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isoquant
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curve showing all possible combinations of inputs that yield the same output
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total product function
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a production function. A total product function with a single input shows how total output depends on the level of the input
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average product function
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output per unit of a particular input
- average product of labor is given by the slope of the line drawn from the origin to the corresponding point on the total product curve
- average product of labor is given by the slope of the line drawn from the origin to the corresponding point on the total product curve
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marginal product function
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additional output produced as an input is increased by one unit
- the marginal product of labor at a point is given by the slope of the total product at the point
- the marginal product of labor at a point is given by the slope of the total product at the point
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marginal rate of technical substitution
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amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant
- similar to marginal rate of substitution
- diminishes as you move down an isoquant
- the marginal rate of technical substitution between two inputs is equal to the ratio of the marginal products of the inputs
- similar to marginal rate of substitution
- diminishes as you move down an isoquant
- the marginal rate of technical substitution between two inputs is equal to the ratio of the marginal products of the inputs
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lower ridge line
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- implies zero marginal productivity of capital
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upper ridge line
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- implies zero marginal productivity of labor
- production techniques are only efficient inside the ridge lines
- production techniques are only efficient inside the ridge lines
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decreasing returns to a fixed factor
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increasing returns to a fixed factor
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constant returns to a fixed factor
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law of diminishing returns factor
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principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease
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decreasing returns to scale
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situation in which output less than doubles when all inputs are doubled
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increasing returns to scale
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situation in which output more than doubles when all inputs are doubled
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constant returns to scale
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situation in which output doubles when all inputs are doubled
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long run expansion path
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- curve passing through points of tangency between a firm's isocost lines and its isoquants
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short run expansion path
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Horizontal line showing the cost-minimizing input combinations for various output levels when capital is fixed in the short run.
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long run total cost function
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relates minimized total cost to output, Q, and to the factor prices (w and r)
- derived from the the long run expansion path
- derived from the the long run expansion path
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long run average cost function
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curve relating average cost of production to output when all inputs, including capital, are variable
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long run marginal cost function
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- curve showing the change in long run total cost as output is increased incrementally by 1 unit
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economies of scale
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situation in which output can be doubled for less than a doubling of the cost
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diseconomies of scale
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situation in which a doubling of output requires more than a doubling of the cost
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constant economies of scale
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total fixed cost function
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total variable cost function
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average fixed cost function
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average variable cost function
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short run total cost function
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short run average cost function
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short run marginal cost function
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Does the total product of labor function exhibit decreasing (marginal) returns to the fixed factor k? why or why not?
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- if k <0 = decreasing returns to scale
- if k > 0 = increasing returns to scale
- if k = 0 = constant returns to scale
- if k > 0 = increasing returns to scale
- if k = 0 = constant returns to scale
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Does the production function exhibit increasing returns to scale? why or why not?
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alpha squared > 1 = increasing returns to scale
0<alpha squared<=1 = decreasing returns to scale
0<alpha squared<=1 = decreasing returns to scale
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what are the relationships among marginal products, the marginal rate of technical substitution, and the slopes of isoquants?
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MP - Marginal Product = change in total product or output due to employment of an additional unit of input
MRTS - amount by which one input has to be reduced when other input is increased to keep the output constant
slope of isoquant - is MRTS as it represents constant output ...
.. so, slope of isoquant = MRTS and MRTS = ratio of Marginal product of inputs
slope of isoquant = MRTS = ratio of MP
MRTS - amount by which one input has to be reduced when other input is increased to keep the output constant
slope of isoquant - is MRTS as it represents constant output ...
.. so, slope of isoquant = MRTS and MRTS = ratio of Marginal product of inputs
slope of isoquant = MRTS = ratio of MP
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without referring to costs or the expansion path, explain why a profit maximizing firm will always produce its output with a basket of inputs that lies between the ridge lines (assuming they are present) up to the point of intersection if there is one
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ridge lines are the locus points of isoquants where the marginal products of factors are zero --
upper = MP of capital = 0
lower = MP of labor = 0
production techniques are only efficient within these ridge lines, not outside
marginal products of factors are negative outside the ridge lines so therefore a profit maximizing firm would not produce its output with a basket of inputs that lies outside of the ridge lines
upper = MP of capital = 0
lower = MP of labor = 0
production techniques are only efficient within these ridge lines, not outside
marginal products of factors are negative outside the ridge lines so therefore a profit maximizing firm would not produce its output with a basket of inputs that lies outside of the ridge lines
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Why does the assumption of profit maximization imply that the firm will produce each output with a basket of inputs that minimizes cost
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if you minimize cost you will be maximizing profit because any higher cost than the minimum cost would not achieve a maximum profit
profit is revenue - cost
profit is revenue - cost
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explain why the cost minimization for each level of output implies that the firm hires that basket of inputs for which
- the marginal rate of technical substitution equals the input price ratio
- the marginal products per dollar of the two inputs are equal
- diagram
- the marginal rate of technical substitution equals the input price ratio
- the marginal products per dollar of the two inputs are equal
- diagram
answer
see scrap paper
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explain how in a two input world, the long run total cost function is derived from the firm's production function or isoquant map
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see scrap
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explain how in a two input world, the short run total cost function is derived from the firm's production function or isoquant map
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see scrap
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describe the relationship between the firm's long run and short run total cost curves and explain how the short run curve can be tangent to the long run curve
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describe the relationship between the firm's long run and short run average cost curves and between the firm's long and short run marginal cost curves, and explain why that relationship occurs
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i do not know wtf this is
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describe the relationship between the different kinds of returns to scale and the different kinds of economies of scale
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see vocab above
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draw a diagram with cost curves illustrating the relationship between long run and short run total cost curves. Explain the tangence's between the long run and short run total cost curves in this diagram using another diagram containing isoquants and the expansion path
answer
same as before
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