Econ 101: Principles of Microeconomics


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1 Econ 101: Principles of Microeconomics Chapter 12  Behind the Supply Curve  Inputs and Costs Fall 2010 Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 Outline 1 The Production Function 2 Marginal Cost and Average Cost 3 ShortRun versus LongRun Costs Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
2 Overview In this chapter we turn our attention to the firm. A firm is an organization that produces goods or services for sale. We will begin by characterizing the relationship between the firm s inputs and the quantity of outputs it produces. The production function describes the relationship between the quantity of inputs and the quantity of outputs that the firm produces. Basic characteristics of the production function has implications for the cost structure for the firm, which in turn has implications for the firm ultimate supply function. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 The Production Function The Short Run and the Long Run It is useful to categorize firms decisions into  Longrun decisions involves a time horizon long enough for a firm to vary all of its inputs  Shortrun decisions involves any time horizon over which at least one of the firm s inputs cannot be varied To guide the firm over the next several years, manager must use the longrun view To determine what the firm should do next week, the short run view is best. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
3 The Production Function Production in the Short Run In the shortrun, the firm s inputs can be divided into one of two categories 1 Fixed inputs  These are inputs whose quantity is constant for some period of time (regardless of how much output is produced).  Typically, fixed inputs will include land and machinery, though they can also include certain types of labor (due to contracts). 2 Variable inputs  These are inputs whose quantity the firm can vary, even in the short run.  Examples of variable inputs often include labor, energy, fuel, etc. When firms make shortrun decisions, there is nothing they can do about their fixed inputs; i.e., they are stuck with whatever quantity they have. However, they can make choices about their variable inputs. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 Total Product The Production Function To fix ideas, suppose we have a firm whose only variable input is labor All other inputs (capital, land, raw materials, etc.) we will assume for now are fixed. Total product is the maximum quantity of output that can be produced from a given combination of inputs. The total product curve shows how the quantity of output depends on the quantity of variable input, for a given quantity of the fixed input. We would generally expect the total product curve to be increasing; i.e., as the quantity of the variable input increases, we would expect total output to increase. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
4 The Production Function Consider John s Woodworking Shop Again Units of Labor Total Product Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 The Production Function The Total Product Curve Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
5 Marginal Product The Production Function Notice that the Total Product curve is always increasing in this case, but that it s slope is not the same throughout.  Initial the slope is increasing  but eventually it starts to flatten out. The slope of the Total Product Curve is the Marginal Product of labor. Formally, Change in Quantity of Output Marginal Product of Labor (MPL) = Change in Quantity of Labor = Q L Tells us the rise in output produced when one more worker is hired Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 The Production Function Units of Labor Total Product Marginal Product Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
6 The Production Function The Marginal Product Curve Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 The Production Function Marginal Returns To Labor As more and more workers are hired, the MPL is at first increasing  This is known as increasing returns to labor  This is typically due to the returns to specialization  It can also arise due to minimum labor requirements for equipment. Eventually, however, the MPL starts to decline  This is known as diminishing returns to labor  This arises as the gains from specialization are exhausted and  The constraints caused by the fixed inputs start to bind This pattern of MPL (and for other inputs) is thought to hold for most industries. Consider the problem of a woodworking shop. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
7 Marginal Cost and Average Cost Production and Firm Costs Understanding the nature of a firm s production function is important in that it has implications for the firm s costs. In the short run, the firm s costs can be divided into two broad categories: 1 Total Fixed costs (TFC): These are costs that do not depend upon the quantity of output produced.  These costs are typically associated with fixed inputs.  Examples of fixed costs might be the rent paid for the firm s building or equipment rentals. 2 Total Variable costs (TVC): These are costs that depend on the quantity output produced.  As the name suggests, these are costs associated with the variable inputs.  In the case of John s Woodworking shop, the TVC = w L where w denotes the wage rate. Total Costs = TFC + TVC. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 Marginal Cost and Average Cost John s Cost Structure Suppose that John has a TFC of $5000 and pays a wage rate of $1200 per week Units of Total Total Fixed Total Variable Total Labor Output Cost (TFC) Costs (TVC) Costs (TC) 0 0 $5000 $0 $ $5000 $1200 $ $5000 $2400 $ $5000 $3600 $ $5000 $4800 $ $5000 $6000 $ $5000 $7200 $ $5000 $8400 $ $5000 $9600 $14600 Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
8 The Cost Curves Marginal Cost and Average Cost Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 Marginal Cost and Average Cost Marginal and Average Cost Curves While the breakdown of Total Cost into Total Fixed and Total Variable Costs is helpful, two other measures of cost will be even more useful: 1 Marginal Cost: Measures the additional cost of producing one more unit of a good or service. 2 Average Cost: Measures the average cost per unit of the good or service (i.e., the costs averaged over all of the output produced by the firm). Understanding the distinction between these two concepts will be key to finding the optimal level of production for the firm. We ll start with average cost Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
9 Marginal Cost and Average Cost Average Costs There are three types of average costs 1 Average Fixed Costs (AFC) = Total Fixed Costs divided by Output AFC = TFC (1) Q Since the numerator is fixed, AFC will decline as output increases. 2 Average Variable Costs (AVC) = Total Variable Costs divided by Output AVC = TVC Q  Since TVC is initial slowing down as output increases (with increasing returns to labor), AVC will initially fall as output increases.  As TVC starts to increase more rapidly with output (with diminishing returns to labor), AVC will start to increase with output. 3 Average Total Costs (ATC) = Total Costs divided by Output (2) ATC = TC Q = AFC + AVC (3) Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 Marginal Cost and Average Cost John s Average Costs Units of Labor Total Product AFC AVC ATC 1 10 $ $ $ $ $68.57 $ $62.50 $45.00 $ $31.25 $30.00 $ $25.91 $31.09 $ $22.94 $33.03 $ $20.92 $35.15 $ $19.46 $37.35 $56.81 Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
10 Marginal Cost and Average Cost The Average Cost Curves Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 Marginal Costs Marginal Cost and Average Cost Another way of looking at the firm s cost structure is to look at its Marginal Costs; i.e., how it s costs increase as output increases. Formally: MC = TC (4) Q If we look at John s Woodworking Shop we have Output Total Cost Q TC MC Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
11 Marginal Cost and Average Cost Adding in the MC Curve Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 Marginal Cost and Average Cost Patterns in the MC and AC Curves Notice that the MC curve is  Initially declining this is due to increasing returns to labor  Eventually increasing this is due to diminishing returns to labor The minimumcost output, Q min, is the quantity at which the average total cost is lowest.  This is at the bottom of the ATC curve.  and occurs where ATC=MC At outputs less than Q min, ATC > MC and ATC is falling. At outputs greater than Q min, ATC < MC and ATC is rising. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
12 ShortRun versus LongRun Costs Production Costs in the Long Run Up until now, we have been focussing on the shortrun, with some of the firm s inputs held fixed. In the long run, costs behave differently Firm can adjust all of its inputs in any way it wants In the long run, there are no fixed inputs or fixed costs; i.e. all inputs and all costs are variable Firm must decide what combination of inputs to use in producing any level of output The firms goal is to earn the highest possible profit To do this, it must follow the least cost rule; i.e., to produce any given level of output the firm will choose the input mix with the lowest cost This yields a LongRun Average Total Cost Curve; i.e., the relationship between the output and the ATC when fixed costs are chosen to minimize total cost for each level of output. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 ShortRun versus LongRun Costs Consider John s Woodworking Shop Suppose that in our first production function, we assumed that John had only one set of tools (e.g., 1 table saw, 1 drill press, and 1 router table). We ll call this one unit of capital The tools (and the space to house his tools) constitute fixed costs for John in the shortrun. In the longrun, John must decide whether or not he wants to expand his capital stock The tradeoff is that additional capital will avoid worker congestion, but imposes a large fixed cost on the firm. At low levels of production, having just one set of tools is not a binding constraint and John would rather avoid the additional capital costs. At higher levels of production, additional capital will avoid congestion problems and the capital costs are spread out over more units of production. Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
13 ShortRun versus LongRun Costs Different Levels of Capital Labor Units of Capital Units of Labor Capital = 1 Capital = 2 Capital = Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 ShortRun versus LongRun Costs The Corresponding ATC Figures are Given by Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
14 ShortRun versus LongRun Costs John s Capital Stock Choice The level of capital stock John chooses depends on his expected level of output Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 ShortRun versus LongRun Costs If Capital Stock Can be Varied Continuously, We Get Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
15 Returns to Scale ShortRun versus LongRun Costs LRATC curves for industries usually exhibit three basic phases: 1 Increasing Returns to Scale: Output range with declining LRATC This is also known as economies of scale Economies of scale often arise due to the gains from specialization. The greatest opportunities for increased specialization occur when a firm is producing at a relatively low level of output Economies of scale can also arise due to minimum size requirements for certain types of equipment. 2 Constant Returns to Scale: Output range with constant LRATC Over some range of production, size may not matter and firms of the same size will be equally costeffective. 3 Decreasing Returns to Scale: Output range with increasing LRATC This is also known as diseconomies of scale As output continues to increase, most firms will reach a point where bigness begins to cause problems This is true even in the long run, when the firm is free to increase its plant size as well as its workforce Diseconomies of scale are more likely at higher output levels Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30 ShortRun versus LongRun Costs Herriges (ISU) Ch. 12 Behind the Supply Curve Fall / 30
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