Question

Функция спроса Qd=100-P,Функция предложения Qs=2P-50,где P-цена в рублях,а Qd и Qs величины спроса и предложения. а)Найти равновесную цену и количество б)Правительство в целях стимуляции снизило цену до 40руб.К чему это приведёт. в)Какая ситуация складывается на рынке? г)Расчитать изменение выручки продавца в обоих случаях.Является ли она максимальной

Answer 1

Решение:
Qd=Qs 
100 – Р = 2Р – 50, 
3Р=150 
Ре=50 - равновесная цена 
Равновесный объем продажи определим, подставив значение Р:

Qe = 100-50 = 50 ед. - равновесное количество 

Выручка составит:

TR1=P*Q=50*50 = 2500 тыс. руб. 
При снижении цены до 40 ед.: 

Объем спроса составит: QD = 100 - 40 = 60;
Объем предложения составит: QS = 2*40-50 = 30.
Объем предложения будет ниже объема спроса, образуется недостаток товара в размере:  

QD - QS =  60-30 = 30. 
Выручка составит:

TR2=P*Q=60*30 = 1800 тыс. руб. 
При цене 40 рублей расходы потребителей снизятся на (2500-1800) = 700

 

Answer 2

Equilibrium Price and Quantity

To find the equilibrium price and quantity, we need to set the quantity demanded (Qd) equal to the quantity supplied (Qs) and solve for the price (P).

The demand function is given as Qd = 100 - P The supply function is given as Qs = 2P - 50.

Setting Qd equal to Qs: 100 - P = 2P - 50

Simplifying the equation: 3P = 150 P = 50

Substituting the equilibrium price (P) back into either the demand or supply function, we can find the equilibrium quantity.

Using the demand function: Qd = 100 - P Qd = 100 - 50 Qd = 50

Therefore, the equilibrium price is 50 rubles and the equilibrium quantity is 50.

Government Intervention and Market Situation

If the government decides to lower the price to 40 rubles, it will create a situation where the price is below the equilibrium price. This is known as a price ceiling.

When the price is set below the equilibrium price, the quantity demanded exceeds the quantity supplied. In this case, the quantity demanded (Qd) at a price of 40 rubles is: Qd = 100 - P Qd = 100 - 40 Qd = 60

The quantity supplied (Qs) at a price of 40 rubles is: Qs = 2P - 50 Qs = 2(40) - 50 Qs = 80 - 50 Qs = 30

As a result, there will be excess demand or a shortage of 60 - 30 = 30 units.

Change in Seller's Revenue

To calculate the change in the seller's revenue in both cases, we need to multiply the price by the quantity.

In the equilibrium situation: Seller's revenue = Price * Quantity Seller's revenue = 50 * 50 Seller's revenue = 2500 rubles

When the government lowers the price to 40 rubles: Seller's revenue = Price * Quantity Seller's revenue = 40 * 30 Seller's revenue = 1200 rubles

Therefore, the seller's revenue decreases from 2500 rubles to 1200 rubles when the government lowers the price to 40 rubles.

It's important to note that the seller's revenue is not maximized in either case. The maximum revenue for the seller would occur at the price and quantity where the demand and supply curves intersect, which is the equilibrium point.