Appunti Microeconomics

CLASC 15

Objective is maximizing π = p f (L,k) - WL - rK => L (k +

Exampio

Lot's state a simple case

In economics there is usually this distinction between

• Short run - time horizon which is short, situation in which some inputs are variable and some fixed (e.g. some labour can be changed and constant in the choice)
• Long run - time horizon which is long, situation in which all inputs are variable, so in the long run all inputs can be changed and constant in the choice

π = p (E(L,k)) - WL - rK and as we said our objective is to maximize profits, choosing the optimal quantity of labor and capital

Long take a short run perspective and to talk about the short run we cannot change capital can think of one factor (in k) as fixed

π = p (E(L,k)) - WL - rK

_Rev

max π fixed

(This cost does not depend on what we are so even if the producer decides to not produce, he must incur this cost)

Short run production function

Y = E(L,K)

Suppose that we have more capital more than K), what is the effect in p

The short run production function will depend on the quantity of capital input we are using changes

ISOPROFIT LINE

Suppose that we have our price π = pY – WL – rK, which will depend on revenues - variable costs – fixed costs

Isoprofit means same price ts, so an isoprofit is a line on which the profit is constant

We give a level of profit π = pY – WL – rK so were considering the possibility of getting the same profit and we to retaining labour and output in such a way that we obtain this level of profit

pY = π + rK + WL

_{Variable U = π rK W L Variable}

_{p P P}

Constant slope

By rearranging the profit expression we find the equation for a line, where there is an intercept and a slope

y_L=^(π+r)(w)/_PL

The meaning of this line is that, by using the quantity of labor L_P and by considering the output level y_L=f(L), we compute the profit π=Py-wL=rL-rL

We get exactly that (level of profit π)

So, all the points on the isoprofit line are production plans (labor, input and output) that give us the same profit.

Suppose that we’re taking a new production level π* then we are going to draw the isoprofit line of a higher level of profit, this new isoprofit line will show the outward effect on the intercept, and the producer I will be better to stay on the highest possible isoprofit line.

But the intercept line is just a combination of production plans, so we need to check which production plans are feasible and which are not.

• Slope c₁ combination c₂ feasible
• Sr. production function
• Can we obtain this profit?
• Yes, because there are production plans, giving us that level of profit that are also feasible
• Any production plan on this segment is feasible, because we are in the decreasing sector (b. increasing production function)

The production plan F_P, and also B, is not efficient because we are on the production function

For the producer II, it will be the same to be in A, in B because he gets the same profit. Of course, in principle, the profit by getting less labor and less by obtaining less output. So, F and B are indifferent, because he is not in the restriction.

The producer is getting a better choice if he considers a higher profit line (he is able to reach a higher profit line, it means that he can make more profit)

For the producer II it is the same to be in C or in D, but it is not better to be in C rather than in A (given they are both efficient), because the production plan that we have in C will give us a higher profit (π_C >π).

Therefore, we will be able to get the highest profit when we reach the highest possible isoprofit line, which means that it will be tangent to the production function (u sub h).

Also here we have a sort of tangency condition, which means that the slopes are the same, so

Slope isoprofit=Slope production function

w/P = u

L