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Law of Diminishing (Marginal) Return
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As use of an input increases, when levels of other inputs are held fixed, increases in output will fall in magnitude
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Marginal Rate of Technical Substitution
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L for k = rate at which the production function for labor to be substituted for capital (MPL/MPK)
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IQ Map
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Set of all possible isoquants
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Isoquants
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curve showing all the input combinations to produce the same quantity of output
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Uneconomic Region
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When output decreases as labor increases (MPL<0)
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Average Product of Labor
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Q/L
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Marginal Product of Labor
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dQ/dL
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When does APL rise?
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MPL>APL
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When does APL fall?
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MPL<APL
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When is APL stationary?
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MPL=APL
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Perfect Substitutes
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MRST is constant
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No Input Substitution
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Creates L shaped isoquant:
1. MRTS = 0 on horizontal portion
2. MRTS = infinity on vertical portion
3. MRTS = undefined at corner point
1. MRTS = 0 on horizontal portion
2. MRTS = infinity on vertical portion
3. MRTS = undefined at corner point
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Elasticity of Substitution for Inputs
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Tells us how easy it is to substitute one good for another
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Increasing Returns to Scale (IRS)
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When output rises more than proportionately
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Constant Returns to Scale (CRS)
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When output rises proportionately
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Decreasing Returns to Scale (DRS)
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When output rises less than proportionately
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Returns to Scale
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How output changes when all inputs are varied by the same proportion
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Cobb-Douglas Production
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Q = K^aL^b
If (a+b) > 1 then IRS
If (a+b) = 1 then CRS
If (a+b) < 1 then DRS
If (a+b) > 1 then IRS
If (a+b) = 1 then CRS
If (a+b) < 1 then DRS
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Economic Cost
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accounting cost + implicit cost - sunk costs
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Accounting Cost
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costs that involve a direct monetary outlay
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Marginal Cost
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increase in total or variable costs associated with prodding an additional unit of output
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Average Total Cost
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total cost per unit of output
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Average Variable Cost
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variable cost per unit of output
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Average Fixed Cost
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fixed cost per unit of output
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MC (Q) =
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(dAC(Q)/dQ)(Q)+AC(Q)
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When MC > AC(AVC)
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AC(AVC) is rising
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When MC = AC(AVC)
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dAC(Q)/d(Q) = 0 or dAVC(Q)/d(Q) = 0
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When MC < AC(AVC)
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AC(AVC) is falling
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Total Product of Labor Curve
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-Q on Y axis and L on X axis
-Convex = IMR
-Concave = DMR
-Convex = IMR
-Concave = DMR
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Labor Requirement Curve
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-Q on X axis and L on Y axis
-Concave = IMR
-Convex = DMR
-Concave = IMR
-Convex = DMR
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Variable Cost Curve
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-$/Q on Y axis and Q on X axis
-slope = MC (Q) = W/MPL
-W inc. = MC dec.
-MPL inc = MC dec.
-MC intersects AVC(Q) at AVC(Q)'s min. point
-slope = MC (Q) = W/MPL
-W inc. = MC dec.
-MPL inc = MC dec.
-MC intersects AVC(Q) at AVC(Q)'s min. point
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Long Run Total Cost =
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wL+rk
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Slope of Total Cost
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-w/r
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MPL/W = MPK/r
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Increase in output from spending another dollar
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The area under the MC captors what
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Variable Cost
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Shapes of MC, AVC, ATC are determined by what
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Marginal Returns to Labor
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MC(Q) =
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-dAVC(Q)/d(Q)
-(w)(dL(Q,K)/dQ)
-(w)(1/MPL)
-(w)(dL(Q,K)/dQ)
-(w)(1/MPL)
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Negative sloped expansion path means...
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good on X axis is inferior and good on Y axis is normal
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What does it mean when the slope of the isocost line becomes steeper?
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increase in wage rate
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Relationship between isocost line and substitution
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Steep slope signals it is hard to substitute, while a flat slope signals it is easy to substitute
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Long Run Total Cost ...
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can never be larger than short-run total cost of producing the same output (LRTC(Q) less than or equal to SRTC(Q))
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Total Cost Curve
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-Concave = IRS
-Convex = DRS
-Convex = DRS
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Increasing output in short run vs long run
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To increase output in the short run you must increase labor as capital is held constant, but in the long run you can increase capital and decrease labor to reduce costs
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Relationship between LRTC(Q) and SRTC(Q)
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LRTC(Q) forms a lower envelope of the SRTC curve
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Relationship between LRAC(Q) and SRAC(Q)
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-LRAC(Q) less than or equal to SRAC(Q)
-both are U-shaped
-LRAC(Q) and LRMC(Q) are both u-shaped and LMAC(Q) intersects LRAC(Q) at LRAC(Q)'s min. point
-both are U-shaped
-LRAC(Q) and LRMC(Q) are both u-shaped and LMAC(Q) intersects LRAC(Q) at LRAC(Q)'s min. point
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Relationship between LRMC(Q) and SMAC(Q)
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SRMC(Q) intersects LRMC(Q), but the LRMC(Q) curve does not form a lower envelope of the SRMC(Q) curve
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Deriving the Demand Function
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-MRTS = w/r = MPL/MPK
-Q =
-Q =
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d(labor demand function)/dw < 0
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demand curve for labor is negatively sloped (w inc. and L dec.)
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d(capital demand function)/dr < 0
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demand curve for capital is negatively sloped (r inc. and L dec.)
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Economies of Scale vs Diseconomies of Scale
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-negative slope of LRAC(Q) = economies of scale (IRS)
-positive slope of LRAC(Q) = diseconomies of scale (DRS)
-slope of 0 of LRAC(Q) = neither (CRS)
-positive slope of LRAC(Q) = diseconomies of scale (DRS)
-slope of 0 of LRAC(Q) = neither (CRS)
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Economies of Scope
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A production characteristic in which the total cost of producing given quantities of two goods in the same firm is less than the total cost of producing those quantities in two single-production firms
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Economies of Experience
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Cost advantages that result from accumulated experience, or as it is sometimes called, learning-by-doing.
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