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ECON6021 Microeconomic Analysis. Production I. Definitions. Short Run Production. Q. Short-run production. pt of inflexion. L. I. I b. II. I a. MP L. III. AP L. L. L 1. L 2. L 3. Short Run Production.
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ECON6021 Microeconomic Analysis Production I
Short Run Production Q Short-run production pt of inflexion L I Ib II Ia MPL III APL L L1 L2 L3
Short Run Production Law of diminishing Marginal Productivity—eventually, if a variable input is combined with a fixed input,its marginal product will, beyond some point decline, i.e., beyond L1,
2KB KB LB 2LB Isoquants Isoquant (the locus of (K,L) that yields the same quantity of good) • Constant returns to scale: a doubling of inputs doubles outputs • Decreasing returns to scale: a doubling of inputs less than doubles output. • Increasing returns to scale: a doubling of inputs more than double output
Properties of Isoquants • Cardinal—each isoquant represents a certain Q whose value is objective. • Coverage—for any point, there is always an isoquant passing through it • Negative Slope—because MPL>0, MPK>0 (assuming not in Region III) • Can’t cross • Bending towards the origin • Farther away from the origin, the greater the quantity.
Cobb-Douglas production function In general,
K L Linear Production Function
K Slope= L Linear Production Function
Leontief Production Function K 2K=L (or aK=bL, in general) 1 L 2
K D A C B Isoquant, L O Cost minimization: Long Run Problem
K Locus of equal MRTSLK (output-expansion path for given input prices) Iso-cost line wL+rK=const L Optimal Input Choice Optimal choice of (K,L) that yields Qo with min. cost.
K Output expansion path L Output Expansion Path
K output expansion path output expansion path L Output Expansion Path
Leontief Production Function From now on, we use cost function, rather than production function. outcome of cost min. problem