ 0.75P times Q_{text{new}} )

Now, solving for ( Q_{text{new}} ):

( Q_{text{new}} frac{1.05PQ}{0.75P} frac{1.05Q}{0.75} frac{1.05}{0.75}Q )

( Q_{text{new}} 1.4Q )

This indicates that the new quantity consumed is 1.4 times the initial quantity, meaning the consumption increases by 40 percent:

( text{Increase in consumption} Q_{text{new}} - Q 1.4Q - Q 0.4Q )

( text{Percentage increase} left( frac{0.4Q}{Q} right) times 100 40% )

Alternative Method: Using a Formula

We can also use a simpler formula to calculate the increase in consumption:

( text{Increase in consumption} frac{text{Expenditure increase}}{text{Price decrease}} times 100 )

Given the expenditure increase of 5 percent and a price decrease of 25 percent:

( text{Increase in consumption} frac{5}{25} times 100 20% )

Further Analysis and Real-world Application

In another example, if the price of wheat is represented as ( x ) per Kg and the consumption as ( y ) Kg, the initial expenditure is ( xy ). With an increase in expenditure by 5 percent, the new expenditure becomes:

( text{Increased expenditure} xy times frac{105}{100} frac{21xy}{20} )

The reduced rate of the price is:

( text{Reduced rate} x times frac{75}{100} frac{3x}{4} )

The increased consumption now becomes:

( text{Increased consumption} frac{frac{21xy}{20}}{frac{3x}{4}} frac{7y}{5} )

The increase in consumption is:

( text{Increase} frac{7y}{5} - y frac{2y}{5} )

The percentage increase in consumption is:

( text{Percentage increase} left( frac{frac{2y}{5}}{y} right) times 100 40% )

Alternatively, if the expenditure on wheat increases by 5 percent and the price decreases by 25 percent, the consumption can be increased by:

( frac{5%}{1.25} 4% )

Conclusion

The mathematical analysis clearly shows that a decrease in the price of wheat by 25 percent can lead to a significant increase in consumption if expenditure increases. Understanding these relationships helps stakeholders make informed decisions regarding production, supply, and demand in the wheat market. Whether using a detailed step-by-step approach or a simpler formula, the principle remains the same - a drop in price combined with an increase in expenditure can lead to a considerable rise in wheat consumption.