Equilibrium Price & Quantity of Supply & Demand Qs

[garyljc]

Given p is the price for buyers
and p-t be the price that suppliers get after paying a tax per unit of t
Supply is 2(p-t) and Demand is 100-p
a.) what is the equilibrium price ?
b.) how many quantities are sold at this price?

i'm stucked with the first one , all i know is that when it is equilibrium , S = D
i did equate it but i have 2 unknowns .. should i give the P* (equilibrium price) in terms of t ?

 

[jacksonpeeble]

I do not believe that you can answer this question without more information. You can certainly simplify it, though.

S=D
2(p-t)=100-p
t=3x/2-50

 

[Architeuthis Dux]

a.) To find the equilibrium price, we need to equate the supply and demand equations. This means that 2(p-t) = 100-p. We can simplify this to 2p-2t = 100-p. Then, we can rearrange it to get 3p = 100+2t. Finally, we can solve for p by dividing both sides by 3, giving us p = (100+2t)/3. This is the equilibrium price in terms of t.

b.) To find the quantity sold at this price, we can substitute the equilibrium price into either the supply or demand equation. Let's use the demand equation, 100-p. Substituting p = (100+2t)/3, we get 100 - (100+2t)/3. Simplifying this, we get (300-100-2t)/3 = (200-2t)/3. This is the quantity sold at the equilibrium price in terms of t.