Managerial Economics (Chapter 6)

SAC equation

SAC = STC / Q = TFC /Q + TVC / Q = AFC + AVC IF TFC = P(k) * K and TVC = P(l) * L then AFC = P(k) * K / Q and AVC = P(l) * L / Q and SAC = P(k) * K / Q + P(l) * L / Q Since AVC = (P(l) * L) / Q we can write AVC = (L / Q) * P(l) = 1 / (Q/L) * P(l) = 1 / AP(l) * P(l) = P(l) / AP(l)

Example Figure 6-9

The greater the average product of the variable input (input L), the smaller is AVC. For example, when the amount of input L is 2 units, AP(l) = 5 units. AVC = P(l) / AP(l) = $36/5 = $7.20. When 5 units of input L are usded, then AP(l) = 10 units, and AVC = $3.60

Example Figure 6-8

The productivity of a variable input and short-run cost vary inversely. If input L is the only variable input, TVC = L * P(l). Note that the more steeply sloped the TP(l) curve, the less steeply sloped the TVC curve (or, the greater the MP(l), the smaller the SMC)

Total fixed cost (TFC)

is equal to the price (P) of output K multiplied by the quantity of input K

Short-run marginal cost (SMC)

is equal to the slope of the STC curve or the slope of the TVC curve. SMC passes through AVC and SAC at their respective minimum points.

STC example

Since input K is fixed at 4 units and P(k) = $50, TFC = P(k) = $200. STC = TVC + TFV

Historical costs or explicit costs

are costs of the firm for which explicit payment has been made sometime in the past for for which the firm is committed in the future. Explicit costs include wages and salaries, rent, materials costs, depreciation, and interest payment

Sem-ivariable costs definition

are costs that are fixed over some ranges of output and variable over others

Fixed cost definition

are costs that do not vary with the level of output in the short run

Variable costs definition

are costs that increase or decrease as a firms output increases or decreases.

dis-economies of scale

are present, so that it is cheaper to produce beyond the point of minimum short-run average cost corresponding to a smaller plant than by producing at the minimum shor-run average cost point corresponding to a larger plant.

Economies of scale definition

are technological and organizational advantages that accrue to the firm as it increases output in the long run. Economies of scale reduce long-run average costs

Dis-economies of scale definition

are technological and organizational disadvantages that the firm encounters as it increases output in the long run. Dis-economies of scale increase long-run average costs

Implicit cost definition

are the costs of using firm-owned resources. They are opportunity costs that cannot be accounted for by payments to outsiders. These costs represent opportunities that a firm gives up by using a resource in one way rather than another

Historical costs or (explicit costs) definition

are those costs of production that involve a specific payment by the firm to some person, group, or organization outside the firm.

Fixed costs

are those costs that are fixed in the short run and therefore do not vary with the level of output produced by the firm during that time period

variable costs

are those costs that do vary with the level of production of the firm

Implicit costs

are those that do not involve costs to the firm in the sense that in order to use certain inputs in the production process, the firm has had to abandon opportunities to use them elsewhere

Incremental costs

associated with some decisions by the firm are the additional costs that a firm would incur if it took one course of action rather than another

Long-run average cost (LAC) or per unit cost

at some output level Q can be found by dividing long-run total cost (LTC) by output (Q): LAC = LTC / Q. Since long-run average costs gives the cost per unit of output in the long run when all costs are variable, it follows that LAC for a particular output level is calculated by dividing LTC at the level of output by the number of units of output. We would find the average value of anything else in the same manner: divide that total value by the number of cases involved.

Short-run average total cost (SAC) equation

average total cost per unit of output, can be found by dividing shor-run total cost by the level of output or by adding AFC and AVC. SAC = AFC + AVC = STC / Q

LMC is obtained

by taking the derivative of LTC with respect to Q, LMC = dLTC / dQ = 10 - 1.2Q + 0.06Q^2

Short-run total cost (STC) definition

includes all of the private economic costs of the firm in the short run. Short-run total cost is equal to total fixed cost plus short-run total variable cost

Marginal product of a variable

input rises, there will be a corresponding fall in short-run marginal cost, and if the marginal product of a variable input falls, short-run marginal cost must rise

Total fixed cost (TFC) equation

is a horizontal straight line at an amount equal to P(k) * K if input K is fixed

Long -run average cost curve

is an envelope curve for the short-run average cost curves. In other words, it is made up of points that indicate the lowest unit costs obtainable for each level of output

Average variable cost (AVC) example page 237

is constant, STC and TVC are straight lines AVC = SMC in this case

Short-run marginal cost (SMC) equation

is defined in the same manner as marginal cost is defined in the long run: the rate of change of short-run total cost with respect to the level of output. Arc short-run margial cost (SMC) between two levels of output can be found by dividing either the change in short-run total cost or the change in short-run total varable cost by the change in quantity: arc SMC = Change in TVC / Change in Q = Change in STC / Change in Q

Total variable cost (TVC)

is equal to P(l) * L

AVC

is equal to P(l) / AP(l) where AP is the average product of input l. In other words, AVC is the reciprocal of AP(l), multiplied by P(l) (Figure 6-9 example). This relationship makes sense because it must be true that if the average productivity of the variable input increases, there will be a corresponding fall in average variable cost. The new value of average variable cost, however will also be determined by the price of the input

Short-run average cost (SAC)

is equal to STC /Q = AVC + AFC

Average fixed cost (AFC)

is equal to TFC / Q

Short-run cost (STC)

is equal to TVC + TFC

Average variable cost (AVC)

is equal to TVC /Q

Long-run average cost (LAC) definition

is equal to long-run total cost divided by the level of output. It measures cost per unit of output when all inputs are variable

LAC for a particular level of output

is equal to the slope of the line segment drawn from the origin to LTC at that same level of output. The slope of this line must equal to LAC because its slope is equal to the change in the vertical distance divided by the change in the horizontal distance between any two points on the line. Between the origin and any other point on the long-run total cost curve, the vertical change is equal to the value of Q at that point. Thus the slope of the line is equal to LTC / Q which is the definition of long-run average cost.

Average fixed cost (AFC) definition

is fixed cost per unit of output in the short run. Average fixed cost is equal to total fixed cost divided by the level of output

Short-run total variable cost (TVC) equation

is given by P(l) * L is the variable input

Marginal Cost (MC)

is greater than average cost, AVC must be risign and when marginal cost is less than average variable cost, AVC must be falling. The same relationship must also hold for short-run average total cost and marginal cost

Incremental costs definition

is the additional cost that a firm will incur if it undertakes one more activity or if it takes one course of action rather than another

Short-run average total cost (SAC) definition

is the cost per unit of output in the short run. It is equal to short-run total cost divided by the level of output. It is also equal to average fixed cost plus short-run average variable cost for each level of output.

Long-run total cost (LTC) definition

is the minimum economic cost of producing each possible level of output when the time period is sufficiently long to change all inputs of the firms production function

Cost elasticity

is the percentage change in the long-run total cost form a 1 percent change in output E(c) = % change in LTC / % change in Q. IT measures the relative responsiveness of long-run total cost to change in the level of output.

Total fixed cost (TFC) definition

is the private economic cost of the firms fixed inputs in the short run. The TFC curve is a horizontal line since these costs do not vary with the level of output in the short run.

Short-run marginal cost (SMC) definition

is the rate of change of either short-run total variable cost as the level of output changes in the short run.

Long-run marginal cost (LMC) definition

is the rate of change of long-run total cost as the level of output change

Short-run total variable cost definition

is the sum of all private economic costs of the firm that vary with its level of output in the short run

Short-run total cost (STC) equation

is the summation (vertical) of TFC and TVC, or STC = TFC + TVC

Short-run average variable cost (AVC) definition

is the variable cost per unit of output produced in the short run. It is equal to short-run total variable cost divided by the level or output

Economies of scope

occur when its is cheaper for a firm to undertake two or more activities together than the sum of the costs that the firm would incur to pursue each activity separately

Economies of scope definition

occur when the average cost of undertaking two or more activities together is less than the sum of the costs of each activity separately

Social costs definitions

of a firm are the private costs of the resources that the firm uses plus and additional costs imposed on society by the firm's operation.

private costs

of a firm are the sum of the explicit and implicit costs that it incurs

social costs

of a firm are those that society in general bears because of the firms activities. Social costs would include the private costs of a firm, since presumably all of the firms resources could be used elsewhere in producing goods of value to society

Private costs definition

of a firm include all of the costs of resource use, both explicit and implicit, the firm must bear to produce its output

Average fixed cost (AFV) equation

or fixed cost per unit of output, if found by dividing a given dollar amount of fixed cost by larger and larger levels of output: AFC = TFC / Q

Long-run marginal cost

or the rate of change of long-run total cost with respect to output, at a particular quantity of output is given by the slope of the total cost curve at that output level.

Fixed cost

since fixed cost does not change in the short-run, the changes in STC and TVC must be equal. Therefore, arc short-run marginal cost measures the average rate of change in either total variable cost or total cost with respect to changes int eh level of output in the short run.

Short-run average variable cost (AVC) equation

variable cost per unit of output, is found by dividing short-run total variable cost by the corresponding level of output. AVC = TVC / Q

Marginal Cost = Average cost

when average cost is at a minimum because of the marginal-average relationship. When marginal cost is greater than average cost, average cost must be rising; and when marginal cost is less than average cost, average cost much be falling. Only when marginal cost is equal to average cost does average cost not change, and this happens only when average cost is at a minimum

Long-run average cost and returns to scale

when the firm experiences increasing returns to scale, LAC declines. When the firm has constant returns to scale, LAC is constant. When the firm has decreasing returns to scale, LAC is increasing

Economies of scale

which means that smaller unit costs can be obtained by producing with larger size plant than by producing at the minimum short-run average cost corresponding to a smaller plant size.

Formula for arc cost elasticity

E(c) = change in LTC / change in Q * Q(2) + Q(1) / LTC(2) + LTC(1)

LMC

In discrete terms, arc marginal cost is an approximation to marginal cost and is the average rate of change of total cost with respect to the quantity of output between two levels of output. Thus, marginal cost answers the question, "How much will production of one more unit of output cost the firm?" Arc long-run marginal cost (LMC) can be found by dividing the change in total cost by the change in the quantity of output, or Arc LMC = Change in LTC / Change in Q

LMC #2

LMC reaches it minimum where the slope of LTC reached its smallest value. LMC is equal to LAC when LAC is at a minimum

E(c) = 1

LTC changes by the same percentage as the percentage change in output. This is constant returns to scale

E(c) > 1

LTC increases by a larger percentage than the percentage increase in output. This is called dis-economies of scale

E(c) < 1

LTC increases by a smaller percentage than the percentage increase in output. This is economies of scale

Least cost combination of inputs for each level of output requires

MP(l) / P(l) = MP(k) / P(k)

Instantaneous short-run marginal cost

SMC = dTVC / dQ = dSTC / dQ Example STC = 1000 + 80Q - 6Q^2 + 0.2Q^3 then TVC = 80Q - 6Q^2 + 0.2Q^3 and SMC = dSTC / dQ = dTVC / dQ = 80 - 12Q + 0.6Q^2