Principles of Microeconomics Lecture 14 – Profit Maximisation
A firm uses inputs j = 1…,m to make products i = 1,…n.
Output levels are y1,…,yn.
Input levels are x1,…,xm.
Product prices are p1,…,pn.
Input prices are w1,…,wm.
The competitive firm takes all output prices p 1,…,pn and all input prices w1,…,wm as given constants.
The economic profit generated by the production plan (x 1,…,xm,y1,…,yn) is
o
Given the prices of inputs and output, and the available technology, the firm chooses the production plan
that maximises its profits
o Optimal amount of production factors
Short run vs Long run
o In a given period it can be difficult to adjust the amount of some inputs, e.g. some inputs in the short
run are fixed
A iso-profit line contains all the production plans that provide a profit level P.
A iso-profit line’s equation is
o
The firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the
firm’s constraint on choices of production plans.
At the short-run profit-maximizing plan, the slopes of the short-run production function and the maximal iso-
profit line are equal.
P x MP1 is the marginal revenue product of input 1, the rate at which revenue increases with the amount
used of input 1.
o If P x MP1 > w1 then profit increases with x1.
o If P x MP1 < w1 then profit decreases with x1.
The equation of a short-run iso-profit line is
so an increase in p causes
o a reduction in the slope, and
o a reduction in the vertical intercept.
An increase in p, the price of the firm’s output, causes
o an increase in the firm’s output level (the firm’s supply curve slopes upward), and
o an increase in the level of the firm’s variable input (the firm’s demand curve for its variable input
shifts outward).
An increase in w1, the price of the firm’s variable input, causes
o a decrease in the firm’s output level (the firm’s supply curve shifts inward), and
o a decrease in the level of the firm’s variable input (the firm’s demand curve for its variable input
slopes downward).
In the long run the firm is free to choose both x1 and x2 hence the profit maximization problem can be
expressed as:
o
The condition for the optimal choice is the same as before, e.g. the value of marginal product for each factor
must be equal to its price (solve the max problem using a Cobb-Douglas production function)
If a competitive firm’s technology exhibits decreasing returns-to-scale then the firm has a single long-run
profit-maximizing production plan.
If a competitive firm’s technology exhibits exhibits increasing returns-to-scale then the firm does not have a
profit-maximizing plan.
A firm uses inputs j = 1…,m to make products i = 1,…n.
Output levels are y1,…,yn.
Input levels are x1,…,xm.
Product prices are p1,…,pn.
Input prices are w1,…,wm.
The competitive firm takes all output prices p 1,…,pn and all input prices w1,…,wm as given constants.
The economic profit generated by the production plan (x 1,…,xm,y1,…,yn) is
o
Given the prices of inputs and output, and the available technology, the firm chooses the production plan
that maximises its profits
o Optimal amount of production factors
Short run vs Long run
o In a given period it can be difficult to adjust the amount of some inputs, e.g. some inputs in the short
run are fixed
A iso-profit line contains all the production plans that provide a profit level P.
A iso-profit line’s equation is
o
The firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the
firm’s constraint on choices of production plans.
At the short-run profit-maximizing plan, the slopes of the short-run production function and the maximal iso-
profit line are equal.
P x MP1 is the marginal revenue product of input 1, the rate at which revenue increases with the amount
used of input 1.
o If P x MP1 > w1 then profit increases with x1.
o If P x MP1 < w1 then profit decreases with x1.
The equation of a short-run iso-profit line is
so an increase in p causes
o a reduction in the slope, and
o a reduction in the vertical intercept.
An increase in p, the price of the firm’s output, causes
o an increase in the firm’s output level (the firm’s supply curve slopes upward), and
o an increase in the level of the firm’s variable input (the firm’s demand curve for its variable input
shifts outward).
An increase in w1, the price of the firm’s variable input, causes
o a decrease in the firm’s output level (the firm’s supply curve shifts inward), and
o a decrease in the level of the firm’s variable input (the firm’s demand curve for its variable input
slopes downward).
In the long run the firm is free to choose both x1 and x2 hence the profit maximization problem can be
expressed as:
o
The condition for the optimal choice is the same as before, e.g. the value of marginal product for each factor
must be equal to its price (solve the max problem using a Cobb-Douglas production function)
If a competitive firm’s technology exhibits decreasing returns-to-scale then the firm has a single long-run
profit-maximizing production plan.
If a competitive firm’s technology exhibits exhibits increasing returns-to-scale then the firm does not have a
profit-maximizing plan.
