Chapter 10 - CostsChapter 10COSTSBoiling Down Chapter 10The reason we spent so much time in the last chapter trying to identify the relationshipbetween inputs and outputs is that inputs represent the cost of producing a given output.As in the case of production inputs, we are concerned with the capital and labor input costsrather than the raw material costs because the raw materials are not part of the valueadded to the product. What follows will sound like technical nonsense unless it is readslowly with a sketch pad to graph the thoughts of the paragraphs. It will make much moresense and clinch much of the material if it is read again after the material is digested andunderstood. The graph below shows some of the concepts discussed here.ATC, AVC ATC& MC Falling AFC overpowers diminishing returns AVC MCQuantity Increasing returns diminishing returns The short-run total cost of a given output is equal to the cost of the fixed inputs plusthe cost of the variable inputs. To find the cost per unit (average cost) of output, the totalcost is divided by the quantity produced. The average total cost is influenced by severalfactors. Because increasing and then diminishing returns are part of the productionfunction characteristics, average variable costs are pulled down initially because earlyadditions of the variable input make the production recipe more efficient. This pulls downall the cost curves shown in the graph. However, at the point of diminishing returns thistrend reverses and marginal cost begins to rise. When MC goes above AVC it pulls up theAVC and when it goes above the ATC it begins to overpower the pull down on averagecosts from falling AFC. At his point the ATC begins to rise indefinitely. 10-1Chapter 10 - CostsThe key factor in understanding cost is to recognize that, as labor is added to a fixedproduction process, the mix between labor and the fixed capital stock varies from beingtoo little labor in the factory to too much labor in the factory. In both cases, ATC will behigher than it is when labor and capital are in the best balance. The U shape of ATC is thusa result of increasing and then diminishing returns to production and the fact that AFCmust continuously decline. Marginal costs can be obtained by calculating the change intotal cost, which means that only variable cost is relevant in the MC calculations. Fixedcosts can never change total cost. In graphing all these relationships, it is important toremember that the slope of any total function is the marginal value, and the slope of a rayfrom the origin to the total function is the average value at that point on the total function.Try sketching graphs from total cost curves, total variable cost curves, and total fixed costcurves.The real reason why we make all this effort to understand the way costs respond todifferent output levels is that we want to find the lowest cost method of producing ouroutput goal. In the short-run this optimal combination will obviously be where averagecost is the lowest possible for the level of output selected.In the long run the choice of inputs is less constrained because there are no fixedinputs in the long run. Both capital and labor can be adjusted to find the right combinationfor least cost production of the desired output. The point where the isoquant is tangent tothe isocost line identifies the input combination that minimizes cost for the level of outputunder consideration. At this point the slope of the isoquant (MPL/MPK) is equal to the slopeof the isocost line (PL/PK), a relationship that could be stated as MPL/PL = MPK/PK.The intuitive sense of this expression is that any factor should be used to the pointwhere the marginal return on the last dollar spent on one input should equal exactly thereturn from the last dollar spent on the other input. If this were not true, the entrepreneurshould substitute toward the input with the higher marginal return until the desiredrelationship is reached. In other words, always hire the input that gives the biggest bangfor the buck.Optimal input choice can be observed for all output levels by observing the tangencypoints of all possible isoquants and isocost lines. Because the isocost line represents thetotal cost of producing the output in question, a total cost for all output levels isdetermined. When plotted as a total long-run cost function, the average and marginal long-run functions also can be derived. The long-run cost curves will be either downwardsloping, horizontal, or U-shaped, depending respectively upon whether economies of scale,constant returns to scale or diseconomies of scale are present in the cost relationships. A long-run cost curve is simply the envelope curve of a series of short-run averagecost curves, because each short-run cost curve will have one point on it that represents alowest possible average cost for the given output. The plant size represented by that pointon the isoquant map shows which particular short-run plant is relevant for that output.When all the technical jargon is done the basic concept is much like getting the rightrecipe in baking. If all inputs are in just the right balance, then the cake has the best taste.In factory life, costs are as low as possible for each level of output when all the inputs toproduction are combined in just the right mix. 10-2Chapter 10 - CostsChapter Outline1. Short-run costs are analyzed in relation to output produced.a. The full opportunity costs are broken down into fixed and variable costs.b. Total, average, and marginal cost characteristics are explored for variable costs while total and average characteristics are considered for fixed costs.c. Total variable cost for a given output is derived from the total product curve by multiplying the amount of variable input needed for that output by its price.d. Total cost is the vertical summation of the total variable cost and the total fixed cost.e. Graphs for average cost functions are derived by finding the slope of a ray from the origin to the total cost function for a given quantity.f. Graphs for marginal cost functions are derived by identifying the slope of the total cost functions for all outputs.2. When production is allocated between two processes, the marginal costs in each process should be the same.3. Average variable cost is the inverse of the average product times the price of the variable input,