# MGEA02H3 Lecture Notes - Lecture 5: Marginal Product

ECMA04H

Week 5

We will finish up Elasticity and Excess Burden of an Excise Tax and then move on to…

Production, Productivity and Costs

Production, productivity and costs

Basic objective….understand diminishing marginal productivity and the shapes of typical cost curves in short run.

Why?: to understand the supply curve. Decisions by firms about how much to produce/supply.

We assume that the objective of firms is to maximize profits!

They hire labour and purchase (or rent) capital equipment and other inputs. These inputs combine together to produce output. Output is

sold to earn a profit (or loss…./)

A simple story to motivate what this week is all about:

Imagine that you and 4 other friends are in a lawn mowing business. You have only one lawnmower (fixed amount of capital). The

following is the “production function”

1 workers + 1 lawnmower = 5 lawns per day

2 workers + 1 lawnmower = 9 lawns per day

3 workers + 1 lawnmower = 12 lawns per day

4 workers + 1 lawnmower = 14 lawns per day

5 workers + 1 lawnmower = 15 lawns per day

The “marginal product of labour” (additional output from the additional worker) is 5 lawns for the first worker, 4 more for the

second, 3 more for the third, 2 more for the fourth, and 1 more for the final worker

The “average product of labour” is 5 lawns per worker when there is 1 worker, 4.5 lawns per worker when there are 2 workers, 4 lawns

per worker when there are 3 workers, 3.5 lawns per worker when there are 4 workers, and 3 lawns per worker when there are 5 workers

If the rental on the lawnmower costs $30 per day (cost of capital equipment) (fixed cost) and the wage paid to each worker is $50 per day

(variable cost), then the cost of cutting the first 5 lawns is $30 + $50 = $80. The cost of cutting 9 lawns per day is $30 + 2*$50 = $130.

The cost of cutting 12 lawns is $30 + 3*$50 = $180. The cost of cutting 14 lawns is $30 + 4*$50 = $230. And the cost of cutting 15 lawns

per day is $30 + 5*$50 = $280.

We can calculate the average cost per lawn, and the marginal cost per lawn (change in costs as output changes).

L K Q = TP MPL APL TC AC MC

0 1 0 0 0 $30 Ø

1 1 5 5 5 $80 $16 $10

2 1 9 4 4.5 $130 $14.44 $12.50

3 1 12 3 4 $180 $15 $16.67

4 1 14 2 3.5 $230 $16.43 $25

5 1 15 1 3 $280 $18.67 $50

L = labour K = fixed costs

Q = output MPL = marginal product of labour

APL = average product of labour TC = total costs

AC = TC / Q = average cost per unit of output MC = dTC / dq = marginal cost

Draw the average cost and marginal cost curves. As long as there are fixed inputs (e.g., capital equipment) in the short run, the AC and

MC curves will have these shapes.

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Most firms, most of the time, have no control over the production technology available. They adopt existing technology.

We write this as q = f(K,L)

K = inputs of capital (machinery, buildings, etc)

L = inputs of labour (hours of standardized worker)

An example of a production function:

q = KALB

(called “Cobb-Douglas” function)

even simpler version of Cobb-Douglas function is to choose

A = B = 0.5

[Note: A and B are parameters of the Cobb-Douglas function]

So, we have q = (KL)0.5

Now define time period: short run, long run, very long run

Short run = period too short for firms to change production capacity (K)

Long run = period long enough for firms to change plant capacity, and for new firms to enter industry (or exit)

Very long run = period long enough for technology to change

SR (K is fixed in amount)

technology capital labour

short run fixed fixed variable

long run fixed variable variable

very long run variable variable variable

e.g., long run: q = (KL)0.5

in short run, we would have to assume K = constant

e.g., K = 9, so q = 3L0.5 (short run production function)

Now define

marginal product of labour = MPL = dq/dL

In example we used earlier

K = 9, so q = 3L0.5

we get MPL = dq/dL = 1.5L-0.5 = 1.5/L0.5

We assume that dMPL/dL < 0

This is called diminishing marginal product

“Law of Diminishing Returns” (or law of diminishing marginal product, or law of variable proportions)

Thomas Malthus (Malthusian economics)

NOW we go to the next stage: we want to link production to costs

TC = PKK + PLL

PKK = (rental) cost of capital equipment

PK = rental price of capital equipment (fixed)

K = amount of capital equipment (in short run, fixed)

PLL = cost of labour

PL = price of labour (wages) (fixed)

L = number of units of labour (in short run, variable)

In short run, K fixed and L variable, so

PKK = fixed cost

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