Micro Production and Cost Essentials 2 WCC

Transcription

1 Micro Production and Cost Essentials 2 WCC In our previous example, we considered how output changes when we change one, and only one, input. This gave us the TPP curve. We then developed a rule to help producers decide how much of a single output to use. Producer s rule Continue using additional units of the variable input as long as MRP i P i So, if labor is our variable input here, that means that we should keep hiring additional workers as long as MR W L Marginal Revenue Product (MR ) - the additional revenue generated by another worker MR = MP X P o Additional output produced by a worker Price of a unit of output That s useful, but in most cases producers aren t trying to decide how much of a single input to use, their trying to decide what mix of inputs to use. They have more than one input that they can adjust. Brave New World Two inputs exist in this world: labor (L), and capital (K). Output depends on the quantities of the two inputs that the producer uses. So, Q o = q(l,k) The producer is free to use more or less of each input. Different combinations of capital and labor can be used to produce the same level of output. How do I decide which combination of labor and capital to use? Start by thinking about cost. Assume that our goal is to produce the profit maximizing level of output. Recognize that, for whatever level of output we choose, we have to be minimizing the cost of producing that level of output in order to be maximizing our profit. Mathematically, cost minimization is a necessary condition for profit maximization.

2 Thinking about total cost A variety of ways exit to produce any given amount of output. We ll want to choose the combination of L and K that minimize cost. How do you calculate cost? TC = + We can graph all of the combinations of labor and capital that will cost a certain amount of money TC 0. We do this by rearranging the TC equation and solving for. This gives us an isocost line. ( iso means same in Greek) = + TC 0 Y = m X + b Graph of isocost line TC 0 isocost line Slope = TC 0 Every combination of capital and labor on this line costs the same amount of money.

3 Isocost lines farther away from the origin represent combinations of L and K that have a higher TC. Isocost lines close to the origin represent combinations of L and K that have a lower TC. > > Production indifference curves Remember, we assumed that you could produce the same amount of output using different combinations of inputs, L and K. We could graph all of the combinations of L and K that produce a given amount of output. This gives us a what we call a production indifference curve, or an isoquant. An isoquant shows all of the possible combinations of K and L that will produce a given level of output. Properties of isoquants 1) Negatively sloped 2) Convex wrt origin (bowed inward) 3) Higher curves correspond to higher levels of output 4) Nonintersecting

4 Isoquant map Determining the best mix of inputs If we put the isocost lines on a graph with an isoquant (Q 0 ), we can determine the best (lowest cost) combination of inputs that will produce that level of output. Combination A produces the right output, but costs too much. Combination B produces the right level of output and costs less. Combination C costs even less, but fails to produce the right level of output. C B * A Q 0 *

5 Tangency The best combination of L and K is found at a point of tangency between the isocost line and the isoquant. Therefore, the slopes of the two are equal at that best combination. Slope of isocost = - / Slope of isoquant = - MP /MP Therefore / = MM /MM Or MM = MM Translation When you are using the best combination of L and K, another dollar spent on L gives you the same additional amount of output as another dollar spent on capital.