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:
eY = % change in quantity demanded / % change in income = [(dQ/Q) * 100] / [(dY/Y * 100] = (Y/Q) * (dQ/dY)
In the question given,
Q = 250 - P3 + 0.7PB + 0.9logY
P = N$3 , PB = 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,
eY = (Y/Q) * (dQ/dY) = (5000/227.7291) * (0.00018) = 0.003952
So, none of the given options is correct.
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