Respuesta :
Answer:
Step-by-step explanation:
The demand function is expressed as
D(p )=1150-50p
The supply function is expressed as S(p)=−200 + 40p
Where
p represents the price
A) The equilibrium price is the price at which the quantity supplied and the quantity demanded would be equal. Therefore
1150 - 50p = - 200 + 40p
40p + 50p = 1150 + 200
90p = 1350
p = 1350/90
p = 15
The equilibrium price is $15
b) For quantity demanded to be greater than quantity supplied, the price would be
1150 - 50p > - 200 + 40p
40p + 50p > 1150 + 200
90p > 1350
p > 1350/90
p > 15
The price would be greater than 15
c) if the quantity demanded is greater than the quantity supplied, the prices of the T shirt would increase.
Law of demand and supply states that; the higher the price, the lower the quantity demanded
- The equilibrium price is [tex]10.56[/tex].
- The quantity demanded will be greater than the supply when the price is less than 10.56
- There will be shortage when demand exceeds supply
We have:
[tex]S(p) = 200 +40p[/tex]
[tex]D(p) = 1150 - 50p[/tex]
(a) The equilibrium price
This is when the demand and supply are equal
i.e [tex]S(p) = D(p)[/tex]
So, we have:
[tex]200 + 40p = 1150 - 50p[/tex]
Collect like terms
[tex]40p + 50p = 1150 -200[/tex]
[tex]90p = 950[/tex]
Divide both sides by 90
[tex]p = 10.56[/tex]
Hence, the equilibrium price is [tex]10.56[/tex]
(b) Price when demand is greater than supply
In (a), we have the equilibrium price to be:
[tex]p = 10.56[/tex]
Using the law of demand and supply;
When the price is less than 10.56, the quantity demanded will be greater than the quantity supplied
(c) When quantity demanded is greater than quantity supplied
When the quantity demanded exceeds the supply, there will be shortage of T-shirts.
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