Question

Q(d) = 50 – 15P; Q(s) = -20 + 20P. Коэффициент прямой эластичности спроса на интервале цен от 1 тыс. руб. за ед. до 1,5 тыс. руб. за ед. составитя хотела бы увидеть само решение

Answer 1

Решение:
Определяем объем спроса при цене 1 тыс. руб.:
Qd1 = 50-15*1=35
Определяем объем спроса при цене 1,5 тыс. руб.:  
Qd2 = 50-15*1,5=27,5
Коэффициент прямой эластичности спроса определяется по формуле:  

((27,5-35) / (1/2 *62,5)) / ((1,5-1) / 1/2*2,5 = -0,24/0,4 = -0,6
Товар является неэластичным.  

Answer 2

Calculation of Price Elasticity of Demand

To calculate the price elasticity of demand, we need to determine the formula for demand and supply and then calculate the derivative of the demand function with respect to price.

Given the demand function: Q(d) = 50 - 15P and the supply function: Q(s) = -20 + 20P, we can calculate the price elasticity of demand on the interval from 1,000 rubles per unit to 1,500 rubles per unit.

The price elasticity of demand is calculated using the formula:

E = (% change in quantity demanded) / (% change in price)

To calculate the percentage change in quantity demanded, we use the formula:

% change in quantity demanded = (Q2 - Q1) / Q1 * 100

To calculate the percentage change in price, we use the formula:

% change in price = (P2 - P1) / P1 * 100

Let's calculate the price elasticity of demand step by step.

1. Calculate the initial quantity demanded (Q1) and initial price (P1): - Q1 = Q(d) at P = 1,000 rubles per unit - P1 = 1,000 rubles per unit

Substituting the values into the demand function: Q1 = 50 - 15 * 1,000 Q1 = 50 - 15,000 Q1 = -14,950

2. Calculate the final quantity demanded (Q2) and final price (P2): - Q2 = Q(d) at P = 1,500 rubles per unit - P2 = 1,500 rubles per unit

Substituting the values into the demand function: Q2 = 50 - 15 * 1,500 Q2 = 50 - 22,500 Q2 = -22,450

3. Calculate the percentage change in quantity demanded: % change in quantity demanded = (Q2 - Q1) / Q1 * 100 % change in quantity demanded = (-22,450 - (-14,950)) / (-14,950) * 100 % change in quantity demanded = -7,500 / (-14,950) * 100 % change in quantity demanded ≈ 50.08%

4. Calculate the percentage change in price: % change in price = (P2 - P1) / P1 * 100 % change in price = (1,500 - 1,000) / 1,000 * 100 % change in price = 500 / 1,000 * 100 % change in price = 50%

5. Calculate the price elasticity of demand: E = (% change in quantity demanded) / (% change in price) E = 50.08% / 50% E ≈ 1.0016

Therefore, the coefficient of price elasticity of demand on the interval from 1,000 rubles per unit to 1,500 rubles per unit is approximately 1.0016.

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