Past sales show that when a scanner is priced at $175, the quantity demanded is

Question

Past sales show that when a scanner is priced at $175, the quantity demanded is 350 units per week. For each $5 drop in price below $175, the quantity demanded rises by 50 units per week. The manufacturer will not market any of the devices if the price is $100 or lower, but for each $10 increase in price, the manufacturer is willing to market an additional 75 items. Write the demand equation and the supply equation. Then find the equilibrium quantity and the equilibrium price

What is the equalibrium quantity in units and the equalibrium price in dollars?

Explanation / Answer

when a scanner is priced at $175, the quantity demanded is 350 units per week. =>(x1,p1)=(350,175)

For each $5 drop in price below $175, the quantity demanded rises by 50 units per week =>(x2,p2)=(400,170)

p-p1=[(p2-p1)/(x2-x1)](x-x1)

p-175=[(170-175)/(400-350)](x-350)

p-175=(-5/50)(x-350)

p-175=(-1/10)(x-350)

p-175=(-1/10)x+35

p=(-1/10)x+210

demand D(x)=(-1/10)x+210

The manufacturer will not market any of the devices if the price is $100 or lower =>(x1,p1)=(0,100)

for each $10 increase in price, the manufacturer is willing to market an additional 75 items. =>(x2,p2)=(75,110)

p-p1=[(p2-p1)/(x2-x1)](x-x1)

p-100=[(110-100)/(75-0)](x-0)

p-100=(2/15)x

p=(2/15)x +100

supply S(x)=(2/15)x +100

for equilibrium D(x)=S(x)

(-1/10)x+210=(2/15)x +100

(2/15)x+(1/10)x =210-100

((20+15)/150)x =110

(35/150)x=110

x =110*150/35

x=471.43 units

p=(-1/10)*471.43 +210

p=162.86$

equalibrium quantity 471.43 units ,equalibrium price 162.86$

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