Need help with supply and demand equation

[riovolt]

ityckhjk

 

[Greg Bernhardt]

moving to homework help. now please show some work or at least some thoughts on the matter

 

[riovolt]

i think I solved it I just want to know if it is right


a. P=120-1.25q, to get the quantity when the price is 80, just represent P with 80 in the equation:
80=120-1.25q
80+1.25q=120
1.25q=120-80
1.25q=40
q=40/1.25
q=32. The quantity demanded when the price is $80.
b. To get the price elasticity between the price 80 and 60, we must first get the quantity at both prices. We already know that of $80 are 32 units. $60 is
60=120-1.25q
60+1.25q=120
1.25q=120-60
1.25q=60
q=60/1.25
q=48.

PED= (%change in quantity)/ (% change in price)

%change in quantity = (chg in qty/ initial qty) * 100
% change in price = 32-48= -16.
Initial quantity is 32.
%change in quantity = (-16/32)*100
= (-.5)*100
= -50%= 50%.

% change in price = (change in price/ initial price)*100
change in price=80-60=20.
Initial price= 80
% change in price= (20/80)*100
= (.25)*100%
=25%

now, the
Price Elasticity of Demand = 50%/25%
Price Elasticity of Demand = 2.

The good is an elastic good.
c. Equilibrium is where demand is equal to supply.
120-1.25q=1.75q
120=1.75q+1.25q
120=3q
q=120/3
q=40. This is the equilibrium quantity.

For the equilibrium price, substitute for the equilibrium quantity in any of the demand or supply equation. Taking the supply equation,
P=1.75q
P=1.75(40)
P=70 the equilibrium price.