Labor Demand in the Long Run The long

Labor Demand in the Long Run

The long run n n in the long run, all inputs are variable, model used in discussion has 2 inputs: L (labor) and K (capital). Q = f(L, K) isoquant - a graph that contains all of the combinations of inputs that result in a given level of output.

Isoquant

Isoquants

Marginal rate of technical substitution The marginal rate of technical substitution of L for K (MRTS) is defined as the additional amount of capital needed to replace a unit of labor, holding output constant. Mathematically, the MRTS can also be expressed as:

Law of diminishing MRTS n Law of diminishing MRTS – the MRTS declines as the level of labor use rises along an isoquant (i. e. , isoquant curves are convex)

Alternative derivation of the MRTS Along an isoquant: With a little manipulation: More precisely: Or:

Isocost curves TC = w. L + c. K where: TC = total cost w = wage c = price of capital L = quantity of labor K = quantity of capital In slope-intercept form, this equation becomes: K = (-w/c)L +(TC/c)

Isocost curve

Isocost curves

Cost minimization

Cost-minimization rule n n n cost minimization occurs when an isocost curve is tangent to the isoquant -MRTS = -w/c MRTS = w/c

Substitution and scale effects n n the substitution effect associated with a change in the wage rate is the change in the mix of inputs that results from the change in relative prices, holding output constant. the scale effect is the change in the mix of inputs that occurs because of the change in the level of output resulting from a change in factor prices, holding relative factor prices constant.

Substitution effect

Scale effect