Chapter 11 Behind the Supply Curve Inputs and Costs The Production Function a firm is an organization that produces goods or services for sale it must transform inputs into output production function the relationship between the quantity of inputs a firm uses and the quantity of output it produces it underlies its cost curves Inputs and Output fixed input an input whose quantity is fixed for a period of time and cannot be varied variable input an input whose quantity the firm can vary at any time long run the time period in which at least one input is fixed ex George and Martha can vary the amount of land they farm by buying or selling land short run the time period in which at least one input is fixed total product curve shows how the quantity of output depends on the quantity of the variable input for a given quantity of the fixed input marginal product of labor MPL is the additional quantity of output from using one more unit of labor where one unit of labor is equal to one worker marginal product of an input is the additional quantity of output that is produced by using one more unit of that input marginal product of labor change in quantity of output produced by one additional unit of labor change in quantity of output change in quantity of labor or MPL change in Q change in L diminishing returns to an input an increase in the quantity of that input holding the levels of all other inputs fixed leads to a decline in the marginal product of that input this makes the MPL curve negatively slope other things equal each successive unit of an input will raise production by less than the last if the quantity of all other inputs is held fixed From the Production Function to Cost Curves fixed cost a cost that does not depend on the quantity of output produced it is the cost of the fixed input variable cost cost that depends on the quantity of output produced it is the cost of the variable input total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output total cost fixed cost variable cost or TC FC VC total cost curve shows how total cost depends on the quantity of output ex slopes upward due to the variable cost the more output produced the higher the farm s total cost unlike the total product curve which gets flatter as employment rises the total cost curve gets steeper Two Key Concepts Marginal Cost and Average Cost Marginal Cost change in total cost generated by producing one more unit of output marginal cost change in total cost generated by one additional unit of output change in total cost change in quantity of output or MC change in TC change in Q if the marginal cost curve slopes upward its because there are diminishing returns to inputs as output increases the marginal product of the variable input declines Average Total Cost average total cost average cost is total cost divided by quantity of output produced ATC average total cost total cost quantity of output TC Q average total cost is important because it tells the producer how much the average or typical unit of output costs to produce U shaped average total cost curve falls at low levels or output then rises at higher levels average fixed cost AFC the fixed cost per unit of output average variable cost AVC the variable cost per unit of output AFC fixed cost quantity of output FC Q AVC variable cost quantity of output VC Q average total cost is the sum or average fixed cost and average variable cost it has a U shape because these components move in opposite directions as output rises average fixed cost falls as more output is produced because the numeration the fixed cost is a fixed number but the denominator the quantity of output increases as more is produced as more output is produced the fixed cost is spread over more units of output the end result is that the fixed cost per unit of output the average fixed cost falls increasing output has two opposing effects on average total cost the spreading effect and the diminishing returns effect spreading effect the larger the output the greater the quantity of output over which fixed cost is spread leading to lower average fixed cost diminishing returns effect the larger the output the greater the amount of variable cost at low levels of output the spreading effect is very powerful because even small increases in output cause large reductions in average fixed cost this causes the average total cost curve to slope downward when output is large the diminishing returns effect dominates the spreading effect causing the average total cost curve to slope upward Minimum Average Total Cost for a U shaped average total cost curve average total cost is at its minimum level at the bottom of the U minimum cost output the quantity of output at which average total cost is lowest the bottom of the U shaped average total cost curve principles that are always true about a firm s marginal cost and average total cost curves at the minimum cost output average total cost is equal to marginal cost at output less than the minimum cost output marginal cost is less than average total cost and average total cost is falling at output greater than the minimum cost output marginal cost is greater than average total cost and average total cost is rising Does the Marginal Cost Curve Always Slope Upward economists believe that marginal cost curves often slope downward as a firm increases its production from zero up to some low level sloping upward only at a higher levels of production this initial downward slope occurs because a firm often finds that when it starts with only a very small number of workers employing more workers and expanding output allows its workers to specialize in various tasks this lowers the firm s marginal cost as it expands output Short Run versus Long Run Costs in the long run a firm s fixed cost becomes a variable it can choose when output is low the increase in fixed cost from the additional equipment outweighs the reduction in variable cost from higher worker productivity there are too few units of output over which to spread the additional fixed cost for such a firm many possible short run average total cost curves will exist each corresponding to a different choice of fixed cost and so giving rise to what is called a firm s family of short run average total cost curves long run average total cost curve LRATC shows the relationship between output and average total cost when fixed cost has been