Answer to Question #147610 in Economics of Enterprise for ABDUL MANNAN

Question

Demand for Orange Juice is given as
Qd = 5000 – 2500 P + 1200 I + 650 E – 255 Ps
Suppose Income is I = Rs.500, Expectations E = 55, and Price of Ps = Rs 25.
a. Find the Demand Equation.
b. Using the demand function from part a.,
Calculate Elasticity of Demand for price range of Rs.125 and Rs.155.
c. What will be the ‘Price Elasticity of Demand’ at P = Rs.125?
d. Interpret the Elasticity of Demand calculated in (C) above.

Answer 1

a. Qd = 5000 - 2500P+ 1200I+ 650E - 255Ps

at I = 500, E = 55, Ps = 25

Qd = 5000 – 2500P + 1200(500) + 650(55) - 255(25)

Qd = 634375 - 2500P

b. at P = 125

Qd = 634375 - 2500(125)

Qd = 321875

at P = 155

Qd = 634375 - 2500(155)

Qd = 246875

∆P = 155 – 125 = 30

∆Q = 246875 - 321875

∆Q = -75000

Elasticity of demand $= \frac{P}{Q} \times \frac{∆Q}{∆P}$

P = 125, Q = 321875, ∆Q = -75000, ∆P = 30

Elasticity $= -\frac{125 \times 75000}{321875 \times 30}$

Elasticity = -0.97

c. Qd = 634375 - 2500P

$\frac{∆Qd}{∆P} = -2500$

At P = 125

Qd = 634375 - 2500(125)

Qd = 321875

Elasticity of demand $= \frac{P}{Qd} \times \frac{∆Qd}{∆P}$

Elasticity of demand $= \frac{125}{321875} \times (-2500)$

Elasticity of demand = -0.97

d. The elasticity of demand is negative which means there exists an inverse relationship between price and quantity demanded Keeping other factors constant.

The value of price elasticity of demand is less than 1 which means the percentage change in quantity demanded is less than the percentage change in price i.e demand is unresponsive to change in price.