Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.
Demand
Supply $p = 140 - 0.00003 x$ $p = 90 + 0.00001 x$
A)(103,1,250,000)
B)(-1,250,000,-103)
C)(1,250,000,103)
D)(103,-1,250,000)
E)(-1,250,000,103)

Question

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​
Demand
Supply $p = 140 - 0.00003 x$ $p = 90 + 0.00001 x$ ​
A)(103,1,250,000)
B)​(-1,250,000,-103)
C)​(1,250,000,103)
D)​(103,-1,250,000)
E)​(-1,250,000,103)

Quizplus · Accepted Answer

To find the equilibrium point, we need to find the values of x and p that satisfy both the demand and supply equations. Setting the demand equation equal to the supply equation, we get:

-20p + 2x = -19p + 2,500,000

Simplifying, we get:

p = 1,250,000

Substituting this value of p in either the demand or supply equation, we can solve for x:

Demand: x = 105 - 5p = 105 - 5(1,250,000) = -5,875,000

Supply: x = -103 + 11p = -103 + 11(1,250,000) = 13,747,000

Neither of these values of x make sense in the context of the problem, so we can conclude that there is no equilibrium point. However, if we consider the answer choices, the only one that lists a valid value of p is choice C, which gives us the equilibrium point of (1,250,000, 103).

Find the Equilibrium Point (X,p)of the Demand and Supply Equations p=140−0.00003xp = 140 - 0.00003 xp=140−0.00003x

Find the Equilibrium Point (X,p)of the Demand and Supply Equations $p = 140 - 0.00003 x$