Question

A group of retailers will buy 96 televisions from a wholesaler if the price is $325 and 136 if the price is $275. The wholesaler is willing to supply 76 if the price is $255 and 156 if the price is $345. Assuming that the resulting supply and demand functions are linear, find the equilibrium point for the market.

Answer 1

finding demand equation

two points are ( 96 , 325 ) and ( 136 , 275 )

slope = ( 275 - 325 ) / ( 136 - 96 ) = -5/4

y - 325 = -5/4 ( x - 96 )

demand equation is

y = -5/4 x + 445

finding supply equation

( 76 , 255 ) and ( 156 , 345 )

slope = ( 345 - 255 ) / ( 156 - 76 )

= 9/8

y - 255 = 9/8 ( x - 76 )

supply equation is  

y = 9/8 x + 339/2

finding equilibrium point by setting equation equal

9/8 x + 339/2 = - 5/4 x + 445

x = 116

y = 9/8 (116) + 339/2

y = 300

hence, equilibrium point is ( 116 , 300 )