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

`(\Delta Q)/(\Delta Y) (Y)/(Q)=0.2(501)/(1300)=0.077`

Step-by-step explanation:

To find the income elasticity we first must recall the formula

`\eta_(q,y)=(\Delta Q)/(\Delta Y) (Y)/(Q)`

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

From the demand curve we can find
`(\Delta Q)/(\Delta Y)` by taking derivative of Q with respect to Y:
`(\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* .50+16* .30+0.2Y\\100+5-4.8=0.2Y\\Y=(100.2)/(0.2)=501`

Then

`\eta_(q,y)=(\Delta Q)/(\Delta Y) (Y)/(Q)=0.2(501)/(1300)=0.077`