Section Notes 11, Econ 100A Spring ’06 1Section Notes 11Covering material from Lecture on February 16thClass Outline1. Costs2. Short Run Costs3. Long Run Costs4. Short Run vs. Long Run Production Decisions1 CostsThere is a difference between accounting c osts and economic costs. We are concerned with economiccosts, which include the opportunity costs.Sunk Cost:A few general equations:1. Total Cost: TC = C(q) =2. Marginal Cost (MC): MC =3. Average Total/Fixed/Variable Costs - All just divided by final quantity of output.2 Short Run CostsWhen we initially deal with costs of production, we are assuming that the costs of inputs are fixed. Thisis why we can write the costs purely as a function of quantity. For example, if we’re in the short run (i.e.there is a single variable input) and our variable input has a fixed cost, how do we find the marginal cost?NB: Thinking about this a little more, what is the relationship between diminishing marginal returns andmarginal costs?Section Notes 11, Econ 100A Spring ’06 2The relationship between diminishing returns and marginal costs can be seen well graphically.6-6-3 Long Run CostsIn this situation, we’re letting both inputs vary. It’s easy to conceptualize the cost of labor, but it’ssometimes tricky to think about the cost of capital. As economists we should see that the cost of capitalis the cost of depreciation of its use, plus the opportunity cost of letting s omeone else use it (i.e. interestrate times the value of capital). We denote the cost as r = Depreciation rate + Interest rate.Isocost Line:Let’s spend some time analyzing some isoquant and isocost lines together.6-6-Section Notes 11, Econ 100A Spring ’06 34 Short-Run vs. Long-Run Production DecisionsProblem: (P&R, Chapter 7, Exercise 11)Suppose that a firm’sproduction function is q = 10L1/2K1/2. The cost of a unit of labor is $20 and thecost of a unit of capital is $80.1. The firm is currently producing 100 units of output and has determined that the cost-minimizingquantitites of labor and capital are 20 and 5, respectively. Graphically illustrate this using isoquantsand isocost lines.2. The firm now wants to increase output to 140 units. If capital is fixed in the short run, how muchlabor will the firm require? Illustrate this graphically and find the firm’s new total cost.3. Graphically identify the cost-minimizing level of capital and labor in the long run if the firm wantsto produce 140 units.4. What is the marginal rate of technical substitution? Find the optimal level of capital and laborrequired to produce the 140 units of output.6-6-Section Notes 11, Econ 100A Spring ’06 4Problem: (P&R, Chapter 7, Exercise 8)You produce engines with a production functionq = 5KL.Each assembly machine rents for r = $10, 000 per week, and each labor team costs w = $5000 per week.The cost of raw materials for each engine is $2000. You have a fixed number of 5 assembly machines.1. What is the cost function of your plant? What are average and marginal costs for producing qengines? How do average costs vary with output?2. How many teams are required to produce 250 engines? What is the average cost of production?3. If you were to design a new facility, what capital to labor ratio (K/L) should the new plant accom-modate if it wants to minimize the total cost of producing at any level of output
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