The production set Production requires inputs - factors of production- for example. labour and capital equipment. A production set is the set of outputs feasible giv articular combination of inputs. The production function escribes the maximum output given a particular combination of inputs. Both are illustrated below y= f(r)= Production function Isoquant Production set Iput =r An isoquant maps all the combinations of the(two)inputs that that are just sufficient to produce a given output. Technology is assumed to be monotonic and conver, producing isoquants like those above Monotonicity(or free disposal) says that more of one input will result in at least as much output. Convexity says that if two different combinations of inputs produce output y, then a weighted average will produce at least iction -Frans Marginal Products When one of the factors is increased a small amount, Ar1, output rises by Ay. The marginal product is MB(xx2)=y=+△m2)-/2≈ Marginal product gives the slope of the production function y= f(zr, I2) How much additional input 2 is required to just continue producing exactly y units of output, given a decrease in RS). If output remains const MP(x1,x2)△r1+MP2(x1,x2)△ This equation can be solved for the change in input 2 divided by the change input 1. It is the slope of the isoquant. TRS=Ar2=_MA(1,r2) Ar1 MP(a1, r2) The "lawof diminishing marginal product states that marginal product will decrease as the amount of the input used is increased, keeping all other inputs constant. Why is this considered a "law"? Diminishing TRS is also assumed -it follows from the convexity of the isoquantProduction — Firms 1 The Production Set • Production requires inputs — factors of production — for example, labour and capital equipment. • A production set is the set of outputs feasible given a particular combination of inputs. The production function describes the maximum output given a particular combination of inputs. Both are illustrated below. . ................................................................................................................. . ............................................................................................... ................................................................................................................................................................................................................................................................................ .................................................................................................................................................................................................................................................................................. 0 Output = y Input = x 0 x2 x1 Production set y = f(x) = Production function Isoquant y = y • An isoquant maps all the combinations of the (two) inputs that that are just sufficient to produce a given output. • Technology is assumed to be monotonic and convex, producing isoquants like those above. Monotonicity (or free disposal) says that more of one input will result in at least as much output. Convexity says that if two different combinations of inputs produce output y, then a weighted average will produce at least y. Production — Firms 2 Marginal Products • When one of the factors is increased a small amount, ∆x1, output rises by ∆y. The marginal product is: MP1(x1, x2) = ∆y ∆x1 = f(x1 + ∆x1, x2) − f(x1, x2) ∆x1 ≈ ∂f ∂x1 • Marginal product gives the slope of the production function y = f(x1, x2). • How much additional input 2 is required to just continue producing exactly y units of output, given a decrease in the amount of input 1? The answer is the technical rate of substitution (TRS). If output remains constant, then: ∆y = MP1(x1, x2)∆x1 + MP2(x1, x2)∆x2 = 0 • This equation can be solved for the change in input 2 divided by the change input 1. It is the slope of the isoquant. TRS = ∆x2 ∆x1 = − MP1(x1, x2) MP2(x1, x2) • The “law” of diminishing marginal product states that marginal product will decrease as the amount of the input used is increased, keeping all other inputs constant. Why is this considered a “law”? • Diminishing TRS is also assumed — it follows from the convexity of the isoquant