term 2 lecture 2 - profit maximisation Flashcards
in the short run, what is constrained for the firm?
the technology cannot be changed in the short run ( the firm is stuck with the technology it got even if its not state of the art)
some factors of production cannot be adjusted upwardly,downwardly or both ways
what is constrained in the long run?
every aspect of technology can be potentially changed
all inputs can be freely adjusted
what is an example of an input which can adjust downwardly but not upwardly?
In the US an employee can be fired in a moment’s notice. But hiring a worker requires a minimum amount of time
what is an example of an input which can adjust upwardly but not downwardly?
Unions object to redundancy, but new staff can be hired from temporary labour markets
what is the defintion of the long run?
every input can be adjusted and the best technology can be aqquired
what is the key assumption of price takers?
the firms have no market power, we assume that our firm is a profit maximised but it cannot change the price of the product and the prices of any inputs
what are the properties of the short run input demand functions
for any technology, the following must be true:
- input demand is increasing in the product price and decreasing in the own input price
- if p and w1 increase by the same proportion, input demand does not change ( homogenous of degree zero in p and w1)
input demand changes if the real input price (w1/p) changes
what is the short run function for input demand on an x1 -p graph?
it is an increasing function where slope starts of flat then increases to a vertical line . the positive side of the x^2 fucntion
what does the short run fucntion for output supply look like on the y - p graph?
it is an postive slope which starts of steep and then gets flatter. opposite of the x^2 diagram
what does the short run function of profit look like for a profit - price graph?
the profit has a negative intercept but is an increasing function that slopes upwards starting steep then flattens out
what are the properties of a proft function?
for all profit functions:
-profit is a convex and increasing function of output price
- if all input prices and the output price are doubled, profit is also doubles (homogenous of degree 1)
why for short run profit functions, price has to be above a critical level to make positive profit?
the price has to be above a critical level because some inputs are fixed
if a + b =1/2 for the cobb douglas function, then what must the output supply function be?
the output supply function must be linear in the output price
what are the properties of the long run profit function?
profit is homogenous of degree 1 in p w1 and w2
partial differential of profit with respect to price is equal to the output
partial differential of profit with respect to w1 is equal to negative x1(w1,p,w2) equation and partial differential of profit with respect to w2 is equal to -x2 (w1,p,w2) equation
long run profit cannot be smaller than the short run profit [ because of fixed input in the short run
how does long run profit function compare to the short run profit function?
long run profit cannot be smaller than the short run profit because of fixed input in the short run
slope of the long run profit function is greater than the slope fo the short run profit function
