Question

1. Let the demand function be Q(d) = 200 – 2P(X).
   1. What is the own price elasticity of demand when P = 10?
   2. What is own price elasticity of demand when P = 80?
   3. Assume the firm is operating at P = 40 and is thinking about lowering price by 1%. Would you recommend such a price decrease? Provide evidence for your conclusion
   4. Briefly discuss why the demand curve slops downward and why, as you travel along the demand curve, you move from the elastic to inelastic portion of the demand curve.

Answer 1

Demand function Q(d)= 200-2P(X)

a. When P=10, Q = 200-2*10 =180

Also, from the demand function, Q/P = -2

Then, own price elasticity of demand = P/Q * Q/P = 10/180 * (-2) = -1/9 = -0.11

b. When P= 80, Q = 200-2*80 = 40

and Q/P = -2

Then, own price elasticity of demand = P/Q*Q/P = 80/40*(-2) = -4

c. When P =40 , Q= 200-2*40 = 120

Own price elasticity of demand = P/Q* Q/P = 40/120*(-2) = -0.67

When firm lowers price by 1% i.e, P = 40- 1/100*40 = 39.6

Then , Q = 200-2*39.6 = 200-79.2 = 120.8

Here, own ;price elasticity of demand = P/Q * Q/P = 39.6/120.8 * (-2) = -0.66

Thus, it can be seen that due to 1% fall in price , there is only (120.8-120)/120 *100 = 0.67 % rise in demand. As such, lowering of price is not very profitable for the firm.

d. For a normal good, if price decreases, quantity demanded increases and vice versa . Hence, demand curve has a negative slope. From the above demand function, at P = 80, own price elasticity of demand = -4 i.e, highly elastic demand and at point P=40 , own price elasticity of demand = -0.67 i.e, inelastic demand. Thus, it can be said that as we move along the demand curve, elasticity of demand curve decreases.