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