how much is the total cost for this firm in the short -run equilibrium
Answers
When two lines on a diagram cross, this intersection usually means something. On a graph, the point where the supply curve (S) and the demand curve (D) intersect is the equilibrium. The equilibrium price is the only price where the desires of consumers and the desires of producers agree—that is, where the amount of the product that consumers want to buy (quantity demanded) is equal to the amount producers want to sell (quantity supplied). This mutually desired amount is called the equilibrium quantity. At any other price, the quantity demanded does not equal the quantity supplied, so the market is not in equilibrium at that price. It should be clear from the previous discussions of surpluses and shortages, that if a market is not in equilibrium, market forces will push the market to the equilibrium.
If you have only the demand and supply schedules, and no graph, you can find the equilibrium by looking for the price level on the tables where the quantity demanded and the quantity supplied are equal (again, the numbers in bold in Table 1 indicate this point).
FINDING EQUILIBRIUM WITH ALGEBRA
We’ve just explained two ways of finding a market equilibrium: by looking at a table showing the quantity demanded and supplied at different prices, and by looking at a graph of demand and supply. We can also identify the equilibrium with a little algebra if we have equations for the supply and demand curves. Let’s practice solving a few equations that you will see later in the course. Right now, we are only going to focus on the math. Later you’ll learn why these models work the way they do, but let’s start by focusing on solving the equations. Suppose that the demand for soda is given by the following equation:
where Qd is the amount of soda that consumers want to buy (i.e., quantity demanded), and P is the price of soda. Suppose the supply of soda is
where Qs is the amount of soda that producers will supply (i.e., quantity supplied). (Remember, these are simple equations for lines). Finally, recall that the soda market converges to the point where supply equals demand, or
We now have a system of three equations and three unknowns (Qd, Qs, and P), which we can solve with algebra. Since
we can set the demand and supply equations equal to each other:
Step 1: Isolate the variable by adding 2P to both sides of the equation, and subtracting 2 from both sides.
16
−
2
P
=
2
+
5
P
−
2
+
2
P
=
−
2
+
2
P
14
=
7
P
Step 2: Simplify the equation by dividing both sides by 7.
14
7
=
7
P
7
2
=
P
The equilibrium price of soda, that is, the price where Qs = Qd will be $2. Now we want to determine the quantity amount of soda. We can do this by plugging the equilibrium price into either the equation showing the demand for soda or the equation showing the supply of soda. Let’s use demand. Remember, the formula for quantity demanded is the following:
Q
d
=
16
−
2
P
Taking the price of $2, and plugging it into the demand equation, we get
Q
d
=
16
–
2
(
2
)
Q
d
=
16
–
4
Q
d
=
12
So, if the price is $2 each, consumers will purchase 12. How much will producers supply, or what is the quantity supplied? Taking the price of $2, and plugging it into the equation for quantity supplied, we get the following:
Q
s
=
2
+
5
P
Q
s
=
2
+
5
(
2
)
Q
s
=
2
+
10
Q
s
=
12
Now, if the price is $2 each, producers will supply 12 sodas. This means that we did our math correctly, since
Q
d
=
Q
s
and both Qd and Qs are equal to 12. That confirms that we’ve found the equilibrium quantity.