1.Total costs
The total cost (TC) curve is found by adding total fixed and total variable costs. Its position reflects the amount of fixed costs, and its gradient reflects variable costs
Total fixed costs Given that total fixed costs (TFC) are constant as output increases, the curve is a horizontal line on the cost graph.
Total variable costs The total variable cost (TVC) curve slopes up at an accelerating rate, reflecting the law of diminishing marginal returns.
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OUTPUT | TOTAL FIXED COST | TOTAL VARIABLE COST | TOTAL COST | 1 | 100 | 50 | 150 | 2 | 100 | 80 | 180 | 3 | 100 | 100 | 200 | 4 | 100 | 110 | 210 | 5 | 100 | 150 | 250 | 6 | 100 | 220 | 320 | 7 | 100 | 350 | 450 | 8 | 100 | 640 | 740 |
Plotting this gives us Total Cost, Total Variable Cost, and Total Fixed Cost.

2.Average total cost
Average total cost (ATC) is also called average cost or unit cost. Average total costs are a key cost in the theory of the firm because they indicate how efficiently scarce resources are being used. Average variable costs are found by dividing total fixed variable costs by output.
Average fixed costs Average fixed costs are found by dividing total fixed costs by output. As fixed cost is divided by an increasing output, average fixed costs will continue to fall.
Average variable costs Average variable costs are found by dividing total fixed variable costs by output. Always rises at a constant rate.

AVC is ‘U’ shaped because of the principle of variable Proportions, which explains the three phases of the curve: 1. Increasing returns to the variable factors, which cause average costs to fall: 2. Constant returns, 3. Diminishing returns, which cause costs to rise.

OUTPUT | AVERAGE FIXED COST (£000) | AVERAGE VARIABLE COST (£000) | AVERAGE TOTAL COSTS (£000) | 1 | 100 | 50 | 150 | 2 | 50 | 40 | 90 | 3 | 33.3 | 33.3 | 67 | 4 | 25 | 27.5 | 52.5 | 5 | 20 | 30 | 50 | 6 | 16.6 | 36.7 | 53.3 | 7 | 14.3 | 50 | 64.3 | 8 | 12.5 | 80 | 92.5 |

Average total cost (ATC) can be found by adding average fixed costs (AFC) and average variable costs (AVC). The ATC curve is also ‘U’ shaped because it takes its shape from the AVC curve, with the upturn reflecting the onset of diminishing returns to the variable factor.
The average fixed cost (AFC) curve will slope down continuously, from left to right.
The average variable cost (AVC) curve will at first slope down from left to right, then reach a minimum point, and rise again.

Long Run Average Cost (LRAC) Long run average cost is the cost per unit of output feasible when all factors of production are variable
In the long run all costs are variable and the scale of production can change (i.e. no fixed inputs)

Long-Run Average and Marginal Cost

When a firm is producing at an output at which the long-run average cost LAC is falling, the long-run marginal cost LMC is less than LAC.
Conversely, when LAC is increasing, LMC is greater than LAC.
The two curves intersect at A, where the LAC curve achieves its minimum.

● long-run average cost curve (LAC) Curve relating average cost of production to output when all inputs, including capital, are variable● short-run average cost curve (SAC) Curve relating average cost of production to output when level of capital is fixed. ● long-run marginal cost curve (LMC) Curve showing the change in long-run total cost as output is increased incrementally by 1 unit. |

The Relationship between Short-Run and Long-Run Cost

The long-run average cost curve LAC is the envelope of the short-run average cost curves SAC1, SAC2, and SAC3.
With economies and diseconomies of scale, the minimum points of the short-run average cost curves do not lie on the long-run average cost curve

3.Marginal costs
The increase in total cost that arises from an extra unit of production, Always rises at a pretty constant rate. It can be found by calculating the change in total cost when output is increased by one unit.
It is important to note that marginal cost is derived solely from variable costs, and not fixed costs.
The marginal cost curve falls briefly at first, then rises. Marginal costs are derived from variable costs and are subject to the principle of variable proportions.

Because fixed cost does not change as the firm’s level of output changes, marginal cost is equal to the increase in variable cost or the increase in total cost that results from an extra unit of output.
We can therefore write marginal cost as

The significance of marginal cost
The marginal cost curve is significant in the theory of the firm for two reasons: 1. It is the leading cost curve, because changes in total and average costs are derived from changes in marginal cost. 2. The lowest price a firm is prepared to supply at is the price that just covers marginal cost.
ATC and MC
Average total cost and marginal cost are connected because they are derived from the same basic numerical cost data. The general rules governing the relationship are: 1. Marginal cost will always cut average total cost from below. 2. When marginal cost is below average total cost, average total cost will be falling, and when marginal cost is above average total cost, average total cost will be rising. 3. A firm is most productively efficient at the lowest average total cost, which is also where average total cost (ATC) = marginal cost (MC).
Total costs and marginal costs
Marginal costs are derived exclusively from variable costs, and are unaffected by changes in fixed costs. The MC curve is the gradient of the TC curve, and the positive gradient of the total cost curve only exists because of a positive variable cost. This is shown below:

4.Short-Run Total Costs * Short-run costs are not minimal costs for producing the various output levels * the firm does not have the flexibility of input choice * to vary its output in the short run, the firm must use no optimal input combinations * the RTS will not be equal to the ratio of input prices

Short-Run Marginal and Average Costs * The short-run average total cost (SAC) function is
SAC = total costs/total output = SC/q * The short-run marginal cost (SMC) function is
SMC = change in SC/change in output = SC/q

Relationship between Short-Run and Long-Run Costs * At the minimum point of the AC curve: * the MC curve crosses the AC curve * MC = AC at this point * the SAC curve is tangent to the AC curve * SAC (for this level of k) is minimized at the same level of output as AC * SMC intersects SAC also at this point AC = MC = SAC = SMC

5.The cost function and returns to scale
Suppose that the production function has constant returns to scale. If the input bundle (z1, z2) is the optimal input bundle to produce the output y, then for any constant a > 0, the input bundle (az1, az2) is the optimal input bundle to produce the output ay. Thus the total cost of producing ay is a times the total cost of producing y, so that the average cost of production is constant, independent of output.
Similarly, if the production function has decreasing returns to scale then the average cost of production increases, and if the production function has increasing returns to scale then the average cost of production falls: CRTS | LAC is constant | DRTS | LAC is increasing | IRTS | LAC is decreasing |
We often think of the "typical" production function as having increasing returns to scale initially, then decreasing returns to scale. For such a production function the LAC is U-shaped. Given the relation between averages and marginals, the LAC and LMC for such a production function look like those in the following figure:

COST IN THE SHORT RUN (Diminishing Marginal Returns and Marginal Cost)
Diminishing marginal returns means that the marginal product of labor declines as the quantity of labor employed increases.
As a result, when there are diminishing marginal returns, marginal cost will increase as output increases.

Economic of scale (Long Run)
The property whereby long-run average total cost falls as the quantity of output increases (left-most downward sloping part of the long-run ATC). Arises because higher production levels allow specialization among workers, allowing each of them to get better at a specific task. a) economies of scale Situation in which output can be doubled for less than a doubling of cost.

b) diseconomies of scale The property whereby long-run average total cost rises as the quantity of output increases (right-most upward sloping part of the long-run ATC). Usually arise because of coordination problems. Situation in which a doubling of output requires more than a doubling of cost

Increasing Returns to Scale: Output more than doubles when the quantities of all inputs are doubled.
Economies of Scale: A doubling of output requires less than a doubling of cost.

c) constant returns to scale The property whereby long run average total cost stays the same as the quantity of output changes

Why this is happen??
As output increases, the firm’s average cost of producing that output is likely to decline, at least to a point.
This can happen for the following reasons: 1. If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive. 2. Scale can provide flexibility. By varying the combination of inputs utilized to produce the firm’s output, managers can organize the production process more effectively. 3. The firm may be able to acquire some production inputs at lower cost because it is buying them in large quantities and can therefore negotiate better prices. The mix of inputs might change with the scale of the firm’s operation if managers take advantage of lower-cost inputs
At some point, however, it is likely that the average cost of production will begin to increase with output.
There are three reasons for this shift: 1. At least in the short run, factory space and machinery may make it more difficult for workers to do their jobs effectively. 2. Managing a larger firm may become more complex and inefficient as the number of tasks increases. 3. The advantages of buying in bulk may have disappeared once certain quantities are reached. At some point, available supplies of key inputs may be limited, pushing their costs up.
Economies of scale are often measured in terms of a cost-output elasticity, EC. EC is the percentage change in the cost of production resulting from a 1-percent increase in output: or

6. expansion path
Curve passing through points of tangency between a firm’s isocost lines and its isoquants.
The expansion path is the locus of cost-minimizing tangencies. The curve shows how inputs increase as output increases * The expansion path does not have to be a straight line * the use of some inputs may increase faster than others as output expands * depends on the shape of the isoquants * The expansion path does not have to be upward sloping * if the use of an input falls as output expands, that input is an inferior input

The Expansion Path and Long-Run Costs
To move from the expansion path to the cost curve, we follow three steps: 1. Choose an output level represented by an isoquant. Then find the point of tangency of that isoquant with an isocost line. 2. From the chosen isocost line determine the minimum cost of producing the output level that has been selected.

In (a), the expansion path (from the origin through points A, B, and C) illustrates the lowest-cost combinations of labor and capital that can be used to produce each level of output in the long run— i.e., when both inputs to production can be varied.
In (b), the corresponding long-run total cost curve (from the origin through points D, E, and F) measures the least cost of producing each level of output

The Inflexibility of Short-Run Production

When a firm operates in the short run, its cost of production may not be minimized because of inflexibility in the use of capital inputs.
Output is initially at level q1.
In the short run, output q2 can be produced only by increasing labor from L1 to L3 because capital is fixed at K1.
In the long run, the same output can be produced more cheaply by increasing labor from L1 to L2 and capital from K1 to K2.

Important Points to Note 1. A firm that wishes to minimize the economic costs of producing a particular level of output should choose that input combination for which the rate of technical substitution (RTS) is equal to the ratio of the inputs’ rental prices 2. Repeated application of this minimization procedure yields the firm’s expansion path. the expansion path shows how input usage expands with the level of output. it also shows the relationship between output level and total cost. this relationship is summarized by the total cost function, C(v,w,q). 3. The firm’s average cost (AC = C/q) and marginal cost (MC = C/q) can be derived directly from the total-cost function. if the total cost curve has a general cubic shape, the AC and MC curves will be u-shaped. 4. All cost curves are drawn on the assumption that the input prices are held constant when an input price changes, cost curves shift to new positions the size of the shifts will be determined by the overall importance of the input and the substitution abilities of the firm technical progress will also shift cost curves 5. In the short run, the firm may not be able to vary some inputs it can then alter its level of production only by changing the employment of its variable inputs it may have to use nonoptimal, higher-cost input combinations than it would choose if it were possible to vary all inputs.