Question

5P1 – 2P2 = 15 and –P1 + 8P2 = 16 Find the equilibrium prices of the two goods.

Answer 1

Step-by-step explanation:

Given that:

The equilibrium conditions for two substitute goods are given below:

5P1- 2P2 = 15 and -P1 + 8P2 = 16

To find :

Find the equilibrium prices of the two goods.

Solution:

To find the equilibrium prices of the two goods,

solve the two equations

$5P_1- 2P_2 = 15 \: \: \: ...eq1 \\ \\ -P_1 + 8P_2 = 16 \: \: \: ...eq2$

Equate the coefficient of P1 by multiplying eq2 by 5

$5P_1- 2P_2 = 15 \\ -5P_1 + 40P_2 = 80 \\ - - - - - - - - - - \\ 38P_2 = 95 \\ \\ P_2 = \frac{95}{38} \\ \\\bold{\red{P_2= \frac{5}{2}}}$

Put the value of P2 in eq1

$5P_1 - 2 \times \frac{5}{2} = 15 \\ \\ 5P_1 = 15+5 \\ \\ 5P_1 = 20 \\ \\ \bold{\blue{P_1 = 4}}$

Thus,

Equilibrium prices of two goods are

P1=4

P2=5/2

Hope it helps you.