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Chapter 20 Profit Maximisation (Long-Run Profit Maximisation (pMP1=w1 …
Chapter 20
Profit Maximisation
Perfect Competition
This chapter study the profit-maximising behaviour of a firm in a perfectly competitive market
same product, many producers, price-takers
Cost
The cost of input must account for
opportunity costs
- what every input could otherwise receive in the market if it were not employed in this firm
Short-Run Profit Maximisation
If x2 is fixed at short run
The profit function
π=pf(x1,x2)-w1x1-w2x2
The only choice variable in the SR is x1 (x2 is fixed).
First order condition
This gives
Graphical Representation
From
we can derive the
Iso-profit line
The iso-profit line is a line that connects all combination of x1 and y that yields the same level of profit
And the technological constraint is given by the production function f(x1,x2)
The highest profit line (corresponding the highest profit) will be one that is tangent to the production function. At the tangency, the slopes are equal
MP1=w1/p
, which is our first-order condition from the profit maximisation problem
Long-Run Profit Maximisation
pMP1=w1
pMP2=w2
The firm will choose each input level so that the value of that input's marginal product equals its cost
Solving these two equations for x1 and x2 gives us the firm's
factor demands
- functions that tell us how much of each factor the form will demand as a function of output price p and factor price w1,w2
Substituting the factor demands into the production will give us
y(p,w1,w2)
- the firm's profit maximising output choice, as a function of output price and input prices
At the optimum, the value of the marginal product of a factor must equal its cost
