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Production function
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a function that defines the maximum amount of output that can be produced with a given set of inputs
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Short-run
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period of time where some factors of production (inputs) are fixed and constrain a manager's decisions
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Fixed inputs
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inputs a manager cannot adjust in the short run
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Long-run
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period of time over which all factors of production (inputs) are variable and can be adjusted by a manager
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Variable inputs
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inputs a manager can adjust to alter production
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Total product (TP)
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maximum level of output that can be produced with a given amount of inputs
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Average product (AP)
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a measure of the output produced per unit of input
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Marginal product (MP)
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the change in total output attributable to the last unit of an input
- negative marginal product means that the last unit of input actually reduced total product
- negative marginal product means that the last unit of input actually reduced total product
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Increasing marginal returns
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range of input usage over which marginal product increases
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Decreasing/diminishing marginal returns
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range of input usage over which marginal product declines
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Negative marginal returns
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range of input usage over which marginal product is negative
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Role of a Manager in the Production Process
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- produce output on the production function (by aligning incentives to induce maximum worker effort)
- use the right mix of inputs to maximize profits
- use the right mix of inputs to maximize profits
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To maximize profits when labor or capital vary in the short run, the manager will hire:
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- labor(L) until the value of the MPL = wage rate
- capital (K) until the value of the MPk = rental rate
- capital (K) until the value of the MPk = rental rate
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Value marginal product
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value of the output produced by the last unit of an input
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Law of diminishing returns
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the marginal product of an additional unit of output will at some point be lower than the marginal product of the previous unit
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Profit-maximization input usage
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to maximize profits, use input levels at which MB = MC
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Linear production function
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a production function that assumes a perfect linear relationship between all inputs and total output
- inputs are perfect substitutes
- inputs are perfect substitutes
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Leontief production function
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a production function that assumes that inputs are used in fixed proportions
- also called "Fixed-proportions production function"
- also called "Fixed-proportions production function"
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Cobb-Douglas production function
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a production function that assumes some degree of substitutability among inputs
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Isoquants
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capture the tradeoff between combinations of inputs that yield the same output in the long run, when all inputs are variable
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Isocost
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combination of inputs that yield the same cost
- isocosts farther from the origin are associated with higher costs
- changes in input prices change slopes of isocost lines
- isocosts farther from the origin are associated with higher costs
- changes in input prices change slopes of isocost lines
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Marginal rate of technical substitutions (MRTS)
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the rate at which a producer can substitute between two inputs and maintain the same level of output
- absolute value of the slope of the isoquant
- absolute value of the slope of the isoquant
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Cost minimization
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producing output at the lowest possible cost
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Cost Minimizing input rule
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produce at a given level of output where the marginal product per dollar spent is equal for all inputs
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Optimal input substitution
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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
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Fixed costs (FC)
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do not change with changes in output, include the costs of fixed inputs used in production
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Variable costs - VC(Q)
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costs that change with changes in outputs, include the costs of inputs that vary with output
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Total costs - TC(Q)
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FC + VC(Q)
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Short-run cost function
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a function that defines the minimum possible cost of producing each output level when variable factors are employed in the cost-minimizing fashion (sum of fixed and variable costs)
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Long-run costs
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- all costs are variable
- no fixed costs
- no fixed costs
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Average fixed cost (AFC)
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FC/Q
- average fixed costs decline continuously as output is expanded
- average fixed costs decline continuously as output is expanded
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Average variable cost (AVC)
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VC/Q
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Average total cost (ATC)
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TC/Q
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Marginal (incremental) cost (MC)
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the change in total costs arising from a change in the managerial control variable Q
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Sunk cost
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a cost that is forever lost after it has been paid
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Irrelevance of sunk costs
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a decision maker should ignore sunk costs to maximize profits or minimize losses
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Cubic cost function
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costs are a cubic function of output; provides a reasonable approximation to virtually any cost function
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Long-run average cost curve
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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
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Economies of scale
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declining portion of the long-run average cost curve as output increases
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Diseconomies of scale
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rising portion of the long-run average cost curve as output increases
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Constant returns to scale
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portion of the long-run average cost curve that remains constant as output increases
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Multiproduct cost function
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a function that defines the cost of producing given levels of two or more types of outputs assuming all inputs are used efficiently
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Economies of scope
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exist when the total cost of producing two products within the same firm is lower than when the products are produced by separate firms
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Cost complementarity
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when the marginal cost of producing one type of output decreases when the output of another good is increased
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Total product per worker is called
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Average product of labor
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Suppose a firm expands its output and experiences lower long-run average cost.
What is this condition called?
What is this condition called?
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Economies of scale
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Suppose it is cheaper for an auto maker to produce hybrid vehicles and diesel SUVs in the same factory than it is to have two separate facilities for each vehicle.
What conditions exists?
What conditions exists?
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Economies of scope
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Which function defines the cost of producing at least two types of output?
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Multiproduct cost function