Ch. 8 – Besanko
Q: How do costs change when output Q increases?
Answer: Long-Run Cost Curves.
LRTC shows how TC varies with output Q holding input prices fixed and
choosing inputs to minimize costs.
Graph of LRTC curve
Plot the LRTC curve from the LR cost minimization problem.
1. LR total cost demoted by TC(Q) shows how minimized total cost varies with
output, holding input prices fixed and and selecting inputs to minimize
Note: When Q=0, LRTC=0. Example 1: Finding the LRTC
L* and K* are the input demand functions, which solve the LR cost
TC = wL* + rK* rQ 1/2 wQ 1/2
TC = w (w) + r ( )r
½ ½ 1/2
TC = 2w r Q
The expression above is the LRTC curve and it tells you how TC vary with w,r,
and Q, the exogenous variables.
One input price changes : Q: How does LR cost vary when 1 input price changes?
-An increase in the price of an input rotates the TC curve upward.
C1 is the initial isocost line. It pivots down to C2 when the price of K rises.
However, to keep production at 1 million TV’s per year, the isocost line shifts
out to the isoquant Q= 1million, but this shift means that TC must increase
to produce the same quantity as before the price change.
-The new TC curve lies above the original TC for every Q>0 and equals 0 when
All input prices change by same percentage : What happens when input
prices all change proportionately?
-A given percentage increase in both inputs prices leaves the cost-minimizing
input combination unchanged, while the TC curve shifts up by exactly the same
percentage. LRMC and LRAC: What are the long run marginal cost and long-run average cost
AC(Q) = TC(Q) /Q
=slope of ray from origin to point on TC curve
=TC per unit ofoutput MC(Q) = ΔTC/ΔQ
= slope of TC curve at a particular output level.
=rate at which TC changes with respect to a change in Q.
Graph: Relationship between TC, AC, and MC.
How do we find LRAC from the graph?
What is LRMC?
Example 2: Derive LRMC and LRAC from TC.
TC = 2w r Q from Ex. 1
AC = TC/Q = 2w ½ r½ Q /Q = 2w ½r ½Q -1/2
½ ½ -1/2
MC = dTC/dQ =2w r Q AC,MC relationships:
LRAC relationship to Economies and Diseconomies of Scale
Typical LRAC curve for a firm is U-shaped. Why? Where are the economies of scale on this graph? Diseconomies of scale?
Economies of Scale = declining LRAC. Usually due to specialization or
Diseconomies of scale = increasing LRAC. Usually due to managerial
Where is the MES?
Minimum Efficient Scale = the smallest quantity at which the LRAC curve
attains its minimum point.
The larger the MES in comparison to overall market sales, the larger the
economies of scale.
Breakfast cereals have high MES as a percentage of output = 9.47.
Mineral water has a low MES as a percentage of output = 0.08.
Relationship of Economies of Scale and Returns to SCALE Output Elasticity of TC can be used to measure Economies of Scale
Output elasticity of TC = percentage change in TC when output increases
=% change in TC/ percentage change in Q SRTC Curve
A. SR – L is variable and K is fixed.
is the total fixed cost (TFC), which is constant at all levels of output.
Example 3: Deriving the SRTC curve
To derive the SRTC curves, substitute the L demand into TC remembering that K is fixed
in the S