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

1.Demand for orange juice is given by the following formula,

$Qd=5000-2500P+1200I+650E-255Ps\ where,\newline I\ is\ income=Rs\ 500\newline E\ is\ expectation =55\newline Ps\ is\ price=Rs\ 25$

Substituting the values to the formula,

$Qd=5000-2500P+1200(500)[phone](25)\newline =5000+600000+35750-6375-2500P\newline =634375-2500P$

Thus, the demand function is

$Qd=634375-2500P$

2.

Price Elasticity of Demand (PED) is the responsiveness of a quantity of a commodity demanded with respect to the variations of price of the commodity.

Given that $P=Rs.\ 155$ ,

$Qd=634375-2500(155)\newline =246875$

$PED=\dfrac{dQd/Qd}{dP/P}$

$=\dfrac{dQd}{dP}*\dfrac{P}{Qd}$

$=\dfrac{d}{dP}(634375-2500P)*\dfrac{155}{246875}$

$=\dfrac{-2500*155}{246875}$

$=-1.57$

d. $Since \ the \ PED\ value \ is\ negative(-1.57)\ it\ means\ the\ demand\ is\ inferior\ good.$