Question

На рынке конкретного товара известны функция спроса QD=9-Р и функция предложения QS = -6 + 2Р. Производители товара уплачивают в бюджет налог в размере 1,5 долл. на единицу товара. Определите выигрыш потребителя и выигрыш производителя до уплаты налога и после уплаты налога.

Answer 1

Решение:
Параметры равновесия данного рынка.
При равновесии Qd = Qs
9 - P = -6 + 2P
3P = 15
Pравн = 5 - равновесная цена.
Подставляя цену в функцию спроса и функцию предложения, получаем равновесный объём.
9-4=-6+2*5Qравн = 4 - равновесный объем.
W = P*Q = 5*4 = 20 - доход продавца до введения налога.

Правительство ввело потоварный налог с каждой проданной единицы товара в размере 1.5 руб. Введение налога на продавца не влияет на уравнение спроса, но изменяет уравнение предложения:
9 - P = -6 + 2(P - 1.5)
3P = 18
Pн.равн = 6 - новая равновесная цена
Подставляя цену в функцию спроса и функцию предложения, получаем равновесный объём.
9-6=-6+2(6-1,5) = 3
Qн.равн = 3 - новый равновесный объем.

Если за одну проданную единицу товара продавец уплачивает 1,5 грн. налога, то за 3 равновесные штуки он обеспечивает 1,5 * 3 = 4,5 ден. ед. в виде налоговых поступлений в бюджет.  
Потери продавца: (5-4,5) * 3 = 1,5 ден. ед.
Потери покупателя: (6-5) * 3 = 3 ден. ед.  

Answer 2

Calculation of Consumer Surplus and Producer Surplus

To determine the consumer surplus and producer surplus before and after the tax payment, we need to analyze the demand and supply functions provided.

The demand function is given as QD = 9 - P, where QD represents the quantity demanded and P represents the price of the product.

The supply function is given as QS = -6 + 2P, where QS represents the quantity supplied.

To find the equilibrium price and quantity, we need to set the demand and supply functions equal to each other:

QD = QS

9 - P = -6 + 2P

Solving this equation, we find that the equilibrium price (P) is $3, and the equilibrium quantity (Q) is 6 units.

Consumer Surplus

Consumer surplus represents the difference between the maximum price consumers are willing to pay for a product and the actual price they pay. It can be calculated by finding the area under the demand curve and above the price line.

Before the tax payment, the equilibrium price is $3. To calculate the consumer surplus, we need to find the area of the triangle formed by the demand curve and the price line.

The formula to calculate the area of a triangle is:

Consumer Surplus = 0.5 * (QD * P)

Substituting the values, we get:

Consumer Surplus = 0.5 * (6 * 3) = 9

Therefore, the consumer surplus before the tax payment is $9.

After the tax payment, the price paid by consumers will increase due to the tax imposed on producers. Let's assume the tax is $1.5 per unit of the product.

The new price paid by consumers will be the sum of the equilibrium price and the tax:

New Price = Equilibrium Price + Tax = $3 + $1.5 = $4.5

To calculate the consumer surplus after the tax payment, we need to find the area of the triangle formed by the demand curve and the new price line.

Using the same formula as before, we get:

Consumer Surplus = 0.5 * (QD * New Price) = 0.5 * (6 * 4.5) = 13.5

Therefore, the consumer surplus after the tax payment is $13.5.

Producer Surplus

Producer surplus represents the difference between the price received by producers and the minimum price they are willing to accept for a product. It can be calculated by finding the area above the supply curve and below the price line.

Before the tax payment, the equilibrium price is $3. To calculate the producer surplus, we need to find the area of the triangle formed by the supply curve and the price line.

The formula to calculate the area of a triangle is:

Producer Surplus = 0.5 * (P * QS)

Substituting the values, we get:

Producer Surplus = 0.5 * (3 * 0) = 0

Therefore, the producer surplus before the tax payment is $0.

After the tax payment, the price received by producers will decrease due to the tax imposed on them. The new price received by producers will be the equilibrium price minus the tax:

New Price = Equilibrium Price - Tax = $3 - $1.5 = $1.5

To calculate the producer surplus after the tax payment, we need to find the area of the triangle formed by the supply curve and the new price line.

Using the same formula as before, we get:

Producer Surplus = 0.5 * (New Price * QS) = 0.5 * (1.5 * 6) = 4.5

Therefore, the producer surplus after the tax payment is $4.5.

Conclusion

In conclusion, the consumer surplus before the tax payment is $9, and it increases to $13.5 after the tax payment. On the other hand, the producer surplus before the tax payment is $0, and it decreases to $4.5 after the tax payment.