# Question e0deb

Mar 24, 2017

$Q = \frac{8}{7} \approx 1.143$ to 3 decimal places

P_0= 15 5/7 =110/7 ~~ 15.714 to 3 decimal places

#### Explanation:

Equilibrium is achieved at the point where ${P}_{d} = {P}_{s}$ so we have:

$50 - 30 Q = {P}_{d} = {P}_{s} = 14 + 1.5 Q$

$50 - 30 Q = 14 + 1.5 Q$

$50 - 14 = 30 Q + 1.5 Q$

$31.5 Q = 36$

$Q = \frac{36}{31.5} = \frac{72}{63} = \frac{8}{7} \approx 1.14285 \ldots$

Substituting for Q

${P}_{d} = 50 - 30 Q \to {P}_{d} = 50 - 30 \left(\frac{8}{7}\right) = 15 \frac{5}{7} = \frac{110}{7}$

${P}_{s} = 14 + 1.5 Q \to P - s = 14 + 1.5 \left(\frac{8}{7}\right) = 15 \frac{5}{7} = \frac{110}{7}$