# Equilibrium price?

#### edy21

##### New member
I have the following problem :

The demand function of a good is qD=2000-4P and the supply function is qS=5P+200.

a) Find equilibrium price and quantity.
b) Buyers receive a government subsidy of 50 for every good bought. Find the new equilibrium price and quantity.

Solution for a) 2000-4P=5P+200 P=200 Q=1200
Solution for b) 2000-4(P-50)=5P+200
9P=2000 P=222.22 Q=1311.11

Could anyone please show me how we get Q=1200 at a) and how we get to P=222.22 therefore Q=1311.11 at b).
Your help would be greatly appreciated!

#### MarkFL

##### Super Moderator
Staff member
a) At equilibrium, demand equals supply:

$$\displaystyle 2000-4P=5P+200$$

Add $$4P-200$$ to both sides:

$$\displaystyle 1800=9P$$

Divide through by 9 and arrange as::

$$\displaystyle P=200$$

Substituting this value of $$P$$ into either the supply or demand functions yields:

$$\displaystyle Q=1200$$

b) If buyers are getting a $50 subsidy, then the price for demand is reduced by$50 and then equating supply and demand, we find:

$$\displaystyle 2000-4(P-50)=5P+200$$

Distribute the -4 on the LHS:

$$\displaystyle 2000-4P+200=5P+200$$

Collect like terms and arrange as:

$$\displaystyle 9P=2000$$

Divide through by 9:

$$\displaystyle P=\frac{2000}{9}\approx222.22\implies Q=\frac{11800}{9}\approx1311.11$$

#### edy21

##### New member
a) At equilibrium, demand equals supply:

$$\displaystyle 2000-4P=5P+200$$

Add $$4P-200$$ to both sides:

$$\displaystyle 1800=9P$$

Divide through by 9 and arrange as::

$$\displaystyle P=200$$

Substituting this value of $$P$$ into either the supply or demand functions yields:

$$\displaystyle Q=1200$$

b) If buyers are getting a $50 subsidy, then the price for demand is reduced by$50 and then equating supply and demand, we find:

$$\displaystyle 2000-4(P-50)=5P+200$$

Distribute the -4 on the LHS:

$$\displaystyle 2000-4P+200=5P+200$$

Collect like terms and arrange as:

$$\displaystyle 9P=2000$$

Divide through by 9:

$$\displaystyle P=\frac{2000}{9}\approx222.22\implies Q=\frac{11800}{9}\approx1311.11$$
Could you please explain how exactly I get to 11800 at Q=11800/9 and the substituting value of P for the first example is basically 1000 since
Q=1200? Thanks!

#### MarkFL

##### Super Moderator
Staff member
I used either one of the expressions we're given for quantity as a function of price, to obtain the needed quantity once price was found. For example, we know:

$$\displaystyle Q=5P+200$$

So, plug in the values we found for $$P$$ to obtain $$Q$$.