Profit Maximisation and Scale of Production Flashcards
(16 cards)
What is the primary objective of firms in standard micro theory?
Profit maximisation, where
Π=Revenue−Cost
How are revenue and cost defined?
Revenue = p⋅f(K,L)
Cost = wL+rK
Where p = output price, w = wage, r = rental rate of capital
What input choices are made in short vs long run?
Short run: Capital fixed, choose 𝐿
Long run: Choose both L and K
What are the first-order conditions for optimal input use?
Short run:
p⋅MP L =w
Long run:
p⋅MP L =w and p⋅MP K=r
What does p⋅MP L=w mean intuitively?
The value of the additional output from one more worker equals the cost of hiring them.
What is an iso-profit line?
A line showing input-output combinations yielding the same level of profit; analogous to an indifference curve.
What is the tangency condition for profit maximisation?
The firm chooses the point where the iso-profit line is tangent to the production function — just like utility maximisation.
What happens when the wage w increases in the short run?
Firm hires less labour → output and profits fall.
What happens if the output price 𝑝 drops?
Profits fall, iso-profit lines rotate inwards → firm reduces input use and output.
What are returns to scale?
How output responds when all inputs are scaled by the same proportion:
Increasing RTS: Output more than doubles
Constant RTS: Output doubles
Decreasing RTS: Output less than doubles
How do we use Cobb-Douglas to determine returns to scale?
If
F(K,L)=K^αL^β:
If α+β>1: Increasing RTS
If α+β=1: Constant RTS
If α+β<1: Decreasing RTS
Are returns to scale the same as diminishing marginal returns?
No. Returns to scale involve scaling all inputs, while diminishing returns hold one input fixed and increase the other.
Why do returns to scale matter for industry structure?
Increasing RTS: Favour few large firms (e.g., monopolies or oligopolies)
Decreasing RTS: Favour many small firms
Do perfect substitutes and fixed proportions exhibit returns to scale?
Yes — depending on the coefficients, we can assess RTS using the scaling method (see function forms in Topic 8).
Why might a firm not immediately adjust all inputs when prices change?
In the short run, some inputs (like capital) are fixed — full adjustment happens only in the long run.
What happens if the rental rate 𝑟 increases?
Short run: No change in capital use
Long run: Firm substitutes away from capital → uses more labour → re-optimises input mix
