What is the Y intercept and equilibrium quantity with these equations?

Here is a question and answer about the economics of solving for an equilibrium quantity value.  The question is:

1. Suppose demand and supply functions are given by Qs = 5 + P and Qd =50 - ½P respectively. Then the equilibrium QUANTITY is what?
2.In the equation Y = 6 - 2.0X the y-intercept is?

Now remember that to solve for equilibrium price and quantity, you need to set the quantity supplied equal to the quantity demanded, and solve for price.  You can then plug your price into either quantity equation (or both to check your math) to solve for equilibrium quantity.  So first set your Qs equal to your Qd:

Qs = Qd = 5 + P = 50 – (1/2)P
5 + P = 50 –(1/2)P

So subtract 5 and add ½ P to both sides to get:

(3/2)P = 45 or P = 30

We can get P = 30 by dividing 45 by 3, and then multiplying it by 2.  We can then plug our equilibrium price back into our quantity equations to get:

Qd= 5 + P = 5 + 30 = 35, and for Qs as well:

Qs = 50 – ½ * 30 = 50 – 15 = 35

So 35 is our equilibrium quantity.

For the second problem, finding the Y intercept from an equation, we need to look for the constant, which is also known as the intercept.  Traditionally, an equation is written as:

Y = a + bX,

Were Y represents a variable (such as quantity) and X represents a variable (such as price) and ‘a’ and ‘b’ are coefficients or fixed values.  You can see that ‘a’ is independent of X, while ‘b’ interacts with X.  ‘a’ is our intercept value, because it is the value of Y when X=0, and ‘b’ is our slope term because it shows how much Y will change as X changes.

So in our example above, 6 is the intercept and the slope is -2

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