Question

Функция спроса выражена уравнением Qd=15-2P, а функция предложения Qs=6+P. Определите размер дефицита или излишка, если P=2. Изобразите графически.

Answer 1

Для определения размера дефицита или излишка необходимо сравнить количество товара, которое покупатели желают приобрести (спрос) и количество товара, которое продавцы готовы продать (предложение) при данной цене.

Когда цена равна 2, функция спроса будет иметь значение:

Q_d = 15 - 2P = 15 - 2(2) = 11

А функция предложения будет иметь значение:

Q_s = 6 + P = 6 + 2 = 8

Таким образом, при цене 2, покупатели хотят приобрести 11 единиц товара, а продавцы готовы продать только 8 единиц товара. То есть, имеется дефицит товара в размере 11 - 8 = 3 единицы.

Ответ: Дефицит товара при цене 2 равен 3 единицам.

Answer 2

Calculation of Deficit or Surplus

To determine the size of the deficit or surplus, we need to find the equilibrium quantity and compare it to the given quantity.

The demand function is given by Qd = 15 - 2P and the supply function is given by Qs = 6P.

To find the equilibrium quantity, we set the quantity demanded equal to the quantity supplied:

Qd = Qs

Substituting the given functions, we have:

15 - 2P = 6P

Simplifying the equation, we get:

15 = 8P

Solving for P, we find:

P = 15/8 = 1.875

Now, we can substitute this value of P back into either the demand or supply function to find the equilibrium quantity. Let's use the demand function:

Qd = 15 - 2P = 15 - 2(1.875) = 15 - 3.75 = 11.25

So, at the equilibrium price of P = 1.875, the equilibrium quantity is Q = 11.25.

Now, let's compare this with the given price of P = 2.

If P = 2, we can substitute this value into the demand and supply functions to find the quantity demanded and supplied:

Qd = 15 - 2P = 15 - 2(2) = 15 - 4 = 11

Qs = 6P = 6(2) = 12

Since the quantity demanded (Qd = 11) is less than the quantity supplied (Qs = 12), there is a deficit of 1 unit.

Graphical Representation

To graphically represent the deficit or surplus, we can plot the demand and supply curves on a graph.

The demand curve is downward sloping, indicating that as the price increases, the quantity demanded decreases. The supply curve is upward sloping, indicating that as the price increases, the quantity supplied increases.

At the equilibrium price of P = 1.875, the demand and supply curves intersect, representing the equilibrium quantity of Q = 11.25.

When the price is P = 2, the quantity demanded (Qd = 11) is less than the quantity supplied (Qs = 12), resulting in a deficit of 1 unit.

Here is a graphical representation of the situation:

        Price (P)
          |
    2     |         S
          |        /
          |       /
          |      /
    1.875 |     /  E
          |    /  /
          |   /  /
          |  /  /
    0     | /  D
          |________________
          0   11.25   12   Quantity (Q)

The point E represents the equilibrium quantity of 11.25 units at the equilibrium price of 1.875. The point D represents the quantity demanded (Qd = 11) at the price of 2, which is less than the quantity supplied (Qs = 12), resulting in a deficit of 1 unit.

Please note that the graph is for illustrative purposes only and may not be to scale.

I hope this helps! Let me know if you have any further questions.