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Cost Theory
Cost minimization is the basic objective of an entrepreneur. We seek to answer following questions
What is an economic profit equation?
We start by answering, what is an economic profit? It is revenues less cost. With the help of an example, we calculate cost.
Mathematical derivation of cost minimization point
Here, we assume a general production function and cost function. Try to set up lagrangean, where our objective function is wL + rK which we seek to minimize subject to constraint q = f(K,L)
Graphical derivation of cost minimization point
When any producer, fix, the amount of output, say q0 at the given level of input prices {w,r}, then with the help of an isoquant and isocost lines, we examine that the point of cost minimization must be the point where slope of an isoquant = slope of an isocost line.
What is firm’s expansion path?
We can find out cost minimizing input choices for a particular q and given input prices. If these input prices remain constant, for the entire range of q, we can trace the locus of cost minimizing input choices. This is firm’s expansion path.
Example of minimizing cost for a cobb douglas production function
This example, gives the point developed in the second and third videos, a concrete evidence. It tells, using cobb douglas technology, how, any firm, minimizes cost, at the point, where MRTS = input price ratio. It further elaborates the point, if firm produces at a point, where, MRTS ≠ input price ratio, then, such a point, will not be cost minimizing input combination.
Derivation of cost function of the form C(w,r,q), AC(w,r,q) and MC(w,r,q)
If you understand this and the previous example, then you can apply more or less similar technique to find the cost function for any type of production function. It gives you all tools required to move from a given production to an associated cost function.
Economic profits equation
Mathematical derivation of cost minimization point
Graphical derivation of cost minimization point
Firm’s Expansion Path
Minimizing cost for a cobb douglas production function
Derivation of cost function of the form C(w,r,q), AC(w,r,q) and MC(w,r,q)
