Question

If the demand curve for coconut oil is expressed as Q=1200-10p+16p_p+0.2Y, 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, p_p is the price of palm oil in cents per pound and Y is the income of consumers. Assume that p is initially 50 cents per pound, p_p is 30 cents per pound, and Q is 1300 thousand metric tons per year. The income elasticity of demand for coconut oil is.

Answer 1

Answer:

$\frac{\Delta Q}{\Delta Y} \frac{Y}{Q}=0.2\frac{501}{1300}=0.077$

Explanation:

To find the income elasticity we first must recall the formula

$\eta_{q,y}=\frac{\Delta Q}{\Delta Y} \frac{Y}{Q}$

which is the percentage change in quantity when income increases in one percent.

From the demand curve we can find $\frac{\Delta Q}{\Delta Y}$ by taking derivative of Q with respect to Y: $\frac{\Delta Q}{\Delta Y} =0.2$

Next we need to know what is the income at the equilibrium quantity of 1300, which we can back out from the data given in the question

$Q=1200-10p+16p_p+0.2Y$

$1300=1200-10\times .50+16\times .30+0.2Y\\100+5-4.8=0.2Y\\Y=\frac{100.2}{0.2}=501$

Then

$\eta_{q,y}=\frac{\Delta Q}{\Delta Y} \frac{Y}{Q}=0.2\frac{501}{1300}=0.077$