Respuesta :
Answer:
The demand function is P=6-0.05Q
The supply function is P=0.05-1
The market equilibrium point occurs where p = 2.5 and q = 70. Therefore, the equilibrium price for each avocado is $2.5
Step-by-step explanation:
We have a linear function for the demand and the supply. We have two points for each one and we have to write the equation from them.
Demand function
- 100 avocados per month at $1
- 60 avocados per month at $3
The linear function can be written as:
[tex]P=mQ+b[/tex]
where Q is the quantity and P is the price.
The parameter m can be calculated as:
[tex]m=\dfrac{P_1-P_2}{Q_1-Q_2}=\dfrac{1-3}{100-60}=\dfrac{-2}{40}=-0.05[/tex]
We can then calculate b as:
[tex]P_1=mQ_1+b\\\\b=P_1-mQ_1=1-(-0.05)*100=1+5=6[/tex]
Then, the demand function is [tex]P=6-0.05QP[/tex].
Supply function
- 60 avocados per month at $2
- 80 avocados per month at $3
The linear function can be written as:
[tex]Q=mP+b[/tex]
where Q is the quantity and P is the price.
The parameter m can be calculated as:
[tex]m=\dfrac{P_1-P_2}{Q_1-Q_2}=\dfrac{2-3}{60-80}=\dfrac{-1}{-20}=0.05[/tex]
We can then calculate b as:
[tex]P_1=mQ_1+b\\\\b=P_1-mQ_1=2-(0.05)*60=2-3=-1[/tex]
Then, the supply function is [tex]Q_s=0.05P-1[/tex]
The market equilibrium will happen when both functions intersect.
That is:
[tex]P_s=P_d\\\\6-0.05Q=0.05Q-1\\\\6+1=0.10Q\\\\Q=7/0.10=70[/tex]
The quantity of equilibrium is 70 avocados.
Replacing this quantity in any of both functions we can calculate the price of equilibrium:
[tex]P_s*=0.05Q_{eq}-1=0.05*70-1=3.5-1=2.5[/tex]
