Question

здравствуйте, не могли бы вы помочь? расситала в задаче равновесную цену, а дальше все не сходится(( заранее спасибоФункция спроса населения на данный товар имеет вид QD = 8 - Р, функция предложения данного товара QS = - 4 + 2Р. Предположим, что на данный товар введен налог в размере 20% от цены, которую платит покупатель. Рассчитать излишки потребителя до и после введения налога.

Answer 1

 Решение:
Равновесная цена до введения налога:
Qd=Qs
8-p=-4+2p
3p=12
p=4 - равновесная цена
Qd=8-4=4
Qs=-4+2*4
Qd=Qs=4
Q=4- равновесное количество  
После введения налога цена на товар составит:
8 – (1+1*20%p) = -4 + 2p
8-1,2р=-4+2р
3,2р=12
р=3,75 – новая равновесная цена  
Излишек потребителя до введения налога:  8 – Р;  Р=8
Sтреугольника = (8-4)/2*4 = 8 ед.
Излишек потребителя после введения налога: 8-1,2Р; 1,2Р=8; Р= 6,67 Sтреугольника = (6,67-3,75)/2*4 = 5,8 ед.

Answer 2

Problem Analysis

The problem requires calculating the consumer surplus before and after the introduction of a tax on a certain product. The demand function for the product is given as QD = 8 - P, and the supply function is given as QS = -4 + 2P. The tax is 20% of the price paid by the buyer.

Calculation of Consumer Surplus

To calculate the consumer surplus before and after the tax, we need to find the equilibrium price and quantity in the absence of the tax and then compare it with the price and quantity after the tax is introduced.

1. Equilibrium Price and Quantity without Tax: - Equilibrium occurs when the quantity demanded (QD) equals the quantity supplied (QS). - Set QD equal to QS and solve for P: ``` 8 - P = -4 + 2P 3P = 12 P = 4 ``` - Substitute the equilibrium price (P = 4) into the demand function to find the equilibrium quantity (Q): ``` QD = 8 - 4 QD = 4 ```

2. Consumer Surplus without Tax: - Consumer surplus is the difference between the maximum price a consumer is willing to pay and the actual price they pay. - To calculate the consumer surplus, we need to find the area under the demand curve up to the equilibrium quantity. - The demand function is QD = 8 - P. Substitute Q = 4 into the demand function to find the price at the equilibrium quantity: ``` 4 = 8 - P P = 4 ``` - Calculate the consumer surplus by finding the area of the triangle formed by the demand curve and the price line: ``` Consumer Surplus = (1/2) * (4 - 0) * (8 - 4) = 8 ```

3. Price and Quantity after Tax: - The tax is 20% of the price paid by the buyer. Therefore, the price paid by the buyer (Pb) is equal to the equilibrium price (P) plus the tax (T): ``` Pb = P + T ``` - The tax is 20% of the price, so T = 0.2P. - Substitute the equilibrium price (P = 4) into the tax equation to find the tax amount: ``` T = 0.2 * 4 T = 0.8 ``` - Calculate the price paid by the buyer after the tax: ``` Pb = 4 + 0.8 Pb = 4.8 ``` - Substitute the price paid by the buyer (Pb = 4.8) into the demand function to find the quantity demanded after the tax: ``` QD = 8 - 4.8 QD = 3.2 ```

4. Consumer Surplus after Tax: - To calculate the consumer surplus after the tax, we need to find the area under the demand curve up to the quantity demanded after the tax. - Calculate the consumer surplus by finding the area of the triangle formed by the demand curve and the price line after the tax: ``` Consumer Surplus = (1/2) * (4.8 - 0) * (8 - 3.2) = 9.6 ```

Conclusion

The consumer surplus before the introduction of the tax is 8, while the consumer surplus after the introduction of the tax is 9.6. The introduction of the tax has increased the consumer surplus by 1.6.

Please note that the calculations provided are based on the given demand and supply functions and assumptions.