Question

Q1. The equilibrium conditions for two substitute goods are given below
5P, - 2P, = 15 and P, + 8P, = 16
Find the equilibrium prices of the two goods.​

Answer 1

Answer:

The equilibrium conditions for two substitute goods are given below: 5P1 – 2P2 = 15 and –P1 + 8P2 = 16 Find the equilibrium prices of the two goods.

Answer 2

Given:

The equilibrium conditions for two substitute goods are given below:

5P₁ - 2P₂ = 15

and

P₁ + 8P₂ = 16

To find:

The equilibrium prices of the two goods

Solutions:

From the given question, let's assume,

"P₁" → equilibrium price of the 1st good

"P₂" → equilibrium price of the 2nd good

We have,

5P₁ - 2P₂ = 15  ....... (i)

and

P₁ + 8P₂ = 16 ....... (ii)

Multiplying eq. (ii) by 5, we get

5P₁ + 40P₂ = 80 ..... (iii)

Subtracting equation (i) from (iii), we get

5P₁ + 40P₂ = 80

5P₁ - 2P₂ = 15

-      +         -

--------------------------

    42 P₂ = 65

--------------------------

∴ P₂ = 1.54

Substituting the value of P₂ = 1.54 in eq. (i), we get

5P₁ - 2(1.54) = 15

⇒ 5P₁ - 3.08 = 15

⇒ 5P₁ = 15 + 3.08

⇒  5P₁ = 18.08

⇒ P₁ = 3.61

Thus,

The equilibrium prices of the two goods are:

$\boxed{\bold{P_1 = 3.61}}\\\\\boxed{\bold{P_2 = 1.54}}$

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