Question

Demand & Supply Schedule Price 8, 5 Quantity Demanded 60, 85 Quantity Supplied 130, 100 Compute the Following: SHOW YOUR SOLUTIONS

1. Demand coefficient of price (b-value) 2. Level of demand independent of price (a-value) 3. Demand Function 4. Supply coefficient of price (d-value) 5. Level of supply independent of price (c-value) 6. Supply Function 7. Equilibrium Price 8. Equilibrium Quantity 

Answer 1

Demand Equation: Qd=a-bP

Here, a is the level of demand independent of price, and b is the demand coefficient of price.

Supply Equation: Qs=c+dP

Here, c is the level of supply independent of price and d is the supply coefficient of price

DEMAND

We will use the equation of a line:

$(y-y_1)=[\frac{(y_2-y_1)}{(x_2-x_1)}]\times (x-x_1)$

y is the dependent variable=Price

x is the independent variable=Qd

$(P-P_1)=[\frac{(P_2-P_1)}{(Qd_2-Qd_1)}]\times(Qd-Qd_1)$

Points:

$(Qd_1,P_1)=(60,8)\\ (Qd_2,P_2)=(85,5)$

Putting in the equation:

$(P-8)=[\frac{(5-8)}{(85-60)}]\times(Qd-60)\\ (P-8)=[-0.12]\times(Qd-60]\\ P=-0.12Qd+7.2+8\\ P=15.2-0.12Qd$

So,

(1)

a value=15.2

(2)

b value=-0.12

(3)

Demand Function: $P=15.2-0.12Qd$

(4)

SUPPLY

We will use the equation of a line:

$(y-y_1)=[\frac{(y_2-y_1)}{(x_2-x_1)}]\times (x-x_1)$

y is the dependent variable=Price

x is the independent variable=Qs

$(P-P_1)=[\frac{(P_2-P_1)}{(Qd_2-Qd_1)}]\times(Qd-Qd_1)$

Points:

$(Qs_1,P_1)=(130,8)\\ (Qs_2,P_2)=(100,5)$

Putting in the equation:

$(P-8)=[\frac{(5-8)}{(100-130)}]\times(Qs-130)\\ (P-8)=[0.1]\times(Qs-130)\\ P=0.1Qs-13+8\\ P=-5+0.1Qs$

So,

c value=-5

(5)

d value=0.1

(6)

Supply Function: $P=-5+0.1Qs$

(7)

For equilibrium price and quantity, we will equate Qd and Qs:

$Qs=10P+50\\ Qd=126.67-8.3P$

 

Qd=Qs

$126.67-8.33P=10P+50\\ -8.33P-10P=50-126.67\\ 18.33P=76.67\\ P=4.18\\ Q=91.8$

Equilibrium price=4.18 and equilibrium quantity=91.8