Question 16 Given the demand and supply system Pb 13010 Qb

Question #16: Given the demand and supply system: Pb = 130-10 Qb & Pv =4.5 + 8.1 Qv How much DWL is created by producing 59 units of output? Hints Answer HINT: 13953.41

Solution

The equilibrium level (demand = supply) should be calculated first; and then the difference from equilibrium is the DWL.

Equilibrium:

Demand = Supply

Pb = Pv

130 – 10Q = 4.5 + 8.1Q

18.1Q = 125.50

Q = 125.50 / 18.1 = 6.93 = Equilibrium quantity

Putting this value in either demand or supply equation, the equilibrium price should be found.

P = 130 – 10Q

= 130 – 10 × (125.5 / 18.1)

   = 130 – 69.34

   = 60.66

Now if quantity is 59 units, the price would be on supply function.

P = 4.5 + 8.1Q

   = 4.5 + 8.1 × 59

   = 4.5 + 477.90

   = 482.40

DWL = 0.5 × Change in quantity × Change in price

          = 0.5 × (59 – 6.93) × (482.40 – 60.66)

          = 0.5 × 52.07 × 421.74

          = 10,980.00 (Answer)