Question

The market demand curve for soy beans is estimated to be Qd = 80 – 4P and the market supply curve is given by Qs = 4P. Show your work so I know what equations you are using.

a. Assume that this industry is perfectly competitive. What is the EQM P and EQM Q of soybeans?

b. Calculate the consumer and producer surplus (CS and PS) at the perfect competitive equilibrium.

Now assume that this industry is monopolized. Show your work so I know what equations you are using. [Round all your answers to the hundredth]

c. Find the Marginal Revenue of the firm (Hint: it has the same intercept as the demand curve but is twice as steep).

d. Find Monopoly quantity (Qm) and price (Pm).

e. Determine the Dead Weight Loss from monopolization

f. Interpret the DWL with respect to the competitive equilibrium. What does it mean (intuitively)?

Answer 1

Qd = 80 - 4P

Qs = 4P

a) At equilibrium, Qd = Qs

80 - 4P = 4P

P = 10

At this P, Q = 40

b) In perfectly competitive equilibrium (P):

Consumer surplus is area of portion A + B + C + D + E whose sum is (1/2) * (20 - 10) * (40 - 0) = 200

Producer surplus is area of portion F + G + H + I whose sum is (1/2) * (10 - 0) * (40 - 0) = 200

If the market is monopoly:

c) TR = P * Qd = 80P - 4P^²

MR = 80 - 8P

d) Monopoly produce at point (M) when S = MR

4P = 80 - 8P

P = 13.33

Q = 26.67

e) Deadweight loss is area of portion E + H whose sum is (1/2) * (13.33 - 6.67) * (40 - 26.67) = 44.44

f) There occurs deadweight loss in case of monopoly while it does not exist in perfectly competitive market because monopoly market operates at less efficient level. Monopolist tends to charge high price than perfectly competitive which reduce net welfare.