A profit maximising monopolist produces a durable good. There are no production costs (so MC=0). There are

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A profit maximising monopolist produces a durable good. There are no production costs (so MC=0). There are two periods. The interest rate is zero (so no need for discounting). Resale is allowed (so price discrimination is not possible). Total demand for use of the good is the same in each period and equals
Qi=32 - Ri
where Qi is the quantity demanded in period i and Ri is the rental rate in period i.

(a) Suppose the monopolist rents the durable good to the consumers.

(i) What rental price per period maximises profit?

(ii) What quantity will the monopolist rent each period?

(iii) What will be the monopolist's total profit (period 1 profit + period 2 profit)?

(b) Suppose the monopolist sells the durable good to the consumers. That is, goods sold in period 1 are used in both periods, goods sold in period 2 are only used in period 2. Hence, the period 1 price is R1 + R2and the period 2 price is R2. R1 and R2 are determined by the quantity available in the relevant period.

(i) What quanity will the monopolist produce in period 1?

(ii) What price will the monopolist charge in period 1?

(iii) What quanity will the monopolist produce in period 2?

(iv) What price will the monopolist charge in period 2?

(v) What will be the monopolist's total profit (period 1 profit + period 2 profit)?