EC Intermediate Microeconomic Theory

Transcription

1 EC Intermediate Microeconomic Theory Lecture: Cost of Production Cont. Bekah Selby rebekahs@uoregon.edu May 5, 2014 Selby EC Lectures May 5, / 23

2 Review A firm faces several types of costs: Economic Costs Opportunity Costs (equals economic costs) Sunk Costs Fixed and Variable Costs (=Total Cost) From this we can find Marginal costs Average Costs Selby EC Lectures May 5, / 23

3 In the short-run, a firm does not have the ability to change capital. Then their production function looks like q = f (L) and variable costs are just a function of the number of labor units and wage: VC = w L In the long-run, a firm can choose capital and will need to choose inputs K and L so as to minimize costs. Selby EC Lectures May 5, / 23

4 The firm s problem is to minimize costs of production in order to produce some quantity min K,L wl + rk s.t F(K, L) = q This says that the firm is minimizing total costs equal to the cost spent on labor plus the cost spent on capital so as to produce q subject to production technology F. Selby EC Lectures May 5, / 23

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6 The curve connecting the best bundles of K and L as q increases is called the expansion path The curve mapping q to the total cost of production q is called the long run total cost curve. Selby EC Lectures May 5, / 23

7 Calculating Firm Decisions As we can see, the firm will choose the bundle of K and L on the iso-quant at the point where the iso-quant is just tangent to the iso-cost line. This means that the slope of the isoquant (MRTS) is exactly equal to the slope of the isocost line (w/r) Recall that It can be shown that MRTS = K L ( ) K = MPL L MPK Selby EC Lectures May 5, / 23

8 Calculating Firm Decisions Then the optimal bundle of K and L is when Examples: MPL MPK = w r Suppose a firm has the following problem: min K,L 0.5K + 10L s.t. K 2 L 2 = q Selby EC Lectures May 5, / 23

9 Calculating Firm Decisions Example, cont.: The w = 10, r = 0.5, and MPL = 2K 2 L MPK = 2K 2 L Then the optimal bundle occurs when MRTS = w/r = 2K2 L 2KL 2 = K L = w r = = 20 Selby EC Lectures May 5, / 23

10 Calculating Firm Decisions Example, cont.: So we can say that K = 20L Substituting into the constraint this gives us: K 2 L 2 = q = (20L) 2 L 2 = q = 400L 4 = q = L = 4 q 400 and K = 20 4 q 400 Selby EC Lectures May 5, / 23

11 Calculating Firm Decisions Example: min K,L 2K + L s.t. K 1/2 L 1/2 = q The optimality condition MRTS = MPL MPK = (1/2)K1/2 L 1/2 (1/2)K 1/2 L 1/2 = 1 2 = w r = K L = 1 2 = K = (1/2)L Selby EC Lectures May 5, / 23

12 Example, cont. Substituting into production function: ((1/2)L) 1/2 L 1/2 = q = (1/2) 1/2 L = q = L = q 1/2 = ( 2)q = K = (1/2)L = ( ) 2 2 q Selby EC Lectures May 5, / 23

13 Long-Run vs. Short-Run Cost Curves Inflexibility in the short run leads to expansion path that looks like this: Selby EC Lectures May 5, / 23

14 Long-Run vs. Short-Run Cost Curves Short-Run Average Cost Curve relates the average cost of producing q when capital is fixed Long-Run Average Cost Curve relates the average cost of producing q when all inputs are variable Long-Run Marginal Cost Curve relates the change in the long-run total cost for a change in output. Selby EC Lectures May 5, / 23

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16 Economies and Diseconomies of Scale Why would long-run average costs decline? In large firms, workers can specialize at tasks in which they are most productive Scale provides flexibility: firms can easily change the amount of capital and labor to produce more efficiently A firm might be able to acquire inputs at lower cost by buying them in bulk. Selby EC Lectures May 5, / 23

17 Economies and Diseconomies of Scale Why would the average costs start to increase? In the short-run, space/limited machinery might makes production inefficient Large firms involve many tasks, which may be hard to manage Advantages of bulk buying may decrease after a certain output is attained Selby EC Lectures May 5, / 23

18 Economies and Diseconomies of Scale Economies of Scale is a situation in which a doubling of costs more than doubles the amount of output Diseconomies of Scale is a situation in which a doubling of costs induces less than double the amount of output Measuring economies of scale: Define the elasticity of cost due to a change in output as E C = C/C q/q = ( ) C 1 q C/q = MC AC Selby EC Lectures May 5, / 23

19 Economies and Diseconomies of Scale When E C = 1, costs increases proportionately with output (MC = AC), so neither economies or diseconomies of scale When E C < 1, costs increase less than proportionately with output (MC < AC), so economies of scale When E C > 1, costs increase more than proportionately with output (MC > AC), so dieconomies of scale Selby EC Lectures May 5, / 23

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21 Relationship between Long-Run and Short-run Cost In the long-run, a firm is going to choose the plant-size (amount of output) that minimizes it s average cost. The long-run average cost curve maps out the optimal minimum short-run average costs for each level of output. Consider the following graph: Selby EC Lectures May 5, / 23

22 Relationship between Long-Run and Short-run Cost Selby EC Lectures May 5, / 23

23 Relationship between Long-Run and Short-run Cost At q < q 2, then firms have economies of scale. They could still benefit by increasing in size because the change total cost is less than proportionate to the change in output At q > q 2, then firms have dieconomies of scale They would benefit from decreasing in size since costs will go down by a factor greater than the decrease in output. Only at q = q 2 are firms producing at a point where they will not benefit from deviating. Selby EC Lectures May 5, / 23