Question

A marketing order for oranges has a fixed total supply of Q = 1,000 crates a month. Demand in the market for fresh oranges is Q1 = 220 − 0.2p and that in the market for processed orange products is Q2 = 1,000 − 2p. Calculate the competitive market-clearing price. What is the deadweight loss in both markets if the price of a crate of fresh oranges is raised to $200?

Answer 1

Demand for fresh oranges is Q₁ = 220 - 0.2P and Demand for processed oranges is Q₂ = 1000 - 2P .

Then, Q₁+Q₂ = 220 - 0.2P + 1000 - 2P

or, Q = 1220 - 2.2P is the aggregate demand curve

or, 1000 = 1220 - 2.2P

or, 2.2P = 220

or, P = 220/2.2 = $100

For the aggregate demand curve ,

When P= 0, Q = 1220

and When Q=0 , P=555(approx)

When price rises to $200,

Q = 1220- 2.2*200 = 780

Plotting all the point on demand and supply graph ,

As price increases to $200 and Q decreases to 780, here area a and b represents the dead weight loss .

Hence , dead weight loss = area a + area b = 1/2* base * height + length * breadth

= 1/2 * (1000-780) * (200-100) + (1000-780)*100

= 1/2*220*100 + 220*100

= 3/2*220*100

  = 33000