Question

unde- ch the bany not on. APPLICATIONS Business and Economics 27. Supply and Demand Suppose that the demand and price for a certain model of a youth wristwatch are related by p = D(q) = 16 – 1.25q, where p is the price in dollars) and q is the quantity demanded (in hundreds). Find the price at each level of demand. (a) O watches (b) 400 watches (c) 800 watches Find the quantity demanded for the watch at each price. (d) $8 (e) $10 (f) $12 (g) Graph p = 16 - 1.25q. Suppose the price and supply of the watch are related by p = S(q) = 0.759, rib- where p is the price (in dollars) and q is the quantity supplied (in hundreds) of watches. Find the quantity supplied at each price.

Answer 1

Solution:

Given Demand function is :

p = D(q) = 16 - 1.25q

To find the price at each level of demand we put the value of q ( which is quantity demanded in hundreds ) in the above equation. We can  then get the value of p (which is the price)

a) quantity demanded =  0 watches, q = 0/100 = 0

Now replacing value of q in the equation

p = 16 - 1.25 x 0

= 16 - 0

p = 16

b) quantity demanded = 400 watches, q = 400/100 = 4

Now replacing value of q in the equation

p = 16 - 1.25 x 4

= 16 - 5

p = 11

c) quantity demanded = 800 watches, q = 800/100 = 8

Now replacing value of q in the equation

p = 16 - 1.25 x 8

= 16 - 10

p = 6

d) Now, we are given the price that is p and we need to find the quantity demanded.

p = $8

now replacing the value of p in the equation we get,

8 = 16 - 1.25 x q

1.25 x q = 16 - 8

q = 8/1.25 = 6.4

Now we convert q into quantity demanded

quantity demanded = 6.4 x 100 = 640 watches.

e)

p = $10

now replacing the value of p in the equation we get,

10 = 16 - 1.25 x q

1.25 x q = 16 - 10

q = 6/1.25 = 4.8

Now we convert q into quantity demanded

quantity demanded = 4.8 x 100 = 480 watches.

f)

p = $12

now replacing the value of p in the equation we get,

12 = 16 - 1.25 x q

1.25 x q = 16 - 12

q = 4/1.25 = 3.2

Now we convert q into quantity demanded

quantity demanded = 3.2 x 100 = 320 watches.

h) Given supply function:

p = S(q) = 0.75q

To find the quantity supplied q ( in hundreds) at each level of price p we just  put the value of p in the given supply function.

p = 0

0 = 0.75 x q

q = 0

Therefore quantity supplied is 100 x 0 = 0 watches

i)

p = $ 10

10 = 0.75 x q

q = 10/0.75 = 13.33

Therefore quantity supplied is 100 x 13.33 = 1333 watches

j)

p = $ 20

20 = 0.75 x q

q = 20/0.75 = 26.67

Therefore quantity supplied is 100 x 26.67 = 2667 watches

l) Equilibrium quantity is found when prices from both demand and supply are equal. We equate the above two equations for price p and then solve for q:

16 - 1.25q = 0.75q

q = 16 / (1.25 + 0.75)

= 16 / 2 = 8

Equilibrium quantity is therefore = 8 x 100 = 800

we get equilibrium price as pitting the value of q in any of the above equations

p = 0.75 x 8 = 6

p = 6