A consumer has a demand for good x where x = 225 – 0.5P, and P is the price of x. If the current market price is $100.
If the price decreases to $90, the resulting expenditure will increase by _____ dollars.
(a.) $1,300
(b.)$1,425
(c.) $1,475
(d.)$1,550
Answer
Current quantity demanded is
x=225-0.5P=225-0.5*100=175
total expenditure =p*x=100*175=17500
after price change quantity demanded is
x=225-0.5*90=180
total expenditure =90*180=16200
change in expenditure =16200-17500=-1300
The expenditure increases by $-1300
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No option is correct:
we can prove it as follow:
the expenditure is highest when the elastcity is 1 in absolute term
elastcity of demand =(dQ/dP)*Q(P/Q) ............ Q=x=quantity
dx/dp=-0.5 ....... first differentiation of demand funtion with respect to price
elastcity is -1 or unit elastic
-1=(-0.5)*(P/(225-0.5P))
225-0.5P=0.5P
P=225
The expenditure is highest at price P=225.
If the price increase or decrease at this point, then the expenditure decreases.
Also, suppose the price is below 225, and it decreases, then expenditure also decreases but if price increases, then expenditure also increases.
If the price is above 225 and it decreases, then expenditure increases but if the price increases even more, then expenditure decreases.
The given question has $100 is the price which is lower than 225 so if the price decreases from 100 to 90, the expenditure also decrease. It means the question is false, or maybe there is a typo.
It is proved by mathematical induction method.