Question

If `P=215-5Q`, what is price elasticity of demand when `P=15`. (1) `43`; (2) `40`; (3) `-5`; (4) `-0.075`?

Is it (1) perfectly elastic; (2) relatively elastic; (3) relatively inelastic and (4) perfectly inelastic

Answer 1

Price elasticity of demand at `P=15` is `-0.075` i.e. [4]
Statement [3] is true.

Explanation:

This is more a question of micro-economics rather than algebra. In fact it uses concepts of calculas. Still the answer is

The price elasticity of demand also known as the price elasticity of demand, measures how demand changes to changes in price of a product. More precisely, it is the percent change in quantity demanded relative to a one percent change in price , holding other things constant.

Mathematically this means `E_d=((dQ)/Q)/((dP)/P)` or `(dQ)/(dP)*P/Q`

As `P=215-5Q` and we need price elasticity of demand at `P=15`, where `Q=-P/5+215/5=-15/5+215/5=-3+43=40`

and `E_d=(dQ)/(dP)*P/Q=-1/5xx15/40=-3/40=-0.075`

However, when we draw a price-quantity graph , price is taken on `y`-axis and quantity on `x`-axis and graph appears as follows.
graph{215-5x [-10, 50, -50, 250]}

Normally, if

• `E_d` is negative and large (say `E_d->-oo`), demand curve is horizontal and perfectly elastic

• `E_d` is negative and but not very large (say `E_d` not greater than `-1`), demand curve is horizontal and relatively elastic

• `E_d` is between `0` and `-1`, demand curve is relatively inelastic, and

• `E_d` is close to `0` demand curve is perfectly inelastic.

In the given question, we are being asked about `|E_d|` and not `E_d`, considering this `E_d` will be elastic, if it is larger and inelastic, if it is too small. Hence statement (3) is true.

Hope it helps.