I am struggling with creating the demand and supply curve into an equation. This

Question

I am struggling with creating the demand and supply curve into an equation. This problem requires finding the equilibrium point, but deriving the equation, I go in circles. The given input is Price: $330, 340, 350, 360, 370 ; Quantity demanded: 100 million, 90m,80,70,60; Quantity supplied: 40Million, 60, 80, 100, 120. My approach for Demand is determine the price where demand of zero = $330. (just by looking at chart); the slope is 1 (??.. change or price/change of quantity). P = 330 - 1 Qd;   this doesn't seem correct!

Supply= slope 1/2 or .5; P = 40 + .5Qs .. Then I solve for Qd=Qs.

Explanation / Answer

As per the above demand and supply schedule and curve,

Equilibrium quantity = 80 million

Equilibrium price = $350

Demand equation will be:

Qd = a + bP

b=slope of demand curve = change in Q / change in P = (80-90)/(350-340) =-1

here, two points (340,90) and (350,80) is taken in to consideration

Qd = a-P

At, P= 100

Qd = 330

Thus

a = 330 + 100 = 430

Hence, demand equation is: Qd = 430 - P

Supply equation will be:

Qs= C+dP

d = change in quantity / change in price = (80-60)/(350-340) = 2

Qs = C+2P

At P= 350,   Qs = 80

80 = C+2*350

C = -620

Thus, supply equation is : Qs = -620+2*P

Solving both equation will give equilibrium quantity and price as mentioned above.

Price (in $) Quantity Demanded (in Millions) Quantity Supplied (in millions) 330 100 40 340 90 60 350 80 80 360 70 100 370 60 120

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