Question

Given the following nonlinear demand function for processed pork Q = 250 - p3 + 0.7logPb +0.9logy, where Q is the quantity demanded for processed pork, P is the price of processed pork, Pg is the price beef and Y is the consumer's income. If P = N$3, PB = N$100 and Y = N$5000, income elasticity is Select one: O A. 19.76% O B. 90% O C. 0.9%

Answer 1

Income elasticity of demand is given by the ratio of percentage change in quantity demanded upon percentage change in income. Its formula is given by:

e_Y = % change in quantity demanded / % change in income = [(dQ/Q) * 100] / [(dY/Y * 100] = (Y/Q) * (dQ/dY)

In the question given,

Q = 250 - P³ + 0.7P_B + 0.9logY

P = N$3 , P_B = N$100 and Y = N$5000

So, at these given values

Q = 250 - (3³) + 0.7log(100) + 0.9log(5000) = 250 - 27 + (0.7*2) + (0.9*3.699) = 250 - 27 + 1.4 + 3.3291 = 227.7291

And,

dQ/dY = 0.9(1/Y) = 0.9/5000 = 0.00018

So,

e_Y = (Y/Q) * (dQ/dY) = (5000/227.7291) * (0.00018) = 0.003952

So, none of the given options is correct.