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The Theory of the Firm and the cost of production
Production Function
States the relationship between inputs and outputs or maximum output from various combinations of
factors in puts.
Inputs β the factors of production classified as:
Input Land Labour Capital
Description All natural resources of the earth.
all physical and mental human effort involved in production
buildings, machinery and equipment not used for its own sake but for the contribution it makes to production
Price paid to acquire Rent Wages Interest
Mathematical representation of the relationship:
π = π (πΎ, πΏ, πΏπ)
Q - Output K - Capital L - Land La - Labor
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Analysis of Production Function (Short Run and Long run):
Short Run
In the short run at least one factor fixed in supply but all other factors capable of being changed
Reflects ways in which firms respond to changes in output (demand)
Can increase or decrease output using more or less of some factors but some likely to be easier
to change than others.
Long Run
The long run is defined as the period taken to vary all factors of production
By doing this, the firm is able to increase its total capacity β not just short-term capacity and
Associated with a change in the scale of production
The period varies according to the firm and the industry
In electricity supply, the time taken to build new capacity could be many years; for a market
stallholder, the βlong runβ could be as little as a few weeks
Marginal Product
The marginal product of any input in the production process is the increase in output that arises from an
additional unit of that input
ππππππππ πππ¦π ππππ πππππ’ππ‘ πππ =ππππππ ππ π‘ππ‘ππ ππ’π‘ππ’π‘
ππππππ ππ ππππ’π‘ ππ’πππ‘ππ‘π¦
Diminishing Marginal Product
Diminishing marginal product is the property whereby the marginal product of an input declines as the
quantity of the input increases.
Example: As more and more workers are hired at a firm, each additional worker contributes less and less
to production because the firm has a limited amount of equipment.
In the short run, a production process is characterized by a fixed amount of available land and capital. As
more labour is hired, each unit of labour has less capital and land to work with.
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Units of L Total Product
(QL or TPL)
Marginal Product
(MPL)
0 0 -
1 2 2
2 6 4
3 12 6
4 20 8
5 26 6
6 30 4
7 32 2
8 32 0
9 30 -2
10 26 -4
TP β Total Product
MP β Marginal
Product
AP β Average product
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Costs
In buying factor inputs, the firm will incur costs
Costs are classified as:
Fixed costs (FC) β costs that are not related directly to production β rent, rates, insurance costs,
admin costs. They can change but not in relation to output
Variable Costs (VC) β costs directly related to variations in output. Raw materials primarily
Short run β Diminishing marginal returns results from adding successive quantities of variable
factors to a fixed factor
Long run β Increases in capacity can lead to increasing, decreasing or constant returns to scale
ππΆ = πΉπΆ + ππΆ
π΄πΆ = ππΆ/ππ’π‘ππ’π‘
ππΆ = ππΆπ β ππΆπβ1 π’πππ‘π
ππΆ =ππππππ ππ π‘ππ‘ππ πππ π‘
ππππππ ππ ππ’π‘ππ’π‘
Total Cost (TC) - the sum of all costs incurred in production
Average Cost (AC) β the cost per unit of output
Marginal Cost (MC) β the cost of one more or one fewer units of production
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Relationships between Costing and Production
Here I guess that first graph is obvious, in second the increasing increase is due to the increasing
increase in the MC as shown in first set of graphs.
Revenue
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Total revenue β the total amount received from selling a given output
ππ = π π₯ π
Average Revenue β the average amount received from selling each unit
π΄π =ππ
π
Marginal revenue β the amount received from selling one extra unit of output
ππ = ππ π β ππ πβ1 π’πππ‘π
Profit
ππππππ‘ = ππ β ππΆ
Profits help in the process of directing resources to alternative uses in free markets
Relating price to costs helps a firm to assess profitability in production
Normal Profit β the minimum amount required to keep a firm in its current line of production
Abnormal or Supernormal profit β profit made over and above normal profit
Abnormal profit may exist in situations where firms have market power
Abnormal profits may indicate the existence of welfare losses
Could be taxed away without altering resource allocation
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Sub-normal Profit β
profit below normal profit Firms may not exit the market even if sub-normal profits
made if they are able to cover variable costs
Cost of exit may be high
Sub-normal profit may be temporary (or perceived as such!)
Assumption that firms aim to maximise profit
May not always hold true β there are other objectives
Profit maximising output would be where MC = MR
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The Cost of Production
Profit = Total revenue - Total cost
Total Cost includes all of the opportunity costs of production
Explicit Costs and Implicit Costs
Explicit costs are out-of-pocket expenses, such as labour, raw materials, and rent.
Implicit costs are foregone expenses, such as the value of your own time, and the value of your
own money (interest earned).
Economic Profit versus Accounting Profit
Economic profit is smaller than accounting profit
Question: If a firmβs total revenue is $80,000, and its explicit and implicit costs are $70,000 and $25,000,
respectively, what are its economic and accounting profits?
Accounting: 35000, Economics: 10000
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Total and Per Unit Costs
Total Variable Cost (TVC)
Total Fixed Cost (TFC)
Total Cost (TC)
Average Variable Cost (AVC)
Average Fixed Cost (AFC)
Average Total Cost (ATC)
Marginal Cost (MC)
Fixed and Variable Costs
Fixed costs are those costs that do not vary with the quantity of output produced. Variable costs are
those costs that do change as the firm alters the quantity of output produced.
Average Costs
Average costs can be determined by dividing the firmβs costs by the quantity of output produced. The
average cost is the cost of each typical unit of product.
Marginal Cost
Marginal cost (MC) measures the amount total cost rises when the firm increases production by one
unit.
Question: Fill in the missing values
Three Important Properties of Cost Curves
1. Marginal cost eventually rises with the quantity of output. [Law of Diminishing Marginal
Returns]
2. The average-total-cost curve is U-shaped.
3. The marginal-cost curve crosses the average-total-cost curve at the minimum of average total
cost.
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The Long-run Average Cost Curve
In the long run, all inputs are variable. A firm has enough time to choose the size of its factory, farm,
office building, or other capital goods. The firm can choose from many short-run cost curves. The
bottom points of the short-run average cost curves make up the long-run average cost curve. Long-run
average costs fall as production first rises. This is called economies of scale. When the firm gets too big,
long-run average costs rise. This is called diseconomies of scale (DOS).
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Returns to Scale
When inputs increase, and production more than proportionately increases, then we speak of increasing
returns to scale (associated with economies of scale).
Example - Inputs increase by 10%, and production increases by 20%.
When inputs increase, and production less than proportionately increases, then we speak of decreasing
returns to scale (associated with diseconomies of scale).
Example - Inputs increase by 10%, and production increases by 5%.
When inputs increase, and production increases by the same percentage, then we speak of constant
returns to scale.
Example - Inputs increase by 10%, and production increases by 10%.