ECON6021 Microeconomic Analysis Production I

Definitions

L Q pt of inflexion Short-run production I IaIa IbIb II III MPLMPL AP L L L1L1 L2L2 L3L3 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 L 1, Short Run Production

2K B KBKB LBLB 2L B Isoquant (the locus of (K,L) that yields the same quantity of good) 1.Constant returns to scale: a doubling of inputs doubles outputs 2.Decreasing returns to scale: a doubling of inputs less than doubles output. 3.Increasing returns to scale: a doubling of inputs more than double output Isoquants

1.Cardinal—each isoquant represents a certain Q whose value is objective. 2.Coverage—for any point, there is always an isoquant passing through it 3.Negative Slope—because MP L >0, MP K >0 (assuming not in Region III) 4.Can’t cross 5.Bending towards the origin 6.Farther away from the origin, the greater the quantity. Properties of Isoquants

Isoquants and Slopes

Output Elasticities

An Example: Cobb-Douglas Production Function

Cobb-Douglas production function In general,

L K Linear Production Function

Slope= L K Linear Production Function

L K 2K=L 2 1 (or aK=bL, in general) Leontief Production Function

Cost Minimization:

The optimal input mix

L K A B C D Isoquant, O Cost minimization: Long Run Problem

Optimal choice of (K,L) that yields Q o with min. cost. Optimal Input Choice L K Locus of equal MRTS LK (output-expansion path for given input prices) Iso-cost line wL+rK=const

L K Output expansion path Output Expansion Path

K L output expansion path Output Expansion Path

Leontief Production Function

From now on, we use cost function, rather than production function. outcome of cost min. problem Leontief Production Function

The End