Economics, 3rd Edition

marginal product

 the increase in output that arises from an additional unit of input

The marginal product of labour, therefore, would be represented as:

MP

L

=

ΔQ

ΔL

---

CHAPTER 6  BACKGROUND TO SUPPLY: FIRMS IN COMPETITIVE MARKETS  137

If we were using calculus the marginal product for an infenitesimal small change in labour input would be 

the partial derivative:

MP

L

=

𝜕

 

Q

𝜕

 

L

We use partial derivatives in this case because the production function has more than one independent 

variable (capital and labour). We are looking at the rate of change of Q when either K  or L varies but with 

the other variables held constant. To find the marginal product of labour, therefore, we are differentiating 

Q with respect to L whilst K  is held constant.

When the number of workers goes from 1 to 2, total pizza production increases from 50 to 90, so the 

marginal product of the second worker is 40 pizzas. When the number of workers goes from 2 to 3, total 

product increases from 90 to 120, so the marginal product of the third worker is 30 pizzas.

Notice that as the number of workers increases, the marginal product (MP) declines. The second worker 

has a MP of 40 pizzas, the third worker has a MP of 30 pizzas and the fourth worker has a MP of 20 pizzas. 

This property of the production function is called