Question

Suppose that the demand curve for pizzas (in thousands per day) is given by P = 12 – 0.5Q. Calculate the price elasticity of demand if the price is equal to $6. Give and explain one factor that could cause the elasticity of demand for pizzas to increase.

Answer 1

The demand curve is given as

P=12-0.5Q

The price is given as 6. Putting it in the equation above, we get

12-6=0.5Q

Q=6/0.5=12

The formula for point elasticity is dQ/dP*P/Q

Here dQ/dp would be the slope of the demand curve which is also the first-order equation of the demand curve.

So the demand curve in terms of P is Q=24-2P.

Now the differentiation would give dQ/dP= -2

Putting it and the values of P and Q in the equation of elasticity we get

Ed= (-)2*6/12=(-)1

So it is unitary elastic demand curve.

An increase in elasticity implies that the price change would cause a higher change in quantity. This could be due to the availability of substitutes of pizza in the market. If an individual assumes pizza as a product for dinner, then there are more diners nearby which provide substitutes for pizza like hamburgers or pasta etc. This would mean the availability of substitutes for Pizza and this would increase the price elasticity ie if the price now increases, people could shift to other alternatives.

Another factor could be income. If the people of a particular region have low earnings and consider pizza as a luxury good and  their necessity good is homemade food , then if pizza company increases the price to a higher one, then it would be elastic, since they would reduce the quantity consumed.

(You can comment for doubts)