CHAPTER 4:
Production
Assot. Prof. Muhammad Zubair Noormal
Two-Input Production Function
◼ We simplify the production function and assume that the firm’s
production depends on only two inputs: capital (K) and labor (L).
❑ 𝑄 = 𝑓(𝐾, 𝐿)
◼ The two general inputs of capital and labor are used here for
convenience, and we frequently show these inputs on a two-
dimensional graph.
Overview and Production Functions
◼ In this Chapter, we show how economists illustrate the relationship between
inputs and outputs using production functions.
◼ The relationship between inputs and outputs is formalized by a production
function in a firm.
◼ Firm: Any organization that turns inputs into outputs.
◼ Production Function: The mathematical relationship between inputs and
outputs.
❑ E.g. 𝑄 = 𝑓(𝐾, 𝐿, 𝑀, … ) where,
❑ Q= Output
❑ K= Machines
❑ L= Labor hours
❑ M= Raw Materials
Marginal Product
◼ How much extra output can be produced by adding one more unit of an input
to the production process?
◼ Marginal Product of an input is defined as the quantity of extra output
provided by employing one additional unit of that input while holding all other
inputs constant.
◼ The marginal product of labor (MPL) is the extra output obtained by
employing one more worker while holding the level of capital equipment
constant.
◼ The marginal product of capital (MPK) is the extra output obtained by using
one more machine while holding the number of workers constant.
Diminishing Marginal Product
◼ We will explain diminishing marginal product in figure in next slide.
◼ The top panel of the figure shows the relationship between output per
week and labor input during the week when the level of capital input is
held fixed.
◼ At first, adding new workers also increases output significantly, but
these gains diminish as even more labor is added and the fixed amount
of capital becomes over-utilized.
◼ The concave shape of the total output curve in panel a therefore
reflects the economic principle of diminishing marginal product.
Marginal Product Curve
Isoquant Maps
◼ To picture an entire production function in two dimensions, we need to look at
its isoquant map.
◼ To show the various combinations of capital and labor that can be employed
to produce a particular output level, we use an isoquant.
❑ Greek word, iso means (equal)
◼ Isoquant: A curve that shows the various combinations of inputs that will
produce the same amount of output.
◼ Isoquants record the alternative combinations of inputs that can be used to
produce a given level of output.
◼ The slope of these curves shows the rate at which L can be substituted for K
while keeping output constant.
Isoquant Maps
◼ For Q=10
❑ A (KA, LA)
❑ B (KB, LB)
◼ Q=10 can be produced
either at point A or point
B.
◼ Same like indifference
curve.
Isoquant
◼ There are infinitely many isoquants in the K–L plane.
◼ Each isoquant represents a different level of output.
◼ The isoquants record successively higher levels of output as we move
in a northeasterly direction because using more of each of the inputs
will permit output to increase.
◼ You should notice the similarity between an isoquant map and the
individual’s indifference curve map>
◼ For isoquants, however, the labeling of the curves is measurable (an
output of 10 units per week has a precise meaning).
Marginal Rate of Technical Substitution (MRTS)
◼ The slope of an isoquant shows how one input can be traded for
another while holding output constant.
◼ The slope of an isoquant (or, more properly, its negative) is called the
marginal rate of technical substitution (MRTS) of labor for capital.
◼ The amount by which one input can be reduced when one more unit of
another input is added while holding output constant.
◼ Mathematically:
𝐶ℎ𝑎𝑛𝑔𝑒𝑠 𝑖𝑛 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐼𝑛𝑝𝑢𝑡 ∆𝐾
𝑀𝑅𝑇𝑆 𝑜𝑓 𝐿 𝑓𝑜𝑟 𝐾 = − 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝐼𝑠𝑜𝑞𝑢𝑎𝑛𝑡 = − =−
𝐶ℎ𝑎𝑛𝑔𝑒𝑠 𝑖𝑛 𝐿𝑎𝑏𝑜𝑢𝑟 𝐼𝑛𝑝𝑢𝑡 ∆𝐿
Diminishing MRTS
◼ The isoquants are drawn not only with negative slopes but also as
convex curves.
◼ At the beginning, the MRTS is a large positive number, indicating that a
great deal of capital can be given up if one more unit of labor is
employed.
◼ But later on, when a lot of labor is already being used, the RTS is low,
signifying that only a small amount of capital can be traded for an
additional unit of labor if output is to be held constant.
Returns To Scale
◼ Returns to Scale: The rate at which output increases in response to
proportional increases in all inputs.
◼ A production function is said to exhibit constant returns to scale if a
doubling of all inputs results in an exact doubling of output.
◼ If a doubling of all inputs yields less than a doubling of output, the
production function is said to exhibit decreasing returns to scale.
◼ If a doubling of all inputs results in more than a doubling of output, the
production function exhibits increasing returns to scale.
Returns to Scale
Graphs
The End
of Chapter one.
