## Cost Minimization Problem - intro idea

• The firm operates in two kinds of markets:
1. Inputs/factor markets (e.g. it buys labor and capital)
2. Final product market
• Let's focus on optimal decisions regarding the first kind of market.

• We will assume for now the firms has a target prod level $q_0$. (i.e. an isoquant!)

• And, it aims to achieve that level of production in the best (most efficient) way possible.

• let the fun begin

## Cost Minimization Problem

• The only decision the firm controls at this point is how much of inputs it uses.

• So the most efficient way in this context refers to what is the "right" combination of (L,K) so achieve $q_0$.

• The right combination is the one that minimize the cost of producing the given target level of output $q_0$.

• Suppose wages are denoted by $w$ and rental price of capital is denoted by $r$.

• So the firm wants to:

minimize: $cost = w L + r K, \quad$ subject to: $f(L,K) = q_0$.

## Isocost

• Isocost: Combinations of input usage that cost the same (say $C): • Example: This is isocost at a cost of$100:

• $w L + r K = 100$

## Types of costs: Fixed and quasi-fixed costs

1. Fixed: costs that must be paid, regardless of output level.

2. Quasi-fixed cost: costs that must be paid, only if output level > 0. (heating, lighting, etc.)

3. Sunk cost: fixed costs that are not recoverable (painting your factory)