Production Costs

Economics studies how choices are made, from among alternatives under conditions of scarcity. Scarcity exists when the resources required for producing the things that people desire are not sufficient to fulfill the needs. When the resources are not in scarcities, there would not be any need to make choices. For choices to make there need to alternatives available; when alternatives are not available then the there is no meaning of freedom to choose. And, so economics studies focused on the choosing an optimized or highest value alternatives.

Opportunity Cost

Choosing a particular alternatives means comparing cost and benefits. The cost of an alternative that must be forgone in order to pursue a certain choice. The opportunity cost of an action refers to the Rupee value of the next best alternative forgone. The opportunity costs are not just restricted to the real or financial cost of output forgone, but it also consider lots of non-monetary costs by translating any their benefit / cost into the monetary values. The financial accounting practices only consider explicit costs whereas in economics opportunity costs are considered which are consists of both explicit and implicit costs.

Accounting profit = Total revenue - Explicit cost

Economic profit = Total revenue - Opportunity cost

where,

Opportunity cost = Explicit cost + Implicit cost

Total, Average, and Marginal Products

In significantly long run of a planning period, a firm can vary all of its production factors. Whereas this is not possible to do in short run, as there will be at lease on input that cannot be changed in shorter period. The quantity of production factor that cannot be changed in short run, it is called as fixed factor of production.  The other production factor that can be varied in short run are called as variable factor of production.

A total product curve shows the quantities of output that can be obtained from different amounts of a variable production factor (e.g. labor), assuming other factors of production are fixed. Average product is defined as the quantity of output that can be obtained for one unit of a variable production factor. It measures the productivity in terms of a particular input product.

Average product (of labor) = Output per unit of a particular input product (e.g. labor) 

Average product (of labor), AP = Q / L

Marginal product is defined as additional quantity of output that can be obtained for one unit increase in a particular input product

 

Marginal product (of  labor), MP = dQ / dL

Law of Diminishing Marginal Returns

It states that (in short run)  the marginal product of any variable production factor will eventually decrease as more input is applied, assuming other production factors remained fixed.

@ MP = 0      =>      Q = Qmax

@ APmax      =>       MP = AP   intersection of two curves

Production Costs in Short Run

Total variable cost (TVC) is cost that varies with the level of output.
Total fixed cost (TFC) is cost that does not vary with output.
Total cost (TC) is the sum of total variable cost and total fixed cost:

Average fixed cost (AFC) = TFC / Q

Average variable cost (AVC) = TVC / Q

Average total Cost (ATC) = (TFC + TVC) / Q = AFC + AVC

Marginal cost (MC) = dTC / dQ & is inversely proportional to MP

Marginal cost (MC) curve  is upward sloping. and by law of diminishing marginal returns, marginal cost (MC) must eventually rise.

Observe the Spreading effect & Diminishing Return effect the in ATC curves. 
At minimum cost output quantity i.e. the bottom of ATC curve, 

ATC = MC
i.e. intersection of two curves.

and at this output quantity, 

AVC = AFC 

i.e. intersection of two curves.

Production Costs in Long Run

In a long-run of planning period, a firm can consider changing the quantities of all its production factors. And so in long run, there is no production cost which will remain fixed. As all production factors are variable in long run, it is assumed that the firm chooses the optimal mix of production factor to generate the output at the lowest cost possible for each level of output.  

Long run total cost = long run variable cost = lowest cost possible for a level of output

At minimum cost output quantity,
LAC = LMC

The long-run average cost (LAC) is the lowest cost per unit at a particular level of output. Since, there is no fixed cost in long run, the U-shape of the LAC cannot be explained by law of diminishing returns. It is explained by Returns to Scale. Due to increasing return to scale (IRS) and decreasing return to scale (DRS), long run average cost takes the U-shape. The decreasing average cost in U-Shape curve is referred as "Economies of scale" whereas the increasing average cost in U-Shape curve is "Dis-economies of scale".

There can also be Constant returns to scale and it is given by Cobs-Douglas production function:

Q = c K^.5 L^.5

Special case, LAC = constant then LAC = LMC i..e no economy or dis-economy of scale