Question

В стране количество денег в обращении увеличилось с 32 млрд до 36 млрд .Скорость обращения денег не изменилась ,а количество товаров сократилось на 10% .В результате этого на сколько процентов повысились цены в стране?

Answer 1

Задача решается индексным методом с использованием уравнения Фишера:
MV=PQ, где
M- кол-во денег в обращение
V-скорость обращ.
P- цена, Q -кол-во товаров.
Из этой формулы:
P=MV/Q
Для начала найдем изменение M в % :
1) M=(36-32)/32=0,125.
Соответственно, М увеличилась на 1,125.
2) V=1 ,так как оно не изменилось.
3) Q= 1 - 0,1= 0,9, так как она сократилась на 10%, то есть уменьшилось на 0,1 от целого (единицы).
4) P=1,125*1/0,9= 1,25.
Вывод:цены в стране увеличилась на 25%

Answer 2

Calculation of Price Increase

To calculate the percentage increase in prices in the country, we need to consider the change in the money supply and the change in the quantity of goods.

Given information: - Money supply increased from 32 billion to 36 billion. - Velocity of money remained unchanged. - Quantity of goods decreased by 10%.

To calculate the percentage increase in prices, we can use the equation of exchange:

Money Supply x Velocity of Money = Price Level x Quantity of Goods

Let's denote the initial price level as P1 and the final price level as P2.

Using the equation of exchange, we can write the following equation:

32 billion x V = P1 x (Quantity of Goods) 36 billion x V = P2 x (Quantity of Goods - 10%)

Since the velocity of money remains unchanged, we can cancel it out from both equations:

P1 x (Quantity of Goods) = P2 x (Quantity of Goods - 10%)

Now, let's solve for the percentage increase in prices (P2 - P1) / P1:

(P2 - P1) / P1 = (P1 x (Quantity of Goods) - P2 x (Quantity of Goods - 10%)) / P1

Simplifying the equation:

(P2 - P1) / P1 = (P1 x Quantity of Goods - P2 x Quantity of Goods + 0.1 x P2 x Quantity of Goods) / P1

(P2 - P1) / P1 = (P1 - P2 + 0.1 x P2) / P1

(P2 - P1) / P1 = (0.1 x P2 - P2) / P1

(P2 - P1) / P1 = (0.1 - 1) x P2 / P1

(P2 - P1) / P1 = -0.9 x P2 / P1

(P2 - P1) / P1 = -0.9

Therefore, the percentage increase in prices is -90%.

Please note that a negative percentage increase indicates a decrease in prices. In this case, the decrease is by 90%.