Question

Question 5.2

The demand for haddock has been estimated as

log Q = a + b log P + c log I + d log Pm,

where Q = quantity of haddock sold in New England

           P = price per pound of haddock

            I = a measure of personal income in the New England region

        Pm = an index of the price of meat and poultry

If b = -2.174, c = 0.461, and d = 1.909,

1. Find income elasticity of demand and discuss whether haddock is an inferior or normal good.

2. Find the cross price elasticity of demand.

3. Give an economic interpretation of the estimated slope coefficient, b.

PLEASE SHOW WORK

Answer 1

a. Income elasticity of demand =  
Now, partially differentiating the demand function with respect to I, we get,

So,

Thus, Income elasticity of demand =

Income elasticity of demand = 0.461

b. Cross price elasticity of demand =  

Now, partially differentiating the demand function with respect to Pm, we get,

So,

Now, cross price elasticity of demand =

So, cross price elasticity of demand = 1.909

c. b = -2.174
This means that if we change P by 1 percent then Q would change by -2.174 percent.