Chapter 5: The production process & costs

If it takes a company 3 years to acquire additional capital machines, what is the long run for its management?

3 years

Automated Labs uses 5 workers and 200 machines to produce a product. The MP of the last worker is 2 units of output/day. The MP of the last machine is 400 units of output/day. Workers are each paid $100/day, and the rental price of the machine is $300/day. What is the MP per dollar spent on a machine?

= MP capital / r = 400/300 = 1.33

Automated Labs uses 5 workers and 200 machines to produce a product. The MP of the last worker is 2 units of output/day. The MP of the last machine is 400 units of output/day. Workers are each paid $100/day, and the rental price of the machine is $300/day. What is the MP per dollar spent on a worker?

= MP labor / w = 2/100 = .02

If you pay non-refundable tuition fees of $1,000, books cost $200, it costs you $2.00 in bus fare to get to class, and then the bookstore will buy back your books for $100 at the end of the semester, what are the variable costs?

= cost each time you visit class = $2.00

If you pay non-refundable tuition fees of $1,000, books cost $200, it costs you $2.00 in bus fare to get to class, and then the bookstore will buy back your books for $100 at the end of the semester, what are the sunk costs?

= fixed costs - sell back books (money getting back) = 1,200 - 100 = $1,100

If you pay non-refundable tuition fees of $1,000, books cost $200, it costs you $2.00 in bus fare to get to class, and then the bookstore will buy back your books for $100 at the end of the semester, what are the fixed costs?

= tuition + books = $1,000 + 200 = $1,200

Linear production function equation

Q = F(K,L) = aK + bL

Leontief production function equation

Q = F(K,L) = {aK, bL}

Production function

an engineering relation that defines maximum amount of output that can be produced with a given set of inputs Q = F ( K,L)

Linear isoquant on graph

are linear (looks diangle to the right from top to bottom)

Accounting costs

are the costs most often associated with the costs of producing & appear on income statement (direct payments to labor & capital to produce output)

Variable factors of production

are the inputs a manager can adjust to alter production

Fixed factors of production

are the inputs the manager can't adjust in the short run

Law of diminishing marginal rate of technical substitution (MRTS)

as less of one input is used, increasing amounts of another input must be employed to produce the same level of output

ATC and AVC curves get closer together

as output increases

Linear production function

assumes a perfect linear relationship between all inputs and total output

Cobb-Douglas production function

assumes some degree of substitutability among inputs

Leontief production function (fixed-proportions production)

assumes that inputs are used in fixed proportions

C is the

cost function

Marginal (incremental) cost

cost of producing an additional unit of output = change in C / change in Q

Changes in input prices change the slopes of what?

isocost lines

The linear production function exhibits what?

isoquants with a constant marginal rate of technical substitution

If it takes a company 3 years to acquire additional capital machines, what is the short run for its management?

less than 3 years

Leontief isoquant on graph

looks like L shape

Automated Labs uses 5 workers and 200 machines to produce a product. The MP of the last worker is 2 units of output/day. The MP of the last machine is 400 units of output/day. Workers are each paid $100/day, and the rental price of the machine is $300/day. Is Automated Labs utilizing workers and machines in the cost-minimizing manner?

no, because MP per dollar spent on machines exceeds that on labor, so Automated Labs is using too many workers & too few machines to minimize cost of production

Does a Leontief production function have MRTS?

no, because there is no substitution among inputs along an isoquant

Cost minimizing

producing output at the lowest cost possible

Cubic cost function

provides a reasonable approximation to virtually any cost function

Marginal product initially increases and then

reaches a maximum, and then decreases

r is the

rental price (price of capital)

Isocost line

represents the combinations of inputs that will cost the producer the same amount of money

To maximize profits, what should a manager do?

should use inputs at levels at which the marginal benefit = marginal cost MB = MC

Total cost (TC)

sum of fixed and variable costs

Marginal rate of technical substitution (MRTS)

the rate at which a producer can substitute between 2 inputs and maintain the same level of output

Value marginal product

the value of the output produced by the last unit of an input

Average total cost (ATC)

total cost divided by the number of units of output = C(Q) / Q

Average variable cost (AVC)

variable costs divided by the number of units of output = VC(Q) / Q

w is the

wage rate (price of labor)

Negative marginal return

the range of input usage over which marginal product is negative

AFC =

ATC - AVC

Isocost function

C = wL + rK

What 2 inputs are used during the production process to produce output?

Capital (K) and Labor (L)

Sunk cost

a cost that is forever lost after it has been paid

To minimize the cost of production,

a firm should employ inputs such that the marginal rate of technical substitution is equal to the ratio of input prices MP of labor / MP of capital = w / r

Slope =

change in K / change in L

C (Q) denotes the

cost to the firm of producing isoquant Q in the cost-minimizing

Variable costs VC(Q)

costs that change with changes in output; include the costs of inputs that vary with outputs

Fixed costs (FC)

costs that do not change with changes in output; include the costs of fixed inputs used in production

Long-run average cost curve (LRAC)

define the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production

Short-run cost function

defines the minimum possible cost of producing each output level when variable factors are employed in the cost-minimizing fashion

Economies of scale

exist when long-run average costs decline as output is increased (left of the U curve on graph)

Constant return to scale

exist when long-run average costs remain constant as output is increased (3 U curves overlap on graph, middle points of each U curves is on the LRAC line)

Diseconomies of scale

exist when long-run average costs rise as output is increased (right of the U curve on graph)

Average fixed cost (AFC)

fixed costs divided by the number of units of output = FC / Q

For given input prices, isoscosts farther from the origin are associated with

higher costs

As the usage of an input increases, marginal product initially ____, then begins to ____, and eventually becomes negative (negative marginal returns).

increases (increasing marginal returns), declines (decreasing marginal returns)

Average product (AP)

is a measure of the output produced per unit of input

Long run

is the horizon over which the manager can adjustable factors of production

Total product (TP)

is the maximum level of output that can be produced with a given amount of inputs

Short tun

is the time frame which there are fixed factors of production (only the function of labor)

Marginal product (MP)

the change in total output attributable tot he last unit of an input

Isoquant

the combinations of inputs that yield the same level of output

Optimal input substitution: To minimize the cost of producing a given level of output,

the firm should use less of an input and more of other inputs when that input's price rises

Linear production function implies isoquants are linear because

the inputs are perfect substitutes for each other and the rate at which the producer can substitute between the inputs is independent of the level of input usage

What does a negative marginal product mean?

the last unit of the input actually reduced the total product

Q is

the level out output produced in the production process

The minimum average cost of producing alternative levels of output, allowing for optimal section of all variables of production, is defined by

the long run average total cost (ATC) curve

Leontief production function implies isoquants are not linear because

the manager can't substitute between capital and labor and maintain the same level of output

Cost-minimizing input rule: To minimize the cost of producing a given level of output,

the marginal product per dollar spent should be equal for all inputs MP of labor / w = MP of capital / r

Decreasing (diminishing) marginal returns

the range of input usage over which marginal product declines

Increasing marginal returns

the range of input usage over which marginal product increases