Please answer with readable text explain your answers 1 25

Please answer with readable text & explain your answers.

1) (25 points) Suppose monopoly input manufacturer sell a good to 3 retailers The retailers face the following demand Q- 100 - P and has no cost except the cost of buying the inputs from the manufacturer. The manufacturer has a constant marginal cost equal to 5 but no other costs. After the manufacturer sets a unit price for the input, 3 retailers compete in quantities. a) Calculate the equilibrium output, price and profit levels of the manufactureir and each retailer. b) Calculate the deadweight loss. Now suppose the manufacturer vertically merge with one of the retailers and the merged firm\'s cost level becomes 0. Cal culate the deadweight loss that would arise in this case and discuss the change in deadweight loss brought by the merger.

Solution

1.a) All the 3 retailers face an identical demand function:Q=100-P or Q-100=-P->100-Q=P

The Marginal Cost(MC) of the monopoly is 5.

The Total Revenue(TR) of the monopoly:P*Q=(100-Q)Q=100Q-Q^2

The Marginal Revenue(MR) of the monopoly:dTR/dQ=100-2Q

Now,based on the profit maximizing condition of the monopoly,we can state:-

MR=MC

100-2Q=5

-2Q=-100+5

-2Q=-95

Q=-95/-2

Q=47.5

Hence,the equilibirum output or profit maximizing output produced by the monopoly manufacturer is 47.5

Now,plugging the equilibrium Qobtained from above equation into the demand equation,we get:-

Q=100-P

47.5=100-P

47.5-100=-P

-52.5=-P

52.5=P

Therefore,the equilibrium price charged by the monopoly manufacturer is 52.5

Now,TR of the manufacturer=P*Q=52.5*47.5=2493.75

Total Cost(TC) incurred by the manufacturer=5*47.5=237.5

Hence,Total Profit earned by the monopoly manufacturer=TR-TC=2493.75-237.5=2256.25

Now,the 3 retailers compete for the quantities and assuming perfect competition among the retailers the total equilibrium quantity Q is divided equally among the retailers.

Hence,each retailer receive=Q/3=47.5/3=15.83 approximately

Equilibrium price per unit P paid by the retailers is 52.5.Thus,the total cost incurred by each retailer=(15.83*52.5)=831 approximately

Notice that the Marginal Cost of purchasing each unit of input is 52.5 and since the retail market is competitive as mentioned in the question each retailer would charge a selling price equal to the marginal cost 52.5

Thus,the profit levels of each retailer would be maximized and in the long run the retailers would earn zero economic profit and market is cleared assuming a competitive structure.

b) Now,if the manufacturer was a competitive firm,it\'s profit maximizing condition would be:-

P=MC

100-Q=5

-Q=-100+5

-Q=-95

Q=95

Thus,if the manufacturer was a competitive firm it would produce an equilibrium quantity of 95.

The difference in equilibirum quantities if the manfucturer is a competitive firm and a monopoly=(95-47.5)=47.5

Now,plugging the equilibrium quantity obtained in above equation into the demand equation,we get:-

Q=100-P

95=100-P

95-100=-P

-5=-P

5=P

Therefore,the equilibrium price charged by the manufacturer if it had been a competitive firm was 5.

The difference between price level if the manufacturer is a monopoly and a competitive firm=(52.5-5)=47.5

Hence,Deadweight loss in this case=0.5*47.5*47.5=1128.125

Now,if one of the retailers and the manufacturer merge,the MC becomes 0.

Recall that the demand equation is:Q=100-P or 100-Q=P

MR=100-2Q

Again,based on the profit maximizng condition of the monopoly,we get:-

MR=MC

100-2Q=0

-2Q=-100

Q=-100/-2

Q=50

Thus,under merger the equilibrium quantity is 50

Now,plugging the equilibrium Q obtained above into the demand equation,we derive:-

Q=100-P

50=100-P

50-100=-P

-50=-P

50=P

The equilibrium price under merger is 50.

The difference between equalibirum quantities if the manufacturer was a competitive firm and merger=(95-50)=45

The difference in equilibrium prices if the manufacturer was a competitive firm and merger situation=(50-5)=45

Hence,deadweight loss in this instance would be=0.5*45*45=1012.5

Observe that under merger the equilibrium quantity is slightly higher than in monopoly or single manufacturer.The equilibrium price is also little less under merger than under absolute monopoly thereby providing some benefits to the consumers/retailers in this case with relatively higher consumer surplus under merger.Therefore,the economic efficiency is higher under merger and deadweight loss to the society is low as the consumer surplus essentially increases under merger due to higher equilibrium quantity offered at lower equilibrium price level.