04 Jun Question Aniko Oery University of California, Berkeley
Question
Aniko Oery University of California, Berkeley
Section 9: Cost minimization and returns to scale
Econ 100A, MICRO-ECONOMIC ANALYSIS
As a first step of solving the profit-maximization problem of the firm, the firm needs to find
the cheapest input combination to produce a specific output goal. Therefore, it solves the costminimization
problem
min
L,K
C(L, K) subject to f(L, K) = Q0
for a output goal Q0, where f(L, K) is the production function we introduced last time. The
solution to this problem will depend on the value of Q0 and it will give us the cost function
C(Q0). In this discussion section we will review how to solve the cost minimization problem. We
will also briefly talk about retruns to scale.
1 The cost minimization problem
Note first that the cost that the firm faces is given by
C(L, K) = wL + rK
where w is the price for input L and r is the price for input K. The level curves of this cost
function are called iso-cost lines and describe input combinations that result in the same cost.
Let us define an output goal Q0 and let us fix the isoquant that corresponds to this output level
Q0, that is f(L, K) = Q0. In order to solve the cost minimization problem we only need to find
the lowest iso-cost line, that touches this isoquant.
As in the consumer choice theory, there are again two types of solutions: inner solutions and
corner solutions. The tangency condition (TC) is given by
MRT S ?
MPL
MPK
=
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