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When p = $5, the quantity demanded of a good is 30 units, and the quantity supplied of the good is 50 units. For every $1 decrease in the price of this good, quantity demanded rises by 5 units and quantity supplied falls by 5 units. The equilibrium price of this good is ___________and the equilibrium quantity of this good is _________ units?

Respuesta :

pristina

Answer: Equilibrium price is $3 and equilibrium quantity is 40 units.

Explanation:

Demand equation is given by,

[tex]Qd= a-bP


When P=$5, Qd=30


30 = a – 5b


Change in Quantity demanded = Change in a – (b Change in P)


5 = 0 – b(-1)


b=5


So, a = 55[/tex]

Therefore the demand equation is given by, [tex]Qd= 55 – 5P[/tex]

Supply equation is given by

[tex]Qs= c + dP


When P=$5, Qs = 50


50 = c + 5d


Change in Quantity supplied = Change in c + d(Change in P)


-5 = 0 + d(-1)


d=5


So, c=25[/tex]

Therefore, the supply equation is given by,  

[tex]Qs= 25 + 5P[/tex]

Equilibrium is given by

[tex]Qd=Qs


55 – 5P= 25 + 5P


30=10P


P=$3


And


Equilibrium quantity is, Q= 55 – 5(3) = 55 – 15 = 40 units.[/tex]