Question

44. Refer to the following figure. Price ($) 1 Supply Demand Q=40-24P Q=10+4P 0 10 20 30 40 Quantity (units) 1) Based on this figure, write the equation for the demand function. (Spts) 2) Based on this figure, write the equation for the supply function. (5pts) 3) According to this figure, the equilibrium price is $12, and the equilibrium quantity is 20. Verify quantitatively by solving the demand function and supply function simultaneously. Do not plug these values back in the supply or demand functions. Show your math. (5pts)

Answer 1

Answer 44

(1)

We can see from above that demand curve is a straight line

Equation of a straight line is given by :

(Y - Y₀) = [(Y₁ - Y₀)/(X₁ - X₀)]((X - X₀))

where X = Variable you put on horizontal axis i.e. Quantity Demanded (Q_d), Y = Variable you put on vertical axis i.e. Price(P)

(X₀ , Y₀) and (X₁ , Y₁) are two coordinated on the line and here these coordinates are :

(Q₀ , P₀) = (40 , 0)and (Q₁ , P₁) = (0 , 24)

Hence demand is given by :

P - 0 = [(24 - 0)/(0 - 40)](Q_d - 40)

=> -5P = 3Q_d - 120

=> Q_d = 40 - (5/3)P ---------------------------Demand function

(2)

We can see from above that demand curve is a straight line

Equation of a straight line is given by :

(Y - Y₀) = [(Y₁ - Y₀)/(X₁ - X₀)]((X - X₀))

where X = Variable you put on horizontal axis i.e. Quantity Supplied (Q_s), Y = Variable you put on vertical axis i.e. Price(P)

(X₀ , Y₀) and (X₁ , Y₁) are two coordinated on the line and here these coordinates are :

(Q₀ , P₀) = (0 , 4)and (Q₁ , P₁) = (20 , 12)

Hence Supply is given by :

P - 4 = [(12 - 4)/(20 - 0)](Q_s - 0)

=> 5(P - 4) = 2Q_s

=> Q_s = 2.5P - 10 ---------------------------Supply function

(3)

Equilibrium Occurs when quantity supplied = quantity demand

Thus at equilibrium we have Q_s = Q_d => 2.5P - 10 = 40 - (5/3)P

=> 7.5P - 30 = 120 - 5P

=> 12.5P = 150

=> P = 12

Hence Equilibrium Price = 12

Thus Equilibrium Quantity Q = Q_s = Q_d = 40 - (5/3)*12(or 2.5*12 - 10) = 20

Hence Equilibrium Quantity = 20