Question

Suppose that a monopoly firm finds that its MR is $54 for the first unit sold each day, $53 for the second unit sold each day, $52 for the third unit sold each day, and so on. Further suppose that the first worker hired produces 5 units per day, the second 4 units per day, the third 3 units per day, and so on. Instructions: Enter your answers as whole numbers. a. What is the firm’s MRP for each of the first five workers? b. Suppose that the monopolist is subjected to rate regulation and the regulator stipulates that it must charge exactly $44 per unit for all units sold. At that price, what is the firm’s MRP for each of the first five workers? c. If the daily wage paid to workers is $186 per day, how many workers will the unregulated monopoly demand? worker(s). If the daily wage paid to workers is $186 per day, how many workers will the regulated monopoly demand? worker(s). Looking at those figures, will the regulated or the unregulated monopoly demand more workers at that wage? . d. If the daily wage paid to workers falls to $85 per day, how many workers will the unregulated monopoly demand? worker(s). If the daily wage paid to workers falls to $85 per day, how many workers will the regulated monopoly demand? worker(s). Looking at those figures, will the regulated or the unregulated monopoly demand more workers at that wage? . e. Comparing your answers to parts c and d, does regulating a monopoly’s output price always increase its demand for resources?

Answer 1

(a).

MRP = (Change in revenue)/(Change in Labour)
For first worker = 54 + 53 + 52 + 51 + 50 = 260/1 = $260 (Since he produces 5 units)
Second Worker = 49 + 48 + 47 + 46 = 174/1 = $190 (Since he produces 4)
Similarly,
Third worker = 45 + 44 + 43 = $132
Fourth worker = 42 + 41 = $83
Fifth worker = $40

(b).

Now all units are charged at $44
First worker = 5*44 = $220
Second = 4*44 = $176
third = 3*44 = $132

fourth = 2*44 = $88

fifth = 1*44 = $44

(c).

Unregulated:
For wage $186 they will hire 2 workers since for second worker MRP = $190 and goes below $186 for the third worker (optimum is 2 because every worker added now would incurr loss instead of profit)
Regulated:
If the wage is $186 it will demand workers until the MRP decreases below $186...
and that happens for worker 2 here (since he can produce only $176 for $186 wage, he should not be hired) hence only one worker will be hired here.

(d).

Unregulated:
3 workers should be hired since for fourth worker MRP = 83 (<85)
3 workers is optimum here...
Regulated:
If the wage falls to $85 the demand of workers will increase....
again for worker 4 MRP is $88 which is above $85 and for worker 5 goes below $85
Hence 4 workers will be hired for maximum profit.

(e).

as we saw regulating a monopoly's output price will always increase its demand...
the (c) and (d) part show it correctly.