Lecture Notes on Short-Run Cost Curve PDF

Lecture Notes on Short-Run Cost Curve Lalith Munasinghe The distinction between the Short-Run (SR) and Long-Run (LR) in production theory hinges on the degree of input flexibility. SR represents a time frame where a firm is unable to change the levels of all inputs. That is, the firm faces constrai...

Lecture Notes on Short-Run Cost Curve Lalith Munasinghe The distinction between the Short-Run (SR) and Long-Run (LR) in production theory hinges on the degree of input flexibility. SR represents a time frame where a firm is unable to change the levels of all inputs. That is, the firm faces constraints in terms of how they can adjust input levels. The simple assumption we introduce is to say the in the SR capital (K) is held constant. And the question we now want to ask is what SR costs are? That is to say, what are the minimum costs that a firm must incur in order to produce some Q level of output, given that they have no flexibility in adjusting the level of capital? Because we have fixed and variable inputs, we can now introduce a few more costs concepts. From our earlier discussion of costs we claimed that: TC = vK + wL Suppose that in the SR capital is fixed at some level K0, then we can define various SR costs functions as follows: STC = vK0 + wL, and let SFC = vK0 (SR fixed costs) SVC = wL (SR variable costs) So, STC= SFC + SVC Short run Fixed Costs are associated with input costs that are fixed in the SR. Short run Variable Costs are associated with those inputs that can be varied in order to change the firm’s level of output. Examples of a Fixed Cost might be the rental price of a building where the firm has signed a 2 year contract. Typical examples of Variable Costs are power and some types of labor. Before getting to a more detailed analysis of these costs curves, and their corresponding unit cost functions, and how they might be related to each other, let us define a few additional costs concepts that are important for decision makers. Sunk Costs: These are costs that existing firms have already incurred and cannot be recovered. For example, if a firm had invested on software unique to its production technology then it is a sunk cost because the firm can never recover these investment costs. For decision makers these irrecoverable costs are irrelevant. 1 Opportunity Costs: These costs refer to the value of inputs in their next best use, and are more relevant to economic decision making than accounting costs. For example, assume that a firm owns the building of operation. For an economist the opportunity cost of this building, a critical input in production, is the foregone earnings by not renting it. However, from an accounting point of view this cost would be zero. In many instances the context will determine whether the costs associated with various production inputs are sunk, fixed, or variable. The TV Listing Case Study highlights some of these important cost distinctions. Let us now return to our analysis of SR costs. The shape of the SVC curve is determined by the marginal productivity of labor (variable input), and the reason it increases rapidly as output increases is because labor is less productive when we have many people working with a fixed amount of capital. Now consider the various per-unit costs curves that correspond to these costs. Short Run Average Costs, SAC = STC/Q = SFC/Q + SVC/Q = SAFC + SAVC Hence SR average costs are equal to SR average fixed costs (which decrease with output) plus SR average variable costs. Short Run Marginal Costs, SMC = ΔSVC/ΔQ (= ΔSTC/ΔQ). SR marginal costs are the extra costs of producing one more unit of output in the SR. What do these curves look like and how are they related? 2 Key Points to Observe (1) Marginal product of labor is rising initially because there is an excess of capital. (2) Marginal product of labor declines as you produce more and more output because the only way you can do it is by adding more and more workers. (3) The shape of the STC is entirely determined by the shape of the SVC (4) SMC is nothing but w/MPL. MPL is the amount of output produced by hiring one more unit of labor. 1/ MPL is the amount of labor required to produce one unit of Q. Hence w/ MPL is the cost of producing one unit of output. So the SMC is nothing but the inverse of the MPL multiplied by the wage rate. (5) Where the SAC and SAVC curves intersect the SMC, both the SAV and SAVC are minimized! 3 Analysis of Short Run Supply by a Price-Taking Firm Suppose the market price is P*, and since the firm is a price taker MR = P*. Profit maximization implies that the firm should supply Q* amount because at this level of output SMC is equal to P*. Graphic Analysis of the SR Supply Curve (1) If P = P* then Profit-Max implies Q = Q* Profits = TR - STC (STC = SFC + SVC; SAC = STC/Q) = TR - SAC.Q = P* Q* - SAC Q* = (P* - SAC) Q* > 0 since P* > SAC 4 (2) If P = P3 then Profit-Max implies Q=Q3 Profits = TR – SAC Q = P3 Q3 – SAC Q3 = (P3 - SAC) Q3 = 0 since P3 = SAC The question is whether the firm should produce or not? Yes, because if the firm shut down then it will make negative profits because of the fixed costs. Profits = TR – STC = 0 – SFC < 0! (3) If P = P2 then Profit–Max implies Q = Q2 Profits = TR – SAC Q = P2 Q2 – SAC Q2 = (P2 - SAC) Q2 < 0 since P2 < SAC Again, the question is whether the firm should produce or not? Note that SAC = SAFC + SAVC. If produce then: Profits = (P2 - SAVC) Q2 – SFC > -SFC [P2 > SAVC, so the first term must be positive. Therefore the left hand side must be greater than -SFC (which is what profits will be if the firm shuts down)] Hence if the firm shuts down it will make even bigger losses than if it stays in operation. The point is that by staying in production the firm is able to defray some of its fixed costs. (4) The firm should shut down only if the price falls below P1! P1 is the so-called shut-down price. In the SR the firm could be operating at a loss because closing down might mean even bigger losses! This is the significance of fixed costs. SR Supply Curve: Represents how much a firm will produce at various output price levels in the short-run. It consists of the positively sloped segment of the SMC above the point of minimum average variable costs. Below this price point the firm’s optimal strategy is to shut down. The market supply curve in the short run is simply the sum of individual SR supply curves as defined above. Example: STC = 100 + Q2; Derive the SFC, SVC, SAC, SAVC, SMC, and SAFC functions. If P = 60 what is the profit maximizing level of Q? What are profits? At what minimum price will the firm produce a positive output? 5 Supply Curve for a Capacity Constrained Firm For many firms, and not just in the short run, fixed costs may be very large and marginal costs very low. Such cost structures typically lead to monopoly power since size of operation gives a cost advantage. We will discuss this case later. However, if firms have capacity constraints then even with these cost structures their supply curves will be well defined within the competitive framework. That is, when firms are still price takers. The firm will produce at capacity (Q*) for all prices above P*, where P* is defined as the break-even price, that is, at Q* average cost is equal to P*. At all prices above P* the firm will make positive profits if the firm produces at capacity (Q*). Note further that if different firms have different AC curves then the market supply curve will be an upward inclined step function. 6