Question

Restaurant provide discounts to seniors because

	a.	They have a less-price elastic demand
	b.	They have a more-price elastic demand
	c.	They are the main source of income
	d.	None of the above

Answer 1

The correct answer is (b) They have a more-price elastic demand.

More price elastic demand means that a small decrease in price will result in large increase in demand. So discounting seniors means that they are charging less to them and this less price will result in huge increase in demand for seniors and that's why they provide discount to seniors.

Mathematically In order to maximize profit a firm produces that quantity at which MR = MC

where MR = d(TR)/dQ = d(P*Q)/dQ = P + Q(dP/dQ) = P(1 + (Q/P)(dP/dQ) = P(1 + 1/e)

where P = Price, Q = quantity, MR = Marginal revenue, MC = Marginal cost and e = elasticity of demand = (dQ/dP)(P/Q)

So, MR = MC => P(1 + 1/e) = MC => P = MC/(1 + 1/e) where e is negative because e is elasticity of demand and is negative.

So, if e becomes more negative then this means that it is more elastic implies 1 + 1/e will increase and hence MC/(1 + 1/e) will decrease and thus in order to maximize profit they should charge lesser or give discount to the seniors.

Hence, the correct answer is (b) They have a more-price elastic demand.