Suppose a monopolist charges the same price for each unit produced. The production technology of this monopolist produces a cost function given by TC = (2*Q) . The industry Demand curve is given by P= 140 -(2*Q) 

a) Find the equilibrium price, quantity, profit, consumer surplus for the uniform price monopoly, who cannot price discriminate. You need to find out marginal revenue and marginal cost.

b)  If this monopoly would become competitive, find the equilibrium price, quantity, profit, consumer surplus for that competitive firm. 

c) If this monopolist is allowed to do first degree price discrimination, then find the equilibrium quantity, profit, and consumer surplus for that first degree price discriminating monopolist

d) Compare the total social surplus for part a, b and c of this question. Who creates the largest social surplus, why? Who creates the largest deadweight loss , why?

e) Draw a Graph showing the equilibrium quantity choices of uniform price monopoly, competitive firm and first degree price discriminating monopoly on a single graph.

a) The equilibrium price is 71, quantity is 34.5, profit is 2380.5, and consumer surplus (CS) is 1190.25 for a monopolist who cannot price discriminate.

b) The equilibrium price is 2, quantity is 69, profit is 0, and CS is 4761 for a perfectly competitive firm.

c) In the case of the first-degree price discrimination, the equilibrium price is variable, quantity is 69, profit is 4761, and CS is zero.

d) The largest social surplus is created in case of perfect competition and first-degree price discrimination. The largest deadweight loss (DWL) is created by a uniform pricing monopolist.

e) The graph showing the equilibrium quantity in three cases is given in the explanation below. 

The total cost (TC) and the demand function for a monopolist are given as,

TC = 2Q

P = 140 - 2Q

Here P is the price and Q is the quantity.

a) The equilibrium condition for a uniform price monopoly (no price discrimination) is given as,

Marginal Revenue (MR) = Marginal Cost (MC)

Total Revenue (TR) = P*Q = (140 - 2Q)Q = 140Q - 2Q²

MR = dTR/dQ = 140 - 4Q

MC = dTC/dQ = 2

MR = MC

140 - 4Q = 2

Q_m* = 34.5

P = 140 - 2Q = 140 - 2(34.5)

P_m* = 71

Profit (π) = TR - TC = P*Q - 2Q = 71 * 34.5 - 2*34.5

π = 2380.5

The consumer surplus (CS) is given as,

CS = 0.5 x Q_m* x (P^max - P_m*)

P^max is the maximum price a consumer can pay that is equal to 140 when Q = 0.

CS = 0.5 * 34.5 * (140 - 71)

CS = 1190.25

Social Surplus (SS) = CS + π = 3570.75

Therefore, the equilibrium price is 71, quantity is 34.5, profit is 2380.5, and CS is 1190.25 for a monopolist who cannot price discriminate.

b) In case of perfect competition,

P = MC

140 - 2Q = 2

Q_pc* = 69

P = 140 - 2Q

P_pc* = 2

π = P*Q - 2Q

π = 0

CS = 0.5 x Q_pc* x (P^max - P_pc*)

CS = 4761

SS = 4761 + 0 = 4761

Therefore, the equilibrium price is 2, quantity is 69, profit is 0, and CS is 4761 for a competitive firm.

c) Under first-degree price discrimination or perfect price discrimination, a monopolist charge consumers their willingness to pay (or reservation price) at each quantity of goods sold. Thus, a different price will be charged to the same consumer for different units of goods sold. As the quantity increases, the price will decrease.

The quantity of output sold in this case will be the same as under perfect competition. This implies Q = 69. There is no fixed price; the price varies (decreases) as the value of Q increases. Since the producer knows each consumer's reservation price, the entire CS will be turned into the producer's profits.

CS = 0

π = 0.5 x Q_pc* x (P^max - P_min*)

The minimum price (P_min) that a producer will charge at Q = 69 is 2.

π = 0.5 * 69 * (140 - 2)

π = 4761

SS = 0 + 4761

Therefore, in the case of first-degree price discrimination, the equilibrium price is variable, quantity is 69, profit is 4761, and consumer surplus is zero.

d) The total SS in part a is 3570.75 and in part b and c, it is 4761. Thus, the largest SS is created in case of perfect competition and first-degree price discrimination. The SS is the same in both cases except that in perfect competition the entire SS corresponds to consumers while in the other case it entirely belongs to producers. The largest deadweight loss (DWL) is created by a uniform pricing monopolist as it produces less than socially efficient output and charges a higher price.

e) The graph below shows the equilibrium prices and quantity in three cases given above. The monopoly price (uniform pricing) is P_m and quantity is Q_m. The output under perfect competition and first-degree price discrimination are Q_pc. The price under perfect competition is P_pc however; the price is not fixed under the price discrimination case. 

please see the attached file for the complete solution.