A manufacturer can sell 400 watches for 11 each and 800 watc

A manufacturer can sell 400 watches for $11 each and 800 watches for $ 6 each. Find a demand and price equation assuming the relationship is linear. P=D(q)=. Find the quantity demanded at $10 per watch. Suppose the price and supply of the watch are related by p = S (q) = .0075q, where p is the price In dollars and q is the number of watches supplied. Find the quantity supplied at $10 per watch. Use algebra to find the equilibrium point and then graph both functions. The equilibrium price is___and the equilibrium quantity is___.

Solution

1)

a) demand equation = D(q) = mq+b

from two points ( 400,11 ) and ( 800,6 )

m = slope = -1/80 = -.0125

6 = 800( -.0125) + b

b = 16

demand equation

D(q) = 16 - .0125q

b) demand of $ 10 per watch

10 = 16-.0125q

q = 10-16 / -.0125

q = 480 watches

c) p = S(q) = .0075q

plugging p = 10

10 = .0075 q

q = 10/.0075 = 1333.33

q = 1333 watches approximately

d) equillibrium occurs when demand = supply

-.0125q + 16 = .0075q

q = -1280

q = 800 watches

equillibrium price = $ 6