Production Function

• Production is the process by which inputs are combined, transformed, and

turned into outputs. Firms vary in size and internal organization, but they
all take inputs and transform them into goods and services for which there
is some demand.
• Production function shows the relationship between the quantity of
inputs used to make a good and the quantity of output of that good.
• For sake of convenience, economists have reduced the number of
variables used in a production function to only two: capital (K) and labor
(L). Therefore, in the analysis of input-output relations, the production
function is expressed as: Q = f(K, L)
• Economists often talk about two types of inputs in the production process:
fixed and variable. A fixed input is an input whose quantity cannot be
changed as output changes. A variable input is an input whose quantity
can be changed as output changes.
SR & LR Production Function; MPP
• If any of the inputs of a firm are fixed inputs, then it is said to
be producing in the short-run. In other words, the short run is
a period of time in which some inputs are fixed.
• If none of the inputs of a firm is a fixed input—if all inputs
are variable—then the firm is said to be producing in the
long run. In other words, the long run is a period of time in
which all inputs can be varied (no inputs are fixed).
• The marginal physical product (MPP) of a variable input is
equal to the change in output that results from changing the
variable input by one unit, holding all other inputs fixed.
Law of diminishing marginal product
• Diminishing marginal returns are common in production—so
common, in fact, that economists refer to the law of
diminishing marginal returns (or the law of diminishing marginal
product). The law of diminishing returns, states that with a
given state of technology if the quantity of one factor input is
increased , by equal increment , the quantities of other
factor inputs remaining fixed , the resulting increment of
total product will first increase but decreases after a
particular point.
• It states that as we go on employing more of one factor of
production, other factor remaining same, the marginal
productivity will diminish after some point.
Costs of Production (SR): Total, Average, Marginal
• Certainly, a cost is incurred whenever a fixed input or variable input is
employed in the production process. The costs associated with fixed
inputs are called fixed costs. The costs associated with variable inputs
are called variable costs.
• The sum of fixed costs and variable costs is total cost (TC). If total fixed
costs (TFC ) are $100 and total variable costs (TVC ) are $300, then total
cost (TC ) is $400.
𝑻𝑪 = 𝑻𝑭𝑪 + 𝑻𝑽𝑪
• Given total cost, we can formally define marginal cost. Marginal cost
(MC) is the change in total cost, TC, that results from a change in
output, Q.
∆𝑻𝑪
𝑴𝑪 =
∆𝑸
AFC, AVC, ATC
• Fixed costs do not change as output changes. Therefore, TFC is
fixed when output is 0 units, 1 unit, or 2 units, and so on. Because
TFC does not change as Q changes, the TFC curve is a horizontal
line. We compute average fixed cost (AFC), which is total fixed cost
divided by quantity of output.
𝑇𝐹𝐶
𝐴𝐹𝐶 = ; the AFC curve continually declines.
𝑄
• The TVC curve rises because variable costs are likely to increase as
output increases. We compute average variable cost (AVC), which
is total variable cost divided by quantity of output.
𝑇𝑉𝐶
𝐴𝑉𝐶 = ; the AVC curve declines and then rises.
𝑄
Average Total Cost (ATC ), which is total cost divided by quantity of output.
Average total cost is sometimes called unit cost.
𝑇𝐶
ATC =
𝑄
Alternatively, we can say that ATC equals the sum of AFC and AVC.
𝐴𝑇𝐶 = 𝐴𝐹𝐶 + 𝐴𝑉𝐶
Profit & Costs
• Economists normally assume that the goal of a firm is to maximize
profit, and they find that this assumption works well in most cases.
• What is a firm’s profit? The amount that the firm receives for the sale of
its output is called total revenue. The amount that the firm pays to buy
inputs is called total cost.
• Profit is a firm’s total revenue minus its total cost:
Profit =Total revenue −Total cost
• Because economists and accountants measure costs differently, they
also measure profit differently. An economist measures a firm’s
economic profit as the firm’s total revenue minus all the opportunity
costs (explicit and implicit) of producing the goods and services sold.
An accountant measures the firm’s accounting profit as the firm’s total
revenue minus only the firm’s explicit costs.
Implicit and Explicit Cost
• An explicit cost is a cost that is incurred when an actual (monetary)
payment is made.
• An implicit cost is a cost that represents the value of resources used in
production for which no actual (monetary) payment is made. It is a cost
incurred as a result of a firm’s using resources that it owns or that the
owners of the firm contribute to it.
• Because the accountant ignores the implicit costs, accounting profit is
usually larger than economic profit.
• In economics, a firm that makes a zero economic profit is said to be
earning a normal profit.
Normal profit = Zero economic profit