suppose that there are two periods and in the following question Alcoa is a mono

Question

suppose that there are two periods and in the following question Alcoa is a monopolist maker of new aluminum with marginal costs of making aluminum of zero.

Part one

Suppose that it not posible to recycle/resell aluminim (e.g. it isn't durable). Demand in period 1 is Q1=100-Psub1 and demand in period 2 is Q2=120-Psub2. Show that Alcoa will set a price of 50 in period 1. What price does it set in period 2? What are Alcoa's total profits? (Hint: this is just a simple static monopoly in each period)

Part two

Now suppose that someone who buys in period 1 can resell their aluminum at zero cost in period 2 (to make it easier think about, just assume that people demand aluminum in period 1 or period 2, but not both ) the demand to use aluminum in each period is the same as above.

Explanation / Answer

PART - ONE

Marginal cost, MC = 0

Demand, Period 1: Q1 = 100 - P1

Or, P1 = 100 - Q1

Total revenue, TR = P1 x Q1 = 100Q1 - Q12

Marginal revenue, MR1 = dTR1 / dQ1 = 100 - 2Q1

The monopolist will equate MR with MC to maximize profits:

100 - 2Q1 = 0

2Q1 = 100

So, Q1 = 50

P1 = 100 - Q1 = 100 - 50 = 50 [Proved]

In period 2, demand Q2 = 120 - P2

P2 = 120 - Q2

TR2 = P2 x Q2 = 120Q2 - Q22

MR2 = dTR2 / dQ2 = 120 - 2Q2

Equating MR with MC:

120 - 2Q2 = 0

2Q2 = 120, So Q2 = 60

P2 = 120 - Q2 = 60

PART - TWO

Only an assumption is stated. What is the question?

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