Question

Explain why a steeper (linear) demand curve e.g. P = 1 - 2Q instead of P = 1 - Q is said to be less elastic. In your answer, you need to explain the assumptions you’re making and provide both an intuitive and mathematical explanation.

Answer 1

Assumption made in this explanation are:

1. Other factors other than the price of the product, remain unchanged.
2. The product has bad substitutes.
3. Given the equation, Q < P.
4. The money income of the consumer is unchanged.

P=1-2Q (equation 2) P=1-Q (equation 3)

First considering the mathematical expression, i.e., y = mx + c (equation 1)

We are taking price of the product on y-axis and quantity produced of the product on the x-axis. Replacing the values of equation 2 and equation 3 in equation 1, we observe the following:

Case 1: P= (-2)Q + 1.

In this equation, the intercept is equal to 1 and the slope of the curve is equal to -2.

Case 2: P= (-1)Q + 1

IN this case, the intercept is same as 1 but the slop has changed to -1.

From the two cases it is clear that the slope of equation 2 is steeper than the slope of equation 3. As the demand curve becomes steeper and tends to become vertical, it is said to be inelastic or less elastic.

This is, however a mathematical explanation. If intuitively explained, if the price of the product increases, the decrease in quantity demanded of the product is proportionately less. This means that the product has bad substitutes or it is rather a necessary good, which is not so much affected by the price changes. This is in reference to equation 2 demand curve. Demand curve of equation 1 is in comparison flatter which means it is more elastic.