Answer to Question #146254 in Economics of Enterprise for muhammad ammar khan

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. Q_d = 5000 – 2500P + 1200I + 650E – 255Ps

I = 500

E = 55

Ps = 25

$Q_d = 5000 - 2500P + 1200 \times 500 + 650 \times 55 - 255 \times 25$

$Q_d = 634375 - 2500P$

b. P = 125

$Q_d = 634375 - 2500 \times 125 = 321875$

P=155

$Q_d = 634375 - 2500 \times 155 = 246875$

∆P = 155 – 125 = 30

∆Q = 246875 – 321875 = -75000

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

P = 125

Q = 321875

∆Q = -75000

∆P = 30

Elasticity $= \frac{125}{321875} \times \frac{-75000}{30} = -0.97$

c. $Q_d= 634375 - 2500P$

$\frac{∆Q_d}{∆P}= -2500$

P=125

$Q_d = 634375 - 2500 \times 125 = 321875$

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

Elasticity of demand $= \frac{125}{321875} \times -2500 = -0.97$

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.