Rudiments of a Theory of Demand
 

Handout #2
 

Marshall's Laws of Derived Demand:

The demand for labor will be less elastic

(1) the smaller the elasticity of substitution

(2) the smaller the elasticity of demand for the final product

(3) the smaller the initial ratio of labor costs to other costs, and

(4) the less elastic the supply of other factors
 

The demand curve represents the quantity of labor a firm is willing to hire at given wage rates.
 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

1. How much labor woule be hired at $3 per hour?
 

The demand curve can be described by the elasticity. The elasticity of demand (Ed) is:
 

The elasticity of demand describes how sensitive firms are in the quantity of labor they demand, given changes in the wage rate.
 

2. Compute the elasticity of demand assuming an initial wage of $2 per hour that rises to $4 per hour.
 

The Production Function
 

Q = f(K, L)
 

An isoquant represents all combinations of capital and labor that yield a given quantity of outputs.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

The slope of an isoquant can easily be derived mathematically. Totally differentiate Q:
 

If output is held constant than dQ=0. The slope of an isoquant is (dK/dL). Solving the above equation implies:
 

The curvature of the isoquant reflects the substitutability of K for L (or L for K) in the production process. A measure of this curvature is the elasticity of substitution denoted by .
 

An isoquant curve represents all combinations of capital and labor that can be purchased for a given expenditure. Since total costs of production can be expressed as:
 

where
 

C = total cost

w = wage per unit of labor

r = rental rate for a unit of capital

K = capital

L = labor
 

then

and the slope of the isocost curve is:

3. If Labor is $2 per hour and capital rents for $4 per hour, what is the slope of the isocost curve?
 

4. Draw the isocost curve if total expenditures are to be limited to (a) $100, (b) $200, (c) $400. Which isocost curve is higher? Are they parallel? Redo if the wage doubles from $2 per hour.
 

Demand and Supply
 

Evidence indicates the climate in an area influences labor supply. As an illustration, assume the following labor supply function:
 

Qs = -200 + 200W -50R
 

where

Qs = quantity of labor supplied

W = wage rate

R = average rainfall per month
 
 
 

The demand for labor is given by:
 

QD = 1500-100W
 

where

QD = quantity of labor demanded
 

1. Do wet areas (ones with large amounts of rain) have higher or lower wages than dry areas? (Explain using equations or a graph).
 
 
 

2. What will be the employment level in Reigns, Rhode Island (a city with an average rainfall of 2 inches per minth)?
 
 
 

3. What would the unemployment rate in Reigns be if the minimum wage were $8 per hour?