Answer
Deadweight loss = 50 dollars
Surplus = 10
Work Step by Step
Forming the demand curve equation,
Gradient of demand curve: $\frac{85-45}{0-20}$ = -2
Equation of curve: P- 45 = -2 (Q-20)
P- 45 = -2Q + 40
P = -2Q + 85
At quantity = 15,
P = -2(15) + 85
P = 55 (thus d= 55 dollars)
Forming the supply curve equation,
Gradient of demand curve: $\frac{5-45}{0-20}$ = 2
Equation of curve: P- 45 = 2 (Q-20)
P - 45 = 2Q - 40
P = 2Q + 5
At quantity = 15,
P = 2(15) + 5
P = 35 (thus e= 35 dollars)
Thus the dead weight loss area is = 0.5 $\times$ 5 $\times$ (55 -35)
= 50
At price = 55, the quantity supplied would be
55 = 2Q + 5
2Q = 50
Q = 25
Therefore since surplus is the difference between the quantity supplied, and the quantity demanded,
Surplus = 25 - 15
= 10
