Cost Minimisation and Cost Curves Flashcards
(16 cards)
What is the firm’s cost minimisation problem?
Minimise cost given an output target:
(on formula sheet)
What is an isocost line?
A line showing all combinations of inputs that cost the same:
wL+rK=C
Slope:
−𝑤/𝑟
What is the tangency condition for cost minimisation?
MP L/MP K= w/r
MRTS = ratio of input prices
What does MP L/w = MP K/r mean
The firm equalises the marginal output per £ spent across inputs — otherwise it could lower cost by reallocating spending.
What are conditional input demand functions?
The optimal input quantities 𝐿∗
and 𝐾∗given output level 𝑌 and input prices — they solve the cost minimisation problem.
What is a cost function?
Minimum cost of producing output Y given prices:
C(Y;w,r)=wL∗+rK∗
What’s the cost function under F(K,L)=K^αL^1−α?
C(Y;w,r)=A⋅Y⋅w^1−αr^α
Where A is a constant derived from the optimisation.
What’s the key difference between short-run and long-run cost functions?
Short-run: At least one input is fixed → less flexibility
Long-run: All inputs variable → costs are fully minimised
What are key properties of the cost function?
Increasing in output
Non-decreasing in input prices
Concave in input prices
Homogeneous of degree 1 in prices
What is the expansion path?
The set of cost-minimising input bundles as output expands — traces out how optimal input mix changes as firm scales up.
How do returns to scale relate to cost behaviour?
Increasing RTS → Decreasing average cost
Constant RTS → Constant average cost
Decreasing RTS → Increasing average cost
What shapes are typical for long-run cost curves?
LAC (long-run average cost): U-shaped
LMC (long-run marginal cost): Cuts LAC at its minimum
How does marginal cost relate to supply?
In perfect competition, the firm’s supply curve is its MC curve above AVC (or AC in the long run).
When does a firm shut down in the short run?
When price < AVC — it cannot cover variable costs.
How do you find the profit-maximising output from cost functions?
Set p=MC(Y) and solve for 𝑌*.
Then calculate:
Π=pY ∗−C(Y∗)
