Question

функция спроса имеет вид qd = 30-4P определите при какой цене эластичность спроса составит - 2

Answer 1

Решение:

Ер = Qd*Р/Qd

Ер = (30-4Р) * Р/30-4Р

-2 = 4Р/30-4Р

4Р = -2*(30-4Р)

4Р = -60 +8Р

4Р=60

Р=15

Answer 2

Understanding the Demand Function

The given demand function is Qd = 30 - 4P, where Qd represents the quantity demanded and P represents the price of the product. To determine the price at which the elasticity of demand will be -2, we need to calculate the price elasticity of demand at that specific price.

Calculating Price Elasticity of Demand

Price elasticity of demand (Ed) is calculated using the formula:

Ed = (% Change in Quantity Demanded) / (% Change in Price)

To find the price at which the elasticity of demand will be -2, we need to calculate the percentage change in quantity demanded and the percentage change in price.

Let's assume the initial price is P1 and the initial quantity demanded is Qd1. We can then calculate the percentage change in quantity demanded as:

% Change in Quantity Demanded = ((Qd2 - Qd1) / Qd1) * 100

Since we want the elasticity of demand to be -2, we can set the percentage change in quantity demanded equal to -2:

-2 = ((Qd2 - Qd1) / Qd1) * 100

Simplifying the equation, we get:

Qd2 - Qd1 = -2 * (Qd1 / 100)

Now, let's calculate the percentage change in price. Since we want the elasticity of demand to be -2, we can set the percentage change in price equal to 1:

1 = ((P2 - P1) / P1) * 100

Simplifying the equation, we get:

P2 - P1 = (P1 / 100)

Now we have two equations:

1. Qd2 - Qd1 = -2 * (Qd1 / 100) 2. P2 - P1 = (P1 / 100)

We can solve these equations simultaneously to find the price at which the elasticity of demand will be -2.

Solving the Equations

Let's solve the equations using the given demand function Qd = 30 - 4P.

Substituting the demand function into the equations, we get:

1. (30 - 4P2) - (30 - 4P1) = -2 * ((30 - 4P1) / 100) 2. P2 - P1 = (P1 / 100)

Simplifying the equations, we get:

1. 4P2 - 4P1 = -0.02(30 - 4P1) 2. P2 - P1 = (P1 / 100)

Solving these equations will give us the price at which the elasticity of demand will be -2.

Please note that due to the complexity of the calculations involved, it would be best to use a numerical method or a graphing calculator to find the exact price at which the elasticity of demand will be -2.