The consumers of a particular water bottle are willing to pu

The consumers of a particular water bottle are willing to purchase 3.000 water bottles at a unit price of $18 but for every $8 decrease in price. they are willing to purchase 9.000 more bottles. The suppliers of the water bottle will not supply any water bottles at a price level of $6 per bottle but are willing to supply 3.000 water bottles at a unit price of $10. The supply and demand are known to be linear. Find the demand equation where times is the number of water bottles demanded at a unit price of $p. Find the supply equation where times is the number of water bottles supplied at a unit price of $p. Find and interpret the market equilibrium point.

Solution

Let x be the number of bottles and $p be the unit price.

rate of $ 18 -----3000 bottles

For every drop of $8 additional bottles they can prchase extra 9000 bottles.So, based on thiswe can say:

rate of $ 10 ----- 12000

Now wefind the demand equation: p = mx +b .Bu using these two points above we can find the equation:

m = ( 10 - 18)/( 12000 -3000) = -8/9000

p = -8x/9000 + b ; 18 = -8*3000/9000 +b

b = 18 +8/3 = 62/3

a) p = -8x/9000 +62/3

b) Supply equation : p= mx +b

We have two points: Rate of $16---- 0 bottles

Rate of $ 10 ------ 3000 bottles.Find the equation

m ( slope) = (10 -6)/( 3000 -0) = 4/3000

p = 4x/3000+b ; 6 = 0 +b

Supply equation : p = 4x/3000 + 6

c) Market Equlibriul point occurs when supply= demand

Solve both the equations above: 4x/3000 + 6 =  -8x/9000 +62/3

12x/9000+ 8x/9000 = 62/3 -6

20x/9000 = 44/3

x = 44*9000/( 20* 3) = 6600 bottles is the equilibrium

Price p of the bottle per unit =   4x/3000 + 6 = 4* 6600/3000 +6 = $ 14.8 per unit