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?
Answers
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
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