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Topic 4: Theory of the Firm DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Dartmouth College, Department of Economics: Economics 1, Fall ‘02 Topic 4: Theory of the Firm Economics 1, Fall 2002 Andreas Bentz Based Primarily on Frank Chapters 9 - 12 Firms demand: supply: inputs: labor, production output capital buy in factor sell in product market market cost revenue Objective: firms are interested in profit = revenue - cost. 2 © Andreas Bentz page 1 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Dartmouth College, Department of Economics: Economics 1, Fall ‘02 Production The Black Box Production X Production for a neoclassical economist is a “black box”: We model production as a function that turns inputs into output: q = f(k, l) where: » q: output » k: capital input » l: labor input » f(·, ·): production function 4 © Andreas Bentz page 2 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Short Run and Long Run X Firms may not immediately be able to change the quantity of all inputs they use. Example: buildings, etc. X The long run is defined as the shortest period of time in which a firm can change the quantity of all inputs it uses. An input whose quantity can be freely adjusted is a variable input. X The short run is the period of time during which one or more inputs cannot be varied. An input whose quantity cannot be freely adjusted is a fixed input. 5 Dartmouth College, Department of Economics: Economics 1, Fall ‘02 Production in the Short Run When not all inputs can be varied. © Andreas Bentz page 3 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Short-Run Production X Suppose a firm produces output according to the production function q = f(k, l). X Suppose that, in the short run, the amount of capital cannot be varied (fixed input) - assume it is fixed at k0. X We can then plot the amount of output produced as we vary the amount of labor (variable input). X This gives us the short-run production function. 7 Short-Run Production Function q X The short-run production function f(k ,l) plots the f(k0,l) 0 quantity of output (total product), as one input (labor) is varied (holding capital fixed at k0). l 8 © Andreas Bentz page 4 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Marginal and Average Product X The marginal product (MP) of a variable factor measures the increase in output from a small increase in the variable factor. ∆ ∆ MPl = q / l MPl is the slope of the short-run production function. X The average product (AP) of a variable factor, measures how much output each unit of input yields on average. APl = q / l APl is the slope of the line from the origin to the corresponding point on the production function. 9 Marginal Product q X The slope of the short- run production function is the marginal product f(k ,l) 0 (MP) of the variable input: ∆q as the variable input is increased by a little, by ∆l how much does output l increase? X The “law of diminishing ∆ ∆ MPl = q / l returns”: after some Note that this changes point, marginal product along the production declines. function. 10 © Andreas Bentz page 5 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Average Product q X The average product (AP) of some input is the quantity of output f(k ,l) 0 produced, on average, with each unit of the variable input: APl = q / l q graphically, it is the slope I l of the line connecting origin and the corresponding point on the production function. 11 Marginal and Average Product q q f(k0,l) f(k0,l) l l q l 12 © Andreas Bentz page 6 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Buzz Group X You own two car production sites, and you have a total workforce of 100. Each site operates a slightly different production technology, but both sites produce the same product. Currently 50 workers are employed at site A, and 50 are employed at site B. If you were to add one more worker to site A, she would raise production at site A by 3 cars per day. If you were to add one more worker to site B, she would raise production at site B by 4 cars per day. At site A, each worker on average produces 10 cars per day. At site B, each worker on average produces 8 cars per day. X Should you reallocate workers between the two sites? 13 Maximizing Profit X A firm’s profit is total revenue less total cost. X In the short run, where capital is fixed at k0, profit is: π = p·q - w·l - r· k0 X A small change in labor input (∆l) changes output by MPl, and profit by: ∆π ∆ / l = p·MPl - w X If this is positive, employing more labor increases profit. If it is negative, decreasing labor input increases profit. So, at a profit maximum: p·MPl - w = 0 MPl = w/p 14 © Andreas Bentz page 7 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Maximizing Profit X So we know that, in order to maximize profit, a firm employs workers until MPl = w/p. X Comparative statics: as the real wage (w/p) increases, the firm will employ fewer workers. X Another way of putting this: each worker is paid her marginal productivity. 15 Dartmouth College, Department of Economics: Economics 1, Fall ‘02 Production in the Long Run When all inputs can be varied. © Andreas Bentz page 8 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Long-Run Production X In the long run, all factors of production can be varied. X Production function q = f(k, l). How do we represent this graphically? X An isoquant (sometimes called production isoquant) is the set of all input combinations that yield the same level of output. Example: q = 2kl. What is the isoquant for q = 16? » 16 = 2kl » k = 8 / l » … and similarly for other levels of output. 17 Isoquants X Isoquants for the production function q = 2kl. k q = 64 q = 32 q = 16 l 18 © Andreas Bentz page 9 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 MRTS k X The (absolute value of the) slope of an isoquant is the marginal rate of technical substitution (sometimes referred to as the technical rate of ∆k substitution): ∆l It is the rate at which, in a l given production process, the firm can substitute a X Note the similarity with little more of one input for the MRS in consumer a little less of the other theory! input. 19 MRTS, cont’d X There is a relationship between MRTS and MP: By how much is output reduced if you reduce capital by ∆k? ∆ » output reduction: MPk k(1) By how much is output increased if you increase labor by ∆l? ∆ » output increase: MPl l(2) Along an isoquant, output is constant, so (1) and (2) are equal: ∆ MPl k » MP ∆k = MP ∆l, or: = = MRTS k l ∆ MPk l 20 © Andreas Bentz page 10 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Returns to Scale X In the long run, all inputs can be varied. X Suppose all inputs were doubled. Would output: double? more than double? less than double? X This is a question of returns to scale: if we “scale up” production, does output increase more or less than proportionately? X Returns to scale is a long-run concept. 21 Returns to Scale, cont’d X Definition: If a proportional change in all inputs leads to a more than proportional change in output, the production process exhibits increasing returns to scale. X Definition: If a proportional change in all inputs leads to a less than proportional change in output, the production process exhibits decreasing returns to scale. X Definition: If a proportional change in all inputs leads to a proportional change in output, the production process exhibits constant returns to scale. 22 © Andreas Bentz page 11 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Dartmouth College, Department of Economics: Economics 1, Fall ‘02 Costs Fixed, Variable, Total; Average, Marginal. And what to do with them. Dartmouth College, Department of Economics: Economics 1, Fall ‘02 Costs in the Short Run When not all inputs can be varied. © Andreas Bentz page 12 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Fixed and Variable Costs X Fixed cost (FC): the cost of fixed inputs. Example: Capital is fixed at k0. The rental rate for capital (the opportunity cost, if capital is owned) is r. » What is the fixed cost? » FC = k0r X Variable cost (VC): the cost of variable inputs. Example: A firm currently uses an amount l of labor input (hrs). The wage rate is w. » What is the variable cost? » VC = wl X Total cost (TC): the sum of FC and VC. 25 Short-Run Prod. & Variable Cost q p TC f(k0, l) VC FC l q 26 © Andreas Bentz page 13 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Average and Marginal Costs p p TC MC VC ATC FC AVC AFC q q X AFC Average Fixed Cost; AVC Average Variable Cost; ATC Average Total Cost; MC Marginal (Total and Variable) Cost. 27 Production and Costs X There is a simple X Similarly, there is a relationship between simple relationship marginal product and between average marginal cost: product and average MC = cost: = ∆VC / ∆q AVC = = ∆(w · l) / ∆q = VC / q = (w · ∆l) / ∆q = (w · l) / q = w / (∆q / ∆l) = w / (q / l) = w / MPl = w / APl 28 © Andreas Bentz page 14 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Production and Costs, cont’d X MC = w / MPl, AVC = w / APl: q AP l p MP MC AVC l (which is proportional to q) 29 Dartmouth College, Department of Economics: Economics 1, Fall ‘02 Application: Predatory Pricing Shut-Down Condition Areeda-Turner Rule © Andreas Bentz page 15 DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1 Predatory Pricing X What is predatory pricing? One firm lowers its price so far that it drives other firms out of the market (“dumping”).
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