A2 Economics 9708: Monopsony, a Trade Union and a Minimum Wage

Solent Ferry Co. is the only significant employer of deckhands in a small coastal town, making it a monopsony employer of this type of labour. To attract more deckhands, it must raise the wage rate paid to all its deckhands, not just the newest recruit. The table below shows the wage rate it must pay to attract each level of employment, together with the marginal revenue product (MRP) of labour, both in dollars per hour.

Deckhands employed	Wage rate paid ($/hour)	Marginal revenue product, MRP ($/hour)
1	15	70
2	18	50
3	21	32
4	24	31
5	27	30

(a) Calculate the total cost of labour and the marginal cost of labour (MCL) for the 3rd and the 4th deckhand. [3]

(b) Determine the number of deckhands Solent Ferry Co. will employ to maximise profit as an unconstrained monopsonist, and the wage rate it will pay them, explaining your reasoning. [3]

(c) The dockworkers' union then negotiates a legally binding minimum wage of $24 per hour for all deckhands. Explain why the marginal cost of hiring the 2nd, 3rd and 4th deckhand becomes exactly $24 once this minimum wage applies, and hence determine the number of deckhands Solent Ferry Co. will now employ. [3]

(d) State the wage rate and level of employment once the $24 minimum wage applies, and explain why this outcome shows that a minimum wage imposed on a monopsony employer, unlike one imposed on a competitive employer, can raise both the wage and the level of employment together. [3]

Part (a): Total cost of labour and marginal cost of labour at 3 and 4 deckhands

Total cost of labour (TCL) is the wage rate multiplied by the number of deckhands employed, since Solent Ferry Co. must pay the same wage to every deckhand it hires:

$TCL(3) = 21\times3 = 63$ $TCL(4) = 24\times4 = 96$

To find the marginal cost of labour (MCL), the extra total cost of hiring one more deckhand, we also need $TCL(2) = 18\times2 = 36$ . Then:

$MCL(3) = TCL(3)-TCL(2) = 63-36 = 27$ $MCL(4) = TCL(4)-TCL(3) = 96-63 = 33$

Note that MCL exceeds the wage rate paid in both cases ($27 $>$ $21, and $33 $>$ $24): hiring one more deckhand costs more than that deckhand’s own wage, because the higher wage must also be paid to every deckhand already employed.

Part (b): Profit-maximising employment and wage as an unconstrained monopsonist

Extending the same method to every row gives the full marginal cost of labour schedule:

Deckhands	Wage rate	Total cost of labour	MCL	MRP
1	15	15	15	70
2	18	36	21	50
3	21	63	27	32
4	24	96	33	31
5	27	135	39	30

A profit-maximising monopsonist hires an extra worker whenever that worker’s MRP is at least as large as the MCL of hiring them:

Deckhands 1 to 3: MRP (70, 50, 32) is greater than MCL (15, 21, 27) at every step, so each is worth hiring.
Deckhand 4: MRP of 31 is less than MCL of 33, so hiring a 4th deckhand would reduce profit.

Profit is therefore maximised at 3 deckhands. Solent Ferry Co. does not need to pay the $27 MCL to attract exactly 3 deckhands, however. From the wage-rate column, only $21 per hour is needed to attract 3 deckhands, and that is the wage it actually pays.

Part (c): Effect of the union’s $24 minimum wage

Once the law requires Solent Ferry Co. to pay at least $24 per hour to every deckhand it employs, the firm must pay this $24 floor even to deckhands who, under the original schedule, would have accepted less. Since the original wage-rate column shows that deckhands 1 to 4 were already willing to work for $15, $18, $21 and $24 respectively, all at or below the $24 floor, the firm can attract all of the first four deckhands simply by paying the flat $24 wage, without needing to bid the wage up further as it hires the 2nd, 3rd and 4th. This means the marginal cost of hiring each of the 2nd, 3rd and 4th deckhand becomes exactly $24, rather than the $21, $27 and $33 implied by the original rising schedule.

Comparing this flat MCL of $24 with MRP: the 4th deckhand’s MRP of $31 still exceeds $24, so this deckhand is worth hiring. A 5th deckhand would require paying above the $24 floor, since the original schedule shows a wage of $27 is needed to attract a 5th deckhand; hiring a 5th would then cost $135-96=39$ at the margin, i.e. $39 (using the original TCL figures), which exceeds that worker’s MRP of $30, so a 5th deckhand is not hired.

Solent Ferry Co. will now employ 4 deckhands.

Part (d): Why the minimum wage raises both wage and employment

Once the $24 minimum wage applies, Solent Ferry Co. employs 4 deckhands at a wage of $24 per hour, both more workers and a higher wage than the unconstrained monopsony outcome of 3 deckhands at $21 per hour found in (b).

This is possible because, before the minimum wage, Solent Ferry Co. was deliberately restricting employment below the point where MRP equals the wage rate, precisely to avoid having to raise the pay of its entire existing workforce each time it hired one more deckhand. A binding minimum wage (provided it is set below the fully competitive wage of $27, where MRP would equal the original wage-rate schedule at 5 deckhands) fixes the marginal cost of labour at the floor over the relevant range and removes this incentive to under-hire, so the firm responds by hiring more workers rather than fewer. This is the opposite of the standard result in a competitive labour market, where employers are already wage-takers and a wage floor set above the market-clearing wage simply causes a movement up a normal, rising demand curve for labour, reducing employment. A monopsonist’s demand for labour is constrained not by the wage rate itself but by its own rising marginal cost of labour, which is exactly what a binding minimum wage can flatten out.

Final answers

(a) $TCL(3)=$ $63, $TCL(4)=$ $96; $MCL(3)=$ $27, $MCL(4)=$ $33
(b) Unconstrained monopsony employment $=$ 3 deckhands (where MCL of $27 $<$ MRP of $32, but the 4th deckhand’s MCL of $33 $>$ MRP of $31); wage paid $=$ $21 per hour
(c) The $24 minimum wage flattens MCL to $24 for the 2nd to 4th deckhand; comparing to MRP, Solent Ferry Co. now employs 4 deckhands
(d) New outcome: 4 deckhands at $24 per hour, both wage and employment rise relative to unconstrained monopsony, because the floor removes the monopsonist’s incentive to under-hire, unlike in a competitive market