Production. Economics II: Microeconomics. November Aslanyan (VŠE Praha) Production 11/09 1 / 25
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1 Production Economics II: Microeconomics VŠE Praha November 2009 Aslanyan (VŠE Praha) Production 11/09 1 / 25
2 Microeconomics Consumers: Firms: People. Households. Internal Organisation. Industrial Organisation. Equilibrium: Holds. Does not hold. Aslanyan (VŠE Praha) Production 11/09 2 / 25
3 Microeconomics Equilibrium De nition A condition in which all acting in uences are canceled by others, resulting in a stable, balanced, or unchanging system. De nition (Economics) A state of the economy in which for every good the excess demand is zero (total supply and demand are exactly equal). De nition (Game theory) A condition which no actor has an incentive to deviate from (given the payo s and available strategies). Aslanyan (VŠE Praha) Production 11/09 3 / 25
4 Microeconomics Consumers: Firms: People. Households. Now Internal Organisation. Industrial Organisation. Equilibrium: Holds. Does not hold. Aslanyan (VŠE Praha) Production 11/09 4 / 25
5 Microeconomics Translate Neoclassical Consumer Theory into Theory of Production Revise graphs from introductory Microeconomics Introduce a few new concepts Aslanyan (VŠE Praha) Production 11/09 5 / 25
6 Microeconomics Firms and technologies De nition A rm is a unit that organises production of a good (or service) for sale in order to maximise its pro t. De nition Technology is the sum total of society s pool of knowledge concerning the art of production. Aslanyan (VŠE Praha) Production 11/09 6 / 25
7 Technology Axioms No Land of Cockaigne or No Free Lunch Zero inputs results in zero output. Free disposal or Monotonicity More inputs can produce at least as much output as less inputs. Convexity Weighted average produces at least as much output as the original inputs. (Kills increasing returns to scale) Other technical Aslanyan (VŠE Praha) Production 11/09 7 / 25
8 Technology Production function De nition Production function is the relationship between the quantities of inputs used and the maximum quantity of output that can be produced. Example Two factors of production: Capital, K, and Labour, L: q = f (L, K ) Aslanyan (VŠE Praha) Production 11/09 8 / 25
9 Technology Variability of inputs and "time" Immediate run All the factors are almost xed. (Basically choice is between inactivity and xed production) q = f ( L, K ) Short run One or more of the inputs (factors) are on xed level. Long run All inputs can be varied. q = f (L, K ) Aslanyan (VŠE Praha) Production 11/09 9 / 25
10 Technology Average and Marginal Products De nitions Average product is the ratio of output to input used for production AP L = q L Marginal product is the change in total output resulting from a marginal change in input (holding other factors constant): MP = f (L, K ) L Aslanyan (VŠE Praha) Production 11/09 10 / 25
11 Technology Average and Marginal Products Fact Marginal product equals to the average product when the average product reaches its highest level: q L L q L L = 0 L L q = 0 q L = q L Aslanyan (VŠE Praha) Production 11/09 11 / 25
12 Technology Law of diminishing marginal returns Fact The law of diminishing marginal returns (or product) holds that, if a rm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will become smaller eventually. Diminishing returns vs. diminishing marginal returns Aslanyan (VŠE Praha) Production 11/09 12 / 25
13 Technology Law of diminishing marginal returns Was the Revd Thomas R. Malthus wrong? Fact The law of diminishing marginal returns (or product) holds that, if a rm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will become smaller eventually. Aslanyan (VŠE Praha) Production 11/09 13 / 25
14 Technology Isoquants De nition Isoquant is a curve that shows the e cient combinations of inputs that can produce single (iso-) level of output (quant-ity). Aslanyan (VŠE Praha) Production 11/09 14 / 25
15 Technology Isoquants: Substitutes and compliments De nition Marginal rate of technichal substitution is the number of extra units of one input needed to replace one unit of another input while keeping the amount of output constant: MRTS = MP L MP K = dk dl Aslanyan (VŠE Praha) Production 11/09 15 / 25
16 Technology Returns to Scale De nition Increasing returns to scale is a property of a production function whereby output rises more than in proportion to an equal increase in all inputs. De nition Decreasing returns to scale is a property of a production function whereby output rises less than in proportion to an equal increase in all inputs. De nition Constant returns to scale is a property of a production function whereby when all inputs are increased by certain percentage, output increases by that same percentage. Aslanyan (VŠE Praha) Production 11/09 16 / 25
17 Costs Expenses of production Costs Aslanyan (VŠE Praha) Production 11/09 17 / 25
18 Costs The isocost line De nition Production costs: rearrange: w 1 x 1 + w 2 x 2 = C x 2 = C w 2 w 1 w 2 x 1 All the combinations of inputs that require the same (iso-) total expenditure (-cost) is called isocost line. Aslanyan (VŠE Praha) Production 11/09 18 / 25
19 Costs Optimisation Problem Production costs: min w 1 x 1 + w 2 x 2 s.t. f (x 1, x 2 ) = ȳ Solution Cost function Condition C = c (w 1, w 2, y) MP 1 MP 2 = [ MRTS =] w 1 w 2 Aslanyan (VŠE Praha) Production 11/09 19 / 25
20 Costs Optimisation Fact Condition MP 1 MP 2 = [ MRTS =] w 1 w 2 Lowest isocost rule! Tangency rule! Last dollar rule (pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input). Aslanyan (VŠE Praha) Production 11/09 20 / 25
21 Costs Short run cost measures De nitions Fixed cost (F) is a production expense that does not vary with output. Variable cost (VC) is a production expense that changes with the quantity of output produced. Cost (total cost, C) is the sum of a rm s variable and xed costs: De nition C = VC + F Marginal cost (MC) the amount by which a rm s cost changes of the rm produces one more unit of output (units being in nitesimally small): MC = C = VC q q Aslanyan (VŠE Praha) Production 11/09 21 / 25
22 Costs Average costs De nitions Average xed cost (AFC) is the xed cost divided by the units of output produced: AFC = F /q Average variable cost (AVC) is the variable cost divided by the units of output produced: AVC = VC /q Average cost (AC) is the sum of the two: AC = AVC + AFC Aslanyan (VŠE Praha) Production 11/09 22 / 25
23 Costs and Returns-to-scale CRS, IRS, DRS Example (CRS) c(2y )= 2c(y ) C(y) c(y ) AC(y) y 2y y y Example (DRS) c(y) MC(y) AC(y) c(y ) AC(y) y 2y y y Aslanyan (VŠE Praha) Production 11/09 23 / 25
24 Costs and Returns-to-scale CRS, IRS, DRS Example (IRS) c(2y ) c(y) AC(y) MC(y) c(y ) AC(y) y 2y y y Fact MC = AVC = VC q = w L w q = MP l VC q = w L w q = AP L Aslanyan (VŠE Praha) Production 11/09 24 / 25
25 Costs Long run vs short run Problem Long run cost minimisation: min x 1,x 2 w 1 x 1 + w 2 x 2 s.t. f (x 1, x 2 ) = ȳ Problem Short run cost minimisation: s.t. min x 1 w 1 x 1 + w 2 x 2 f (x 1, x 2 ) = ȳ Fact SR problem is LR problem with constraint x 2 = x 2 Example y Short run x 2 output y expansion path y x 2 x 2 x 2 x 1 x 1 x 1 x 1 Aslanyan (VŠE Praha) Production 11/09 25 / 25
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