Order 1369245: Long Run Average Cost
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Ch07THETHEORYANDESTIMATIONOFCOST-Revised.pptChapter Seven
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Chapter 7
The Theory and
Estimation of Cost
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Chapter Seven
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Overview
- Definition and use of cost
- Relating production and cost
- Short run and long run cost
- Economies of scope and scale
- Supply chain management
- Ways companies have cut costs to remain competitive
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Chapter Seven
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Learning objectives
- define the cost function
- distinguish between economic cost and accounting cost
- explain how the concept of relevant cost is used
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Chapter Seven
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Learning objectives
- understand total, variable, average and fixed cost
- distinguish between short-run and long-run cost
- provide reasons for the existence of economies of scale
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Chapter Seven
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Definition and use of
cost in economic analysis
- Historical cost: cost incurred at the time of procurement. (vs. replacement cost).
- Opportunity cost: amount or subjective value that is forgone in choosing one activity over the next best alternative. Called Economic (real) cost. Compare it with Accounting cost.
- Incremental cost: the change in total cost when the range of options available in the decision changes. (vs. marginal cost).
- Sunk cost: the cost that cannot be restored or recovered, partially or entirely.
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Chapter Seven
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Relationship between
production and cost
- The production function describes the production technology in physical units.
- Q = f(X1, X2, etc.), where Q, X1, X2, etc. are all expressed in physical units.
- The cost function still describes the production technology, just as the production function does, but in monetary units.
- TC = f(Q), where TC is the monetary value of all inputs.
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- Each of the production function or the cost function describes the relationship between the inputs X1, X2, etc. and the output Q.
- In reality, we may not find data on physical units of inputs, especially capital inputs because it is difficult of to measure.
- Data on costs are usually available.
- This is the reason of studying production function and then cost function.
Chapter Seven
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Relationship between
production and cost
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- We will assume here (for simplicity) that the firm is a ‘price taker’ in the input market. That is to say the factor prices are given from the market. The firm does not determine them.
- This assumption helps us focus on the relationship between inputs and output away from the disturbance coming from the change in input prices.
Chapter Seven
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Relationship between
production and cost
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Chapter Seven
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Relationship between
production and cost
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Chapter Seven
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- Using the same procedure, we can find:
- Average variable cost (AVC) = the total variable cost divided by the units of labor, (labor is assumed to be the only variable input)
AVC = TVC/Q = w/APL
- The law of diminishing returns (Chapter 6) implies that AVC will eventually increase.
- Graphical presentation of these relations is given as follows.
Relationship between
production and cost
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Chapter Seven
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Plotting APL and MPL (chapter 6) in the upper graph and plotting AVC and MC (chapter 7) in the lower graph, shows that the cost curves are mirror images for the product curves.
Relationship between
production and cost
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Chapter Seven
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Short-run cost function
- For simplicity use the following assumptions:
- the firm employs two inputs, labor and capital
- the firm operates in a short-run production period where labor is variable, capital is fixed
- the firm produces a single product
- the firm employs a fixed level of technology
- the firm operates at every level of output in the most efficient way
- the firm operates in perfectly competitive input markets and must pay for its inputs at a given market rate (it is a ‘price taker’)
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Chapter Seven
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Short-run cost function
- Standard concepts in the short-run cost function:
Quantity (Q) is the amount of output that a firm can produce in the short run
Total fixed cost (TFC) is the total cost of using the fixed input, capital (K). Plotting TFC against Q we get the TFC curve as a horizontal straight line.
Short-run cost function
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Chapter Seven
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- Standard concepts in the short-run cost function:
Total variable cost (TVC) is the total cost of using the variable input, labor (L).The TVC curve is increasing continuously with the increase in Q. It starts from the origin.
Total cost (TC) is the total cost of using all the firm’s inputs,
TC = TFC + TVC
What is the difference between TC and TVC curves?
Short-run cost function
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Chapter Seven
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Short-run cost function
- Standard concepts in the short-run cost function:
Average fixed cost (AFC) is the average per-unit cost of using the fixed input K. It falls continuously as Q increases. Why?
AFC = TFC/Q
Average variable cost (AVC) is the average (per-unit) cost of using the variable input L. It takes a U shape. Why?
AVC = TVC/Q
Short-run cost function
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Chapter Seven
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Short-run cost function
- Standard concepts in the short-run cost function:
Average total cost (ATC) is the average (per-unit) cost of all the firm’s inputs. It takes the U shape like AVC but it reaches its minimum after the minimum of AVC. Why?
ATC = AFC + AVC = TC/Q
Short-run cost function
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Chapter Seven
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Short-run cost function
- Standard concepts in the short-run cost function:
Marginal cost (MC) is the change in a firm’s total cost (or total variable cost) resulting from a unit change in output. It takes the U shape. Why?
MC = DTC/DQ = DTVC/DQ
Short-run cost function
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Chapter Seven
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Short-run cost function
- Graphical example of the cost variables
Short-run cost function
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Chapter Seven
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Short-run cost function
- Important observations
- AFC declines steadily
- when MC = AVC, AVC is at a minimum
- when MC < AVC, AVC is falling
- when MC > AVC, AVC is rising
The same three rules apply for average total cost (ATC) as for AVC
Short-run cost function
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Chapter Seven
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Short-run cost function
- A reduction in the firm’s fixed cost would cause the average total cost curve to shift downward.
- A reduction in the firm’s variable cost would cause all three cost curves (AC, AVC, MC) to shift downward.
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Chapter Seven
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Short-run cost function
- Alternative specifications of the Total Cost function (relating total cost and output)
- cubic relationship
- as output increases, total cost first increases at a decreasing rate, then increases at an increasing rate
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Chapter Seven
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Short-run cost function
- Alternative specifications of the Total Cost function (relating total cost and output)
- quadratic relationship
- as output increases, total cost increases at an increasing rate
- linear relationship
- as output increases, total cost increases at a constant rate
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Short-run cost function
- The minimum point on the ATC curve is associated with the rate of output that is called “Full Capacity”.
- The full capacity of the firm indicates the “the firm size or plant size”.
Chapter Seven
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Chapter Seven
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Long-run cost function
- In the long run, all inputs to a firm’s production function are subject to change. They are all variable inputs.
- All costs are variable costs, no fixed costs.
- the firm’s long run marginal cost pertains to returns to scale. Why?
- Because it measures the change in long run total cost when the firm moves from its current size (current full capacity) to a larger size (higher full capacity).
- Planning to move to a larger size, the firm may face IRS, CRS or DRS. Review ch.6.
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Chapter Seven
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Long-run cost function
- When the firm experiences increasing returns to scale IRS:
- a proportional increase in all inputs increases output by a greater proportion (percentage).
- as output increases by some percentage, total cost of production increases by lesser percentage
- Notice that input prices are given.
- See the following illustration.
Long-run cost function
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Chapter Seven
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- Let the firm use three inputs X1, X2, X3 with given unit prices w1, w2, w3 to produce Q units of the product. The long run average cost is calculated as:
LRAC = (w1×X1+w2×X2+w3×X3)/Q
Now if doubling all inputs results in 3 times the output, this means IRS. The new long run average cost, call it LRAC’ will be
LRAC’ = 2(w1×X1+w2×X2+w3×X3)/3Q
= (2/3) LRAC
Therefore IRS decreasing or falling LRAC
Long-run cost function
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Long-run cost function
- IRS (called Economies of scale): Situation where a firm’s long-run average cost (LRAC) declines as the plant size or firm size increases.
- DRS (called diseconomies of scale): Situation where a firm’s LRAC increases as the plant size or firm size increases.
- CRS (constant returns to scale): Situation where a firm’s LRAC is constant as the plant size or firm size increases.
- LRAC curve is U-shaped in general. It is also called planning curve. Why?
Long-run cost function
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Chapter Seven
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Long-run cost function
- Reasons for long-run scale economies
- Better specialization of labor and capital
- Economizing on the cost of capital (machines, equipment, constructions…)
- larger firms may be able to spread out promotional costs.
- larger firms may be able to spread out management costs.
- Notice that any price advantage the larger firm gains is ignored here. Considering these advantages is called “Externalities” not “Scale Economies”
Long-run cost function
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Chapter Seven
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Long-run cost function
- Reasons for long-run DRS
- transportation costs may tend to rise as production grows, due to handling expenses, insurance, security, and inventory costs.
- Cost of coordination among different levels of management may rise.
- Notice that any price disadvantage the larger firm incurs is ignored here. Considering these disadvantages is called “Negative Externalities”.
Long-run cost function
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Chapter Seven
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Long-run cost function
In long run, the firm can choose any level of capacity
Once it commits to a level of capacity, at least one of the inputs must be fixed. This then becomes a short-run problem
The LRAC curve is an envelope of SRAC curves, and outlines the lowest per-unit costs the firm will incur over a range of output
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Chapter Seven
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Long-run cost function
- The long-run average cost curve is a planning curve that tells the firm the plant that minimizes the average cost of producing a given output range.
- Once the firm has chosen its plant size, the firm incurs the costs that correspond to the ATC (i.e. SRAC) curve for that plant.
Long-run cost function
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- LRAC curve is tangent to SRAC to the left of minimum SRAC (i.e. its full capacity) in the range of IRS.
- LRAC curve is tangent to SRAC to the right of minimum SRAC (i.e. its full capacity) in the range of DRS.
- LRAC curve is tangent to SRAC to at the minimum SRAC (i.e. its full capacity) in the range of CRS. This indicates the minimum efficient scale or the optimal plant size.
- Refer to the graph.
Chapter Seven
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Long-run cost function
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Chapter Seven
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Economies of scope
- Economies of scope: reduction of a firm’s unit cost by producing two or more goods or services jointly rather than separately
Closely related to economies of scale
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Chapter Seven
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Supply chain management
- Supply chain management (SCM): efforts by a firm to improve efficiencies through each link of a firm’s supply chain from supplier to customer.
transaction costs are incurred by using resources outside the firm (outsourcing).
coordination costs arise because of uncertainty and complexity of tasks.
information costs arise to properly coordinate activities between the firm and its suppliers.
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Chapter Seven
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Supply chain management
- Ways to develop better supplier relationships
- strategic alliance: firm and outside supplier join together in some sharing of resources.
- competitive tension: firm uses two or more suppliers, thereby helping the firm keep its purchase prices under control.
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Chapter Seven
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Ways companies cut
costs to remain competitive
- the strategic use of cost
- reduction in cost of materials
- using information technology to reduce costs
- reduction of process costs
- relocation to lower-wage countries or regions
- mergers, consolidation, and subsequent downsizing
- layoffs and plant closings
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Chapter Seven
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Global application
- Example: manufacturing chemicals in China
- labor content relatively low
- high use of equipment and raw materials
- noncost reasons for outsourcing
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