Unformatted text preview: Production Definitions Production: The process of combining inputs to make outputs. Factors of production: ‐ Land ‐ Labor (physical force) ‐ Raw materials ‐ Capital: financial capital, physical capital (goods that are used to produce other goods), human capital (skills – what you are getting by taking classes at Cornell) Production function f(x1, x2) tells us the maximum amount of output y we can produce with amount x1 of Good 1 and amount x2 of Good 2, given currently available technology. Isoquants are the level sets of the production function: for a given level of output y, they show the combinations of x1 and x2 that can produce y. Examples of production functions: Fixed proportions (Leontief): f(x1, x2) = min{x1, x2} Perfect substitutes: f(x1, x2) = x1 + x2 Cobb‐Douglas: f(x1, x2) = Ax1ax2 b, where 0<a,b<1, A>0 Like with utility functions, we generally make two assumptions about production functions: Monotonicity: If you increase the amount of at least one of the inputs, you can get at least as much output. Convexity: If you have two ways to produce y units of output, their weighted average will product at least y units of output. Marginal product of factor 1 is the amount of additional output when we increase the amount of input by 1 unit, holding constant the amount of all other inputs: MP1 (x1, x2) = ∂f(x1, x2)/∂x1. Most production technologies have the property of diminishing marginal product. Technical rate of substitution (TRS) is the additional amount of factor 2 that you need when you give up a bit of factor 1 to produce the same amount of output y: the slope of the isoquant, TRS(x1, x2) = dx2/dx1 f(x1, x2)=constant = ‐ ∂f(x1, x2)/∂x1 / ∂f(x1, x2)/∂x2 = ‐ MP1 (x1, x2) / MP2 (x1, x2) The production function is convex if and only if the isoquants exhibit diminishing TRS. Diminishing MP is different from diminishing TRS because MP holds constant the level of the other inputs (so output changes), while TRS adjusts the level of other inputs to hold constant the level of output. Diminishing MPs implies diminishing TRS (but you can have diminishing TRS without diminishing MPs). Constant returns to scale (CRS): t f(x1, x2) = f(tx1, tx2) for any t>0. Increasing returns to scale (IRS): t f(x1, x2) < f(tx1, tx2) for any t>1. Decreasing returns to scale (DRS): t f(x1, x2) > f(tx1, tx2) for any t>1. “Returns to scale” is about scaling all inputs by the same factor. Note that CRS and IRS are possible even with diminishing MPs because we’re doubling all inputs in the definitions of CRS and IRS. Profit = revenues – costs Per unit time, e.g., in a year. π = pf(K,L) – wL – RK – fixed costs where π is profit, p is output price, w is the wage rate, and R is the rental rate on capital. Accounting profit: Input costs valued at what was paid for them (historical cost). Economic profit: All inputs valued at what else you could currently do with them (opportunity cost; “mark to market”). Fixed factor: Required in fixed amount regardless of how much you produce. (Generates a fixed cost.) Example: lease on a building. Variable factor: Required amount depends on how much you produce. (Generates a variable cost.) Example: labor. Quasi‐fixed factor: Required in fixed amount, as long as output is positive. (Generates a quasi‐fixed cost.) Example: electricity. Short run: Some factors of production are fixed. Long run: All factors of production are variable. (Neither of these is a specific length of time; it depends on which industry and which factor we are interested in analyzing.) ...
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This note was uploaded on 04/02/2011 for the course ECON 3010 at Cornell.
 '07
 WISSINK
 Microeconomics

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