the demand of a good is d=102 - 8.2p; the supply of it is s=8.1p - 31. the market price is 10.1. please find…

Question 12

Explanation:

Step1: Calculate quantity - demanded

Substitute $P = 10.1$ into the demand function $D=102 - 8.2P$. $D=102-8.2\times10.1=102 - 82.82 = 19.18$

Step2: Calculate quantity - supplied

Substitute $P = 10.1$ into the supply function $S = 8.1P-31$. $S=8.1\times10.1-31=81.81 - 31=50.81$

Step3: Calculate surplus

Surplus = $S - D$. Surplus = $50.81-19.18 = 31.63$

Answer:

$31.63$

Question 13

Explanation:

At equilibrium, $D = S$. So set $142-2.8P=2.4P - 20$.

Step1: Rearrange the equation

Add $2.8P$ to both sides and add $20$ to both sides of the equation $142-2.8P=2.4P - 20$. $142 + 20=2.4P+2.8P$

Step2: Combine like - terms

$162 = 5.2P$

Step3: Solve for $P$

$P=\frac{162}{5.2}=\frac{1620}{52}=\frac{810}{26}=\frac{405}{13}\approx31.15$

Answer:

$\frac{405}{13}\approx31.15$

Question 14

Explanation:

Step1: Calculate quantity - demanded

Substitute $P = 5.1$ into the demand function $D = 100-8.2P$. $D=100-8.2\times5.1=100 - 41.82=58.18$

Step2: Calculate quantity - supplied

Substitute $P = 5.1$ into the supply function $S = 8P-31$. $S=8\times5.1-31=40.8 - 31 = 9.8$

Step3: Calculate shortage

Shortage = $D - S$. Shortage = $58.18-9.8 = 48.38$

Answer:

$48.38$