$Q _ { s } = 40 + 6 P - 8 P _ { I } + 10 F$ where $Q _ { s }$ is the quantity supplied of the good, P is the price of the good, $P _ { I }$ is the price of an input, and F is the number of firms producing the good.
-When $P _ { I }$ = $40 and F = 50, the INVERSE supply function is

Question

Quizplus · Accepted Answer

The inverse supply function is found by solving the supply function for P.$$Q _ { s } = 40 + 6 P - 8 P _ { I } + 10 F$$$$Q _ { s } - 40 = 6 P - 8 P _ { I } + 10 F$$$$6 P = Q _ { s } - 40 + 8 P _ { I } - 10 F$$$$P = \frac { Q _ { s } - 40 + 8 P _ { I } - 10 F } { 6 }$$When $P _ { I }$ = $40 and F = 50, the inverse supply function is$$P = \frac { Q _ { s } - 40 + 8 ( 40 ) - 10 ( 50 ) } { 6 }$$$$P = \frac { Q _ { s } - 40 + 320 - 500 } { 6 }$$$$P = \frac { Q _ { s } - 180 } { 6 }$$$$P = -30 + 0.1667Q _ { s }$$

Qs=40+6P−8PI+10FQ _ { s } = 40 + 6 P - 8 P _ { I } + 10 FQs​=40+6P−8PI​+10F

$Q _ { s } = 40 + 6 P - 8 P _ { I } + 10 F$