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Economics 103 Lecture # 10 Costs of Production When we introduce the idea of Comparative Advantage, we’re talking about different people or different inputs having different costs. Now we want to look at a different situation: the same input may experience different costs when used in different proportions with other inputs. We start with the idea of a production function: The production function embodies the best technology. It gives you the most output for a given input. What will your dog do? For the “moment” this function describes “the firm”. (2L, 2K) 2Q (3L,3K) 3Q But we are not going to worry about returns to scale, we will focus in on changes in proportions. That is, changing the L/K ratio. Let’s assume that K is fixed. Then changes in L will change the L/K ratio. Let’s also define the Marginal Product of Labor as: ΔQ/ΔL We’ll define the Average Product of Labor as: Q/L We’ll also assume the production function has three stages when the L/K ratio changes. This three stage function includes our 5th principle. In stage 1 we have: In stage 3 we have: But in Stage 2 we have what is relevant. Now let’s go back to the graph. What section shows diminishing MP? What is happening to AP over these three stages? What is the use of a marginal product curve? A marginal product curve (in stage 2) is actually the demand for labor ... When you multiply by the price of the output. Demand for labor. The equilibrium amount of labor hired is where the price equals the value of the marginal product. Even if you’re the best darn rock picker in the world, why might your wage be low? When there is more than one variable input, it still holds that the demand for labor equals the value of the marginal product. So, suppose both capital and labor are variable. Then we have the following equilibrium. Now the equilibrium conditions are: w = pMPL v = pMPK If we have : w = pMPL v = pMPK Then we get: Equating marginal products is what lies behind: Triage: In an emergency you first help the ones who are at the margin. In Oregon, the state health insurance will not pay for care that I) is extremely expensive, or II) has no proven benefit. Again, this equates the marginal product per dollar. Should the government devote research money to finding cures for extremely rare diseases? The most effective naval weapon in the Second World War was: 90% of enemy shipping was destroyed by subs. But then why have battleships? Moneyball. So at the margin, the first battleship was more productive than the 1000th submarine. This explains why we don’t see a hockey team made up of: Back to Marginal Products Marginal Products and Marginal Costs are inversely related. What is the intuition behind this? So now we have two reasons for why MC curves are increasing. 1. As output increases, different inputs are used. At first the low cost inputs are used, then the high cost inputs are used. That is, there is an extensive adjustment. 2. As output increases, each input is used more intensively relative to the amount of capital. This lowers the inputs marginal product, and increases the marginal cost. This is an intensive adjustment. Aside from Marginal Costs, there are three other types of costs we need to worry about. 1. Average Fixed/Sunk costs: AFC = FC / Q. Total cost = fixed costs + variable costs. ATC = AFC + AVC. Divide by Q If we have the three stage production function, then these cost curves look as follows: Why would they be this shape? Where would the Marginal Cost curve fit in here? What would happen to the cost curves if you put on a a. tax per unit of output? b. a lump sum tax? What would happen to the cost curves if a. labor became more productive? b. wages increased?