30. In the country, only two goods are produced: apples and oranges. The nominal GDP in 2008 was 23 monetary units and matched the nominal GDP in 2009. The volume of apple production in 2008 was 2 units and matched the volume of orange production in 2009. The number of oranges produced in 2008 was the same as the number of apples produced in 2009. The price of one apple in 2008 matched the price of one orange in 2009. Apples in 2008 were sold for 8 monetary units, and the real GDP in 2009 was 22 monetary units. Determine the volume of apple production and their price in 2009.
Solution:

Let's create a table according to the conditions of the problem and denote the unknown variables as $X$, a, b, and c:

| goods | 2008 |  | 2009 |  |
| :---: | :---: | :---: | :---: | :---: |
|  | $\mathrm{Q}_{0}$ | $\mathrm{P}_{0}$ | $\mathrm{Q}_{1}$ | $\mathrm{P}_{1}$ |
| apples | 2 | $\mathrm{c}$ | $\mathrm{X}$ | $\mathrm{b}$ |
| oranges | $\mathrm{X}$ | $\mathrm{a}$ | 2 | $\mathrm{c}$ |

Since the revenue ($TR=2c$) from apples in 2008 was 8 monetary units, the price of apples in 2008 and the price of oranges in 2009 is: $c=\frac{TR}{Q}=\frac{8}{2}=4$ monetary units;

Since nominal GDP 2008 = nominal GDP 2009, then $8+aX=8+bX$, so $a=b$

It remains to find the value of $X$ and $a$, for this we solve the system of equations (the first equation is nominal GDP 2008, the second equation is real GDP 2009):

$8+aX=23$

$2a+4X=22$

Solving the system of equations, we get: $X=5, a=3$

Answer: The production volume of apples in 2009 is 5 units, and their price is 3 monetary units.