The production chapter of economics

1. Production
Salman Almutawa

2. Aims
• To understand the difference between isoquants and indifference curves
• To present isoquants and isocost line on a diagram
• To illustrate the impact of variations in input prices on isoquants and
isocost line

3. Profit Maximisation
Profits are calculated using the following formula:
Profits = Revenues – Costs
However, each of these variables will depend on the level of quantity (q). Hence,
the profit function can be defined as:
π(q) = R(q) − C(q)
In simple terms, a firm seeks to maximise the difference between total revenue
(TR) and total cost (TC).

4. Technology
In economics, production functions take the following form:
Y = f (l, k)
Where; Y is the output, l and k are labour and capital inputs, respectively.
This represents the maximum amount of output, Y, for l and k units of labour and
capital. We can model the production relationship using isoquants.

5. Isoquant: is the set of all possible combinations of inputs l and k which are (just)
sufficient to produce a particular amount of output, Y. The prefix ‘iso’ means
‘same’, so all points along an isoquant result in the same quantity being produced.
Isoquants are similar to indifference curves (along an isoquant there is the same
quantity of output; along an indifference curve there is the same level of utility).
However, there is a crucial difference. Output is actually observed and quantifiable
and is subject to the available technology. In contrast, utility is an arbitrary value
with only ordinal properties.

6. Examples of Technology
Suppose that we have the following production function:
Y = f (l, k) = al + bk
Y = f (l, k) = min {l, k}
How will the shape of isoquants look like in both scenaiors?

7. For the production function Y = f (l, k) = al + bk, the isoquants are identical to the
indifference curves for perfect substitutes. Whereas, for Y = f (l, k) = min {l, k}, it is
identical to the shape of perfect complements.

8. • Nonlinear isoquants are identical to
typical indifference curves.
• Higher isoquants represent greater levels
of output.

9. Cost Functions
A firm’s total cost of production (isocost line), c, when using l and k units of labour
and capital is denoted as:
c = wl + rk
Where, wages (w) and rent (r) are the prices of labour and capital respectively.
Rearranging to make k as a function of l. We have:
𝑐 − 𝑤𝑙
𝑟
= 𝑘
What would be your slope and intercept?

10. • When a firm is purely labour intensive,
our intercept is c / w.
• Whereas, when the firm is purely capital
intensive, our intercept is c / r.
What would happen to the isocost line when there is a rise in the price of labour?

11. • An increase in w pivots the isocost line
inward since labour is now more
expensive. This makes the firm worse off.
• The firm now recruits fewer workers.
What would happen to the isocost line when there is a fall in the price of capital?

12. • A decrease in r means that capital is less
expensive leading to an outward pivot
shift in the isocost line.
• This makes the firm better off as the
usage of more machinery has become
cheaper.

13. Combining Isoquants and Isocost Line
• The standard producer choice problem of
cost minimisation to produce Y units of
output subject to the production function.
• The producer wants to be on the lowest
possible isocost line, when faced with
factor input prices l and k, and technology
represented by the production function Y
= f(l, k).