Question

A consumer’s annual income increases by $200, causing a 10% increase in the number of units of salmon the consumer demands. If the consumer has an income elasticity of demand for salmon of 1, what is her new income?​

Answer 1

If the consumer’s annual income increases by $200, causing a 10% increase in the number of units of salmon and has an income elasticity of demand for salmon of 1, then her new income is $ 2200.

Explanation:

Step 1:

Let the initial annual income of the consumer be $ “P”.

We are given that the annual income increases by $ 200

Then, the new income, Pnew = $ [P + 200] …. (i)

Now,  

The percentage increase in the price is given as,

= [{Pnew – P} / P] * 100

= [{P + 200 – P} / P] * 100

= [200/P] * 100 …… (ii)

Step 2:

Also we are given that, the % increase in consumer demand in the no. of units of salmon = 10%

And,

The income elasticity of demand for salmon, ed = 1

We have the formula for elasticity of demand as,

ed = [% increase in demand] / [% increase in price]  

substituting ed = 1 and other values from (i) & (ii), we get

1 = 10 / [{200/P}*100]

⇒ 200/P = 10/100

⇒ 200/P = 1/10

⇒ P = $ 2000  

Thus, by substituting the value of P = $ 2000 in eq. (i), we get

The new income of the consumer as

= P new

= $ [2000 + 200]

= $ 2200

Hope this is helpful!!!