ECON 295 - Chapter 5
The Role of the Manager in the Production Process
(1) to ensure that the firm operates on the production function: the maximum possible output that can be produced with given inputs. and (2) to ensure that the firm uses the correct level of inputs.
cubic cost function
Costs are a cubic function of output; provides a reasonable approximation to virtually any cost function
Cost minimization
Producing output at the lowest possible cost.
decreasing (diminishing) marginal returns
Range of input usage over which marginal product declines.
increasing marginal returns
Range of input usage over which marginal product increases.
negative marginal returns
Range of input usage over which marginal product is negative.
Average total cost (ATC)
total cost (TC) divided by the number of units of output
Average variable cost (AVC)
variable cost (VC) divided by the number of units of output
long-run average cost curve
A curve that defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production
Irrelevance of Sunk Costs
A decision maker should ignore sunk costs to maximize profits or minimize losses.
multiproduct cost function
A function that defines the cost of producing given levels of two or more types of outputs assuming all inputs are used efficiently.
production function
A function that defines the maximum amount of output that can be produced with a given set of inputs.
Isocosts
A line that represents the combinations of inputs that will cost the producer the same amount of money
average product
A measure of the output produced per unit of input Check the formula
Linear production function
A production function that assumes a perfect linear relationship between all inputs and total output inputs are perfect substitutes.
Cobb-Douglas production function
A production function that assumes some degree of substituability among inputs some degree of substitutability between the inputs, albeit not perfect substitutability.
Leontief production function (fixed-proportions production function)
A production function that assumes that inputs are used in fixed proportions
law of diminishing marginal rate of technical substitution
A property of a production function stating that as less of one input is used, increasing amounts of another input must be employed to produce the same level of output
Phases of Marginal Returns
As the usage of an input increases, marginal product initially increases (increasing marginal returns), then begins to decline (decreasing marginal returns), and eventually becomes negative (negative marginal returns).
Explain the deifference between the law of diminishing marginal returns and the law of diminishing marginal rate of technical substitution
Diminishing marginal returns is one of the three classical stages of production. It occurs in a firm when the total physical product of the firm strat increasing at decreasing rate, as the number of variable inputs is increased with the fixed ones. The marginal product in this stage keeps falling but remain positive. The marginal rate of technical substitution is the rate at which a firm can substitute between the two inputs while maintaining the same level of output. It is the absolute value of the slope of the isoquant and it is the ratio of the marginal products. For convex isoquants, the marginal rate of technical substitution falls as more variable input is used, This is known as the law of diminishing marginal rate of technical substitution. It is the property of the production function stating that s less of one input is used, increasing amounts of other input must be employed to produce the output to the same level.
economies of scale
Exist when long run average costs decline as output is increased.
Constant returns tot scale
Exist when long-run average costs remain constant as output is increased.
Dis-economies of scale
Exist when long-run average costs rise as output is increased
Changes in Isocosts
For given input prices, isocosts farther from the origin are associated with higher costs. Changes in input prices change the slopes of isocost lines.
the demand for coal is significantly lower than you expected. A farmer approaches you and offers to sublease the railcar from you for $2,000. If the terms of your lease permit you to sublease the railcar, should you accept the farmer's offer?
In this case your optimal decision is to sublease the railcar because doing so provides you with $2,000 in revenues that you would not get otherwise.
marginal product
The change in total output attributable to the last unit of an input. Check the formula
marginal (incremental) cost
The cost of producing an additional unit of output.
total product
The maximum level of output that can be produced with a given amount of inputs
the marginal rate of technical substitution (MRTS).
The rate at which a producer can substitute between two inputs and maintain the same level of output.
Value marginal product
The value of the output produce by the last unit of an input
Profit-Maximizing Input Usage
To maximize profits, a manager should use inputs at levels at which the marginal benefit equals the marginal cost. More specifically, when the cost of each additional unit of labor is w, the manager should continue to employ labor up to the point where VMPLw in the range of diminishing marginal product.
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
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: Equivalently, 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
cost complementarity
When the marginal cost of producing one type of output decreases when the output of another good is increased.
economies of scope
When the total cost of producing two types of outputs together is less than the total cost of producing each type of output separately.
Fixed cost
a cost that does not change when output changes.
sunk cost
a cost that is lost forever once it has been paid
the short run decision.
determine how much of each input to use to produce output. some factors of production are fixed, and this limits your choices in making input decisions. the time frame in which there are fixed factors of production. Q=f(L)+F(K*, L)
Average fixed cost (AFC)
fixed costs (FC) divided by the number of units of output
Isoquants
the combinations of inputs (K and L) that yield the producer the same level of output. any combination of capital and labor along an isoquant produces the same level of output.
Technology summarizes..
the feasible means of converting raw inputs, such as steel, labor, and machinery, into an output such as an automobile. Q=F(K,L)
The long run
the horizon over which the manager can adjust all factors of production.
short-run cost function
the minimum possible cost of producing each level of output when variable factors are being used in the cost-minimizing way.