Question

The coconut oil demand function (Bushena and Perloff, 1991) is Q-1,200-9.5p+16.2pp+0.2 where Q is the quantity of coconut oil demanded in thousands of metric tons per year, p is the price of coconut oil in cents per pound, Pp is the price of palm oil in cents per pound, and Y is the income of consumers. Assume that p is initialy 45 cets per pound, Pp is 29 cents per pound, and Q is 1,375 thousand metric tons per year. Calculate the income elasticity of demand for coconut oil The income elasticity of demand is ε -0.096. (Enter your response rounded to three decimal places.)

Answer 1

Here, p=45 cents, Pp =29 cent per pound and Q is 1,375.

Q=1200-9.5P+16.2Pp+0.2Y

Putting all the values in the equation

1375=1200-9.5(45)+16.2(29)+0.2Y

1375=1200-427.5+469.8+0.2Y

1375=1242.3+0.2Y

1375-1242=0.2Y

133=0.2Y

Y=133/0.2

Y=665

Now keeping P and Pp constant, assume that the income increased by 1%

So New Y= 665+ 1%(665)

New Y=665+6.65

New Y=671.65

New Q= 1200-9.5(45)+16.2(29)+0.2(671.65)

New Q=1200-427.5+469.8+134.33

New Q=1376.63

New Q is 1376.63 while Originally Q was 1375

Hence New Q is 0.118% more than Original Q. [(1376.63-1375)/1375]

hence income elasticity of Income = percentage change in qty demanded/percentage change in income

Hence, Income elasticity is = 0.118