Question

Функция спроса и предложения для условного товара имеют вид: Qd=30-5p Qs=-10+5p Правительство страны ввело налог на данный товар размером в 1 ден. ед., вносимый в госбюджет производителями товара. Определите, как изменится объем налоговых поступлений в бюджет страны, если спрос на товар возрастет на 100%

Answer 1

Решение:

Параметры равновесия данного рынка.
При равновесии Qd = Qs
30 -5P = -10 + 5P
10P = 40
Pравн = 4 - равновесная цена.
Подставляя цену в функцию спроса и функцию предложения, получаем равновесный объём.

30-5*4=-10+5*4

Qравн = 10 - равновесный объем.

Правительство ввело потоварный налог с каждой проданной единицы товара в размере 1 руб.

Для нахождения новой равновесной цены при введении налога с продажи изменяем функцию предложения:
30 -5P = -10 + 5(P - 1)
10P = 45
Pн.равн = 4.5 - новая равновесная цена.
Qн.равн = 7.5 - новый равновесный объем.
Доля покупателя в новой цене: 4.5 - 4 = 0.5.
Доход государства от введения данного налога составит:
T*Qн.равн = 1 * 7.5 = 7.5

Если цена спроса на продукцию повысилась на 100%, то цена устанавливается на уровне:

4,5*100%+4,5=9  – новая равновесная цена
Qн.равн = -10+5*9 = 35 - новый равновесный объем.

Answer 2

Function of Demand and Supply

The function of demand and supply for a hypothetical product is given as follows:

- Demand function: Qd = 30 - 5p - Supply function: Qs = -10 + 5p

Where Qd represents the quantity demanded, Qs represents the quantity supplied, and p represents the price of the product.

Introduction of Tax

The government of the country has introduced a tax on this product, which is equal to 1 monetary unit. This tax is collected by the producers of the product and is deposited into the government budget.

Impact on Tax Revenues

To determine how the volume of tax revenues in the country's budget will change if the demand for the product increases by 100%, we need to analyze the effects on both the demand and supply sides.

Increase in Demand

If the demand for the product increases by 100%, we can calculate the new quantity demanded using the demand function:

Qd_new = 30 - 5p + 100% * (30 - 5p)

Simplifying the equation, we get:

Qd_new = 60 - 10p

Impact on Tax Revenues

To calculate the change in tax revenues, we need to determine the difference between the tax collected before and after the increase in demand.

Before the increase in demand, the quantity demanded was given by the original demand function:

Qd_original = 30 - 5p

The tax collected per unit is 1 monetary unit, so the tax revenues before the increase in demand can be calculated as:

Tax_revenues_original = (30 - 5p) * 1

After the increase in demand, the quantity demanded is given by the new demand function:

Qd_new = 60 - 10p

The tax revenues after the increase in demand can be calculated as:

Tax_revenues_new = (60 - 10p) * 1

To determine the change in tax revenues, we subtract the original tax revenues from the new tax revenues:

Change_in_tax_revenues = Tax_revenues_new - Tax_revenues_original

Substituting the expressions for tax revenues, we get:

Change_in_tax_revenues = (60 - 10p) - (30 - 5p)

Simplifying the equation, we find:

Change_in_tax_revenues = 30 - 5p

Therefore, the change in tax revenues in the country's budget will be equal to 30 - 5p monetary units.

Please note that the specific value of p (price) is not provided in the question, so we cannot determine the exact change in tax revenues without this information.