Question

3.1 Функция спроса на товар имеет вид QD = 250 –2P, функция предложения QS = 120 + P, где QD – объем спроса в месяц в штуках, P – цена в рублях, QS – месячный объем предложения. Правительство ввело потоварный налог в размере 5 рублей за единицу продукции, равновесное количество товара после введения налога будет составлять (в штуках).

Answer 1

Решение: 
 До введения налога рыночное равновесие составит:  
Qd = Qs 
250 - 2Р=120+Р
3Р=130
Р=43,3 
250-2*43,3=163,3
Q0=163,3 ед. 
Параметры рыночного равновесия после введения налога: 
Qd = Qs
 250 - 2Р = 120+Р 
Pd - Ps = 5 
Введение налога на потребителей приведет к росту цены продажи: 

Pd = Ps + 5.

Answer 2

Equilibrium Quantity after Tax Introduction

The given problem provides information about the demand and supply functions for a product, as well as the introduction of a per-unit tax by the government. We are asked to determine the equilibrium quantity of the product after the tax is imposed.

Demand and Supply Functions

The demand function is given as QD = 250 - 2P, where QD represents the quantity demanded in units and P represents the price in rubles. This equation suggests an inverse relationship between price and quantity demanded, with a slope of -2.

The supply function is given as QS = 120 + P, where QS represents the quantity supplied in units. This equation suggests a positive relationship between price and quantity supplied, with a slope of 1.

Equilibrium Quantity before Tax

To find the equilibrium quantity before the tax is imposed, we need to set the quantity demanded equal to the quantity supplied and solve for the price. Mathematically, this can be represented as:

QD = QS

Substituting the given demand and supply functions, we have:

250 - 2P = 120 + P

Simplifying the equation, we get:

3P = 130

Solving for P, we find:

P = 43.33

Substituting this value back into either the demand or supply function, we can find the equilibrium quantity. Using the supply function, we have:

QS = 120 + 43.33 = 163.33

Therefore, the equilibrium quantity before the tax is imposed is approximately 163.33 units.

Equilibrium Quantity after Tax

After the government introduces a per-unit tax of 5 rubles, the price paid by consumers will increase by that amount. Therefore, the new price (P') will be equal to the original price (P) plus the tax amount:

P' = P + Tax

Substituting the values, we have:

P' = 43.33 + 5 = 48.33

To find the new equilibrium quantity after the tax is imposed, we need to set the new quantity demanded equal to the new quantity supplied. Using the updated price (P') in the demand and supply functions, we have:

QD' = 250 - 2P' = 250 - 2(48.33) = 250 - 96.66 = 153.34

QS' = 120 + P' = 120 + 48.33 = 168.33

Therefore, the equilibrium quantity after the tax is imposed will be approximately 153.34 units.

Conclusion

In summary, the equilibrium quantity of the product after the introduction of the tax will be approximately 153.34 units. This is a decrease from the original equilibrium quantity of 163.33 units. The tax increases the price paid by consumers, leading to a decrease in quantity demanded and an increase in quantity supplied.