Bramble Furniture Co. makes wooden chairs. It sells every chair it produces for a constant price of $60 in a perfectly competitive product market, and it can hire as many workers as it wants at the going wage rate in a perfectly competitive labour market. The table below shows t…

Answer: ((a)) MPP for workers 1 to 7 is 20, 18, 16, 14, 12, 10 and 8 chairs; the corresponding MRP is $1200, $1080, $960, $840, $720, $600 and $480 per week ((b)) The MRP of a worker is the extra revenue that worker adds to the firm, which is exactly the most a profit-maximising firm is willing to pay to employ them, so the MRP curve traces out how many workers the firm demands at every possible wage rate ((c)) Bramble Furniture should employ 5 workers, since the 5th worker's MRP of $720 exceeds the $700 wage, while a 6th worker's MRP of only $600 would be less than the $700 wage ((d)) A rise in the price of chairs from $60 to $75 raises the MRP of every worker, since MRP equals MPP multiplied by price, shifting the whole demand for labour curve to the right rather than causing a movement along it, because the change comes from a rise in the marginal revenue e…. Part (a): Marginal physical product and marginal revenue product The marginal physical product (MPP) of each worker is the extra output produced when that worker is added, found by subtracting each row's total product from the previous row…

A2 Economics 9708: Marginal Revenue Product and the Demand for Labour

Workers employed	Total product (chairs per week)
0	0
1	20
2	38
3	54
4	68
5	80
6	90
7	98

Workers employed

Total product (chairs per week)

Part (a): Marginal physical product and marginal revenue product

The marginal physical product (MPP) of each worker is the extra output produced when that worker is added, found by subtracting each row’s total product from the previous row’s:

Workers	Total product	MPP	MRP $=$ MPP $\times$ price ($60)
1	20	$20-0=20$	$20\times60=1200$
2	38	$38-20=18$	$18\times60=1080$
3	54	$54-38=16$	$16\times60=960$
4	68	$68-54=14$	$14\times60=840$
5	80	$80-68=12$	$12\times60=720$
6	90	$90-80=10$	$10\times60=600$
7	98	$98-90=8$	$8\times60=480$

So MPP falls steadily as more workers are added (the law of diminishing returns), and MRP falls with it since price is constant at $60 per chair.

Part (b): Why the MRP curve is the firm’s demand curve for labour

The marginal revenue product of a worker is the extra revenue the firm earns by employing that worker (their marginal physical product multiplied by the extra revenue (here, the price) each unit of output earns. A profit-maximising firm will only employ an extra worker if doing so adds at least as much to revenue as it adds to cost, i.e. if that worker’s MRP is at least equal to the wage. This means, at any given wage rate, the number of workers the firm is willing to hire is exactly the number whose MRP is greater than or equal to that wage) which is precisely what the MRP curve shows. The MRP curve therefore traces out the quantity of labour demanded at every possible wage, making it the firm’s demand curve for labour.

Part (c): Profit-maximising employment at a wage of $700

Bramble Furniture should keep hiring workers as long as the next worker’s MRP is greater than the wage, since such a worker adds more to revenue than to cost:

The 5th worker has an MRP of $720, which exceeds the wage of $700, so hiring this worker adds $720-700=20$ dollars to profit, worth hiring.
The 6th worker has an MRP of only $600, which is less than the wage of $700, so hiring this worker would reduce profit by $700-600=100$ dollars, not worth hiring.

So the profit-maximising number of workers is 5.

Part (d): Effect of a rise in the price of chairs

Since $MRP = MPP \times \text{price}$ , and MPP is unchanged, a rise in price from $60 to $75 raises the MRP of every single worker in the table (for example, the first worker’s MRP rises from $20\times60=1200$ to $20\times75=1500$ ). Because the MRP curve is the firm’s demand curve for labour, this means the entire demand curve for labour shifts to the right: at any given wage rate, more workers are now profitable to employ than before.

This is a shift of the demand curve, not a movement along it, because the wage rate itself has not changed. The cause is a change in the price of chairs (the marginal revenue earned per unit of output), which is a non-wage-rate influence on the demand for labour, exactly as a change in the price of the firm’s product shifts (rather than moves along) its MRP/demand-for-labour curve.

Final answers

(a) MPP: 20, 18, 16, 14, 12, 10, 8. MRP: $1200, $1080, $960, $840, $720, $600, $480
(b) MRP measures the extra revenue (and so the most the firm will pay) for each extra worker, so it directly gives the quantity of labour demanded at every wage. it is the firm’s demand curve for labour
(c) Profit-maximising employment $=$ 5 workers (5th worker’s MRP of $720 $>$ wage of $700; 6th worker’s MRP of $600 $<$ $700)
(d) The demand for labour curve shifts to the right. A higher chair price raises MRP at every level of employment, and this is a shift (caused by a non-wage factor), not a movement along the curve