Question 3. Assume that a monopolist is selling its products in 4 of the states

Question

Question 3. Assume that a monopolist is selling its products in 4 of the states of Australia: NSW QLD, VIC, SA. Each state can consume up to 100 units of goods and the reservation price (maximum willingness to pay) of each good in each state is provided in the third column of the table below. Note that the reservation price for each good is the same within each state. The details of the monopolist's production technology are given in the table below. Unless otherwise is stated, assume that monopolist cannot charge different prices in different states (a) Fill cols 4 and 6

Explanation / Answer

a) using formula

revenue = p * Q

MR = Revenuen - Revenue(n-1) and

Marginal Revenue ($/per output) = MR / Q

Market Demand ($/per output) (P)

Revenue ($)  (R = P*Q)

b) Profit maximizing quantity and price for the monopolist is determined at the point MR = MC and MR = MC = 1 at the units per day 200 that means profit maximizing quantity is 200 and profit maximizing price = 3 corresponding to the level of output 200.

c) When MC = $0 for all the quantity level, then profit maximizing price and quantity will be at MR = MC = 0 when the quantity is 300 and price is $2.

so profit maximizing price and quantity is $2 and 300units respectively.

Monopolist is not selling the efficient level of output because even at this level of output (300 units) price is greater than MC (2> 0) and efficient level of output is where P = MC, so the monopolist does not produce nor sell efficient level of output.

d) When monopolist charge different prices from different consumers ( and he knows the reservation price of each consumer) so he will charge the reservation price from each consumer and MC = $1.

The profit maximizing price and quantity determined from the point where MR = MC,but in this case the MR of the monopoly (when he charges reservation price from each consumer) is same as demand of the consumer that is given in the table in column 3 (P)

So now column 3 (P) become MR and column 5 become MC

MR = MC quantity is 400 and price is $1.

so profit maximizing price is $1 and proft maximizing quantity is 400 when monopoly charge reservation prices from each consumer.

e) Yes, when monopoly charges reservation price from each consumer he produce efficient level of output because in this case P = MR and MR = MC is monopoly profit maximizing condition.

it means that P = MR = MC implies that P = MC so the efficient level of output is produced.

1 2 3 4 5 6 Workers per day (w) Units per day (Q)

Market Demand ($/per output) (P)

Revenue ($)  (R = P*Q)

Marginal Cost ($/per output) (MC) Marginal Revenue ($/per output) (MR) 0 0 - 0 _ _ 1 100 4 (NSW) 4 * 100 = $400 1 (400 - 0)/Q = 400/100 = 4 2 200 3 (QLD) 3 * 200 = $600 1 (600 - 400)/Q = 200/200 = 1 3 300 2 (VLC) 2*300 = $600 1 (600 - 600)/Q = 0/300 = 0 4 400 1 (SA) 1*400 = $400 1 (400 - 600)/Q = -200/400 = -0.5

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