Some Cost concepts for ECON3 / EEP1 (from B&B and class notes)
C(q) is the least amount of money needed to buy inputs that will produce output q. It is the cost function.
TC(Total cost) It is the overall cost or the addition of all costs incurred in production or investment.( FC + VC). Even if q=0, TC could be greater than 0 because of fixed costs.
FC (fixed costs): The costs incurred even if there is no production. FC = C(0).They are costs that do not vary with the level of output.
VC(q) (variable costs). It is a cost, which vary with the level of output. VC(q) = C(q) - FC.
AC(q) (average cost) is the average cost of producing one unit of output. Which is the total cost divided by the total output. AC(q) = C(q)/q.
AVC (average variable cost): This is the average variable cost of producing one unit of output. That is the total variable cost divided by the total output. AC (q) = VC(q)/q.
AFC (average fixed cost): This is the average fixed cost of producing one unit of output. AFC is always falling. AFC(q) = FC/q. Note AFC (0) is infinite and AFC (inf.) is zero.
MC(q) ( marginal cost):. It is the cost of making the next unit. MC (q) is approximately C(q+1) - C(q). Put the other way, C(q+1) is approximately C(q) + MC(q). The cost of making q+1 units is the cost of making q units plus marginal cost at q. Another simple definition is the increase in total cost that arises from the production of an additional unit of output.
Firms behavior: As we are assuming a perfect competition, firms choose quantity to maximize profits. The market determines prices so we say firms are price takers
A market operates under perfect competition when there are numerous small firms producing homogenous products, when information is perfect and when there is no impediment to the entry or exit of firms
Profit Maximizing Output is the output level at which firms maximize output which is either at 0 or where P=MC.
Why P=MC? If P is greater than MC and MC is rising in quantity. Then a firm can increase profits by increasing output until P=MC. Similarly, if price is less than MC then what the firm is getting for the extra unit of output is less than cost hence output should be reduced and MC would fall until P=MC. Hence P=MC would be the point where there is no incentive to increase or decrease output. Note P=MC is a necessary but not sufficient condition for maximizing profit.
Economic profits (Π=PQ-C(Q)) is the difference between total revenue and total costs This total costs include all opportunity costs of production. Another definition is economic profit equals business profit minus the opportunity cost of capital and any other input supplied by the firm owners.
Business profit is the accountant’s calculation of profit, which are basically net earnings. That is total revenue minus explicit costs. These costs do not include opportunity costs.
Opportunity cost The opportunity cost of some decision is the value of the next best alternative that must be given up because of that decision. Another definition is that opportunity cost is the best alternative foregone when a decision is made either by the producer or consumer. That is the economic benefits (UTILITY) that you did without because you bought (invested) that particular something and thus can no longer use it for its next best alternative.
Why does the Marginal cost curve cut the Average cost curve from below? Because whenever average cost is increasing marginal cost must be higher than AC.
Proof:
Whenever AC is increasing, MC is above AC. When decreasing MC is below AC.
AC(q+1) - AC(q) = c(q+1)/(q+1) - c(q)/q = c(q)/(q+1) + mc(q)/(q+1) - c(q)/q
= -c(q)/(q(q+1) + mc(q)/q+1)
= (1/(q+1)) (mc(q) - ac(q) ) so mc greater than ac means ac(q+1) > ac(q) or ac increasing.
This means that MC goes through the minimum point of AC. Note that MC = VC(q+1) - VC(q). (Why?) so the above proof also shows that MC goes through the minimum point of AVC.
Increasing costs- A firm has increasing costs when average costs rises with the level of output. Decreasing cost A firm can be said to be experiencing decreasing costs when its average cost is falling with rise in output. Finally a Firm is experiencing constant costs when average costs are constant with changes in output.
Why do cost curves have a U shape? We can attribute its downward sloping segment to increasing marginal physical product or to the fact that the firm spreads its fixed costs over even larger quantities of outputs. Similarly, we can attribute the upward-sloping segments primarily to the disproportionate rise in administrative cost that occur, as a firm grows large.
Short-run supply curve of the perfectly competitive firm is that portion of its marginal cost curves that lies above the point where it intersects the average (short run) variable cost curve. That is the part above the minimum level of AVC. Note if Price falls below this level, the firm quantity drops to zero
The long-run supply curve of the competitive industry is also the industry’s long-run average cost curve. The industry is driven to that supply curve by entry and exit of firms and by adjustments of firms already in the industry.
Long-run competitive equilibrium: At this point, every firm produced at the minimum point on its average cost curves. Thus the output of competitive firms is produced at lowest cost to the society. P=MC=AC