Microeconomics exam revision notes

XVI. Short-run & long-run cost minimisation
- Difference long run & short run
o Long run: firm able varying all inputs levels
o Short run: firm only able varying labour level ≠ capital level  capital level
fixed K
- Comparing short-run & long-run costs of producing y output units
XVI. a. The short-run & long-run cost minimisation problems
- Long-run cost minimisation problem
min wL+ vK
L≥0 , K ≥ 0


subject to f ( L, K ) = y


- Short-run cost minimisation problem
min wL +v K
L≥0


subject to f ( L, K ) = y
- Single variable input  ≠ substitutability between inputs
- Level of capital fixed at K  production function only in one variable
- Algebra solution: finding conditional demand for labour (see slide for example)
o ≠ possible optimisation considering only two inputs including fixed capital K
o Inverse production function:
c −1
L (K , y)=f ( K , y )
- Firm’s short run total cost function
c
C s ( w , v , y , K ) =w L ( K , y)+ v K
−1 2
C s ( w , v , y , K ) =w K y +v K

o Fixed costs: F=v K
o Variable costs: C v ( w , y , K ) =¿ w K −1 y 2

 Short-run cost minimisation problem = long-run cost minimisation problem
subject to additional constraint of fixed capital level K=¿ K
o Note: case of long-run cost minimising level of capital K = K for producing y
output units  additional constraint K=¿ K ≠ actually constraining  short-
run & long-run costs of producing y output units identical
o Note: case of long-run cost minimising level of capital K ≠ K for producing y
output units  extra constraint K= K preventing firm in short-run from
achieving long-run production cost  short-run total cost > long-run total
cost of producing y output units

1) Long-run costs