Question

A firm’s demand equation is given by: Q = 60 – 60P + 2Y, where Q is quantity, P is price, and Y is income. If price increases by $2 and income increases by $86.7, then quantity demanded will change by ___ units.

Answer 1

given demand function

Q=60-60P+2Y

change in P=$2 and change in income =$86.7

dQ/dQp=-60 ....... the first differentiation of demand function concerning price

it means one dollar increase in price decreases quantity by 60 units

total change because of an increase in price =(-60)*2=-120 units

dQ/dY=2

it means a $1 increase in income increases demand by 2 units

total increase =2*86.7

=173.4

the total change because of both changes =change because of price +change because of income

=(-120)+173.4

=53.4

the quantity demanded will change by 53.4units

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example:

suppose Y=100 and P=0.5

Q=60-60*0.5+2*100

=230

after change

P=2.5 and Y=186.7

Q=60-60*2.5+2*186.7

=283.4

change in quantity=283.4-230

=53.4