Question

Если функция спроса на товар задана уравнением QD=20-3Р, тогда дуговая эластичность спроса по цене при ее снижении с 5 руб.лей до 4 руб.лей составляет …

Answer 1

Решение:
Подставляем первоначальное и последующее значение цены в формулу спроса и находим соответствующие значения объёма спроса:
Q1 = 20 – 3*5 = 5
Q2 = 20 – 3*4 = 8

Находим дуговую эластичность по следующим формулам:
∆Q = (Q2 - Q1 )/(Q2 + Q1 ) 
∆Q = (8-5)/(8+5) = 0,231
∆Р = (P2 – P1 )/(P2 + P1 ) 
∆Р = (4-5)/(4+5) = -0,111
Е=∆Q/∆P
Е= 0,231/-0,111 = -2,08  

Answer 2

Calculation of Arc Elasticity of Demand

To calculate the arc elasticity of demand, we need to determine the percentage change in quantity demanded and the percentage change in price. The formula for arc elasticity of demand is:

Arc Elasticity of Demand = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)

Given that the demand function is QD = 20 - 3P, we can calculate the initial quantity demanded and price by substituting the given values into the equation.

When the price is 5 rubles: QD1 = 20 - 3(5) = 20 - 15 = 5

When the price is 4 rubles: QD2 = 20 - 3(4) = 20 - 12 = 8

Now, we can calculate the percentage change in quantity demanded and the percentage change in price:

Percentage Change in Quantity Demanded = ((QD2 - QD1) / QD1) * 100

Percentage Change in Price = ((P2 - P1) / P1) * 100

Substituting the values:

Percentage Change in Quantity Demanded = ((8 - 5) / 5) * 100 = 60%

Percentage Change in Price = ((4 - 5) / 5) * 100 = -20%

Now, we can calculate the arc elasticity of demand:

Arc Elasticity of Demand = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)

Arc Elasticity of Demand = 60% / -20% = -3

Therefore, the arc elasticity of demand when the price decreases from 5 rubles to 4 rubles is -3.