Chapter 11 The Production Function Production Function the relationship between the quantity of inputs a firm uses and the quantity of output it produces Production is the process of turning inputs into outputs The cost structure of a firm depends on the nature of the production process Inputs and Output o Fixed input an input whose quantity is fixed for a period of time and cannot be varied o Variable input an input whose quantity can be changed by the firm at any time o The long run the time period in which all inputs can be varied o The short run the time period in which at least one input is fixed o 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 Fixed inputs cannot be changed in the short run so any changes in quantity are a result of the variable inputs o 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 is the change in output resulting from oneunit increase in the amount of labor input MPL change in quantity of output change in quantity of labor MPL Q L Because slope is rise run and in the graph of total product curve y quantity rise and x labor run the marginal product of labor is equal to the total product curve slope is rise run quantity labor and marginal product of labor is quantity labor Marginal product initially rises as more workers are hired this is because of specialization Then it declines diminishing marginal product aka diminishing returns to an input an increase in the quantity of that input holding the levels of all other inputs equal leads to a decline in the marginal product of that input Total product marginal product and fixed input o With more land changing the fixed input each worker can produce more the total product curve shifts upwards o Additionally the MPL is higher with a higher fixed input the MPL curve shifts up From the Production Function to Cost Curves o A fixed cost is a cost that does not depend on the quantity of output produced short run It is the cost of the fixed input o A variable cost is a cost that depends on the quantity of output produced short run It is the cost of the variable input o The 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 TC FC VC Total cost curve shows how total cost depends on the quantity of output The total cost curve becomes steeper as more output is produced a result of diminishing returns As shown even when there is no output the producer still has to pay the fixed cost because that cost is there regardless of any changes in output Marginal Cost and Average Cost Marginal cost the change in total cost generated by one additional unit of output o MC change in total cost change in quantity of output TC Q o As in the case of marginal product marginal cost is equal to the increase in total cost divided by the increase in the quantity of output o Marginal cost is equal to the slope of the total cost curve same logic as above o o o o Why is the marginal cost curve upward sloping Diminishing returns to inputs as output increases the marginal product of the variable input declines This implies that more and more of the variable input must be used to produce each additional unit of output as the amount of output already produced rises And since each unit of the variable input must be paid for the cost per additional unit of output also rises Average Total Cost o Average total cost aka average cost total cost divided by quantity of output produced ATC TC Q Total cost quantity of output o Average fixed cost the fixed cost per unit of output AFC FC Q fixed cost quantity of output o Average variable cost the variable cost per unit of output AVC VC Q variable cost quantity of output Average total cost curve o Increasing output has two opposing effects on average total cost The spreading effect the larger the output the more output over which fixed cost is spread leading to lower average fixed cost The diminishing returns effect the larger the output the more variable input required to produce additional units which leads to higher average variable cost o Minimum cost output the quantity of output at which ATC is lowest the bottom of the ATC curve the lowest point on the curve The marginal cost curve intersects the ATC curve from below crossing the ATC curve at its lowest point o At min cost output the ATC curve the MC curve o Where marginal cost is above ATC the ATC is rising o Where marginal cost is below ATC the ATC is falling Increasing specialization leads to a lower marginal cost at first which shows why the MC curve originally has negative slope but diminishing returns set in and marginal cost starts to rise this happens at the point where the MC curve starts having positive slope Short Run vs Long Run Costs All inputs are variable in the long run o For example you can t change the size of your factory in the short run so it is a fixed cost but in the long run you could move to a larger factory or build on to your existing one making it a variable cost The firm will choose its fixed cost in the long run based on the level of output it expects to produce The Long Run ATC curve shows the relationship between output and ATC when fixed cost has been chosen to minimize ATC for each level of output o There are increasing returns to scale economies of scale when long run ATC declines as output increases o There are decreasing returns to scale diseconomies of scale when longrun ATC cost increases as output increases o There are constant returns to scale when long run ATC is constant as output increases Problems for Chapter 11 on pages 340 343