Consider a static model of labor supply. Assuming individuals have preferences represented by the utility function...

Consider a static model of labor supply. Assuming individuals have preferences represented by the utility function ? = ?α?(1-α) and face the following constraints ? = ?ℎ + ?, and ℎ = ? − ?, where C is consumption, L is hours of leisure, w is the hourly wage, h is hours of work, Y is non-labor income, and H is total time to split between work and leisure. (Hint: you can normalize the price of consumption to be one.)

a. What is the labor supply function?

b. What does the parameter ? represent?

Solutions

Expert Solution

Part a)

Part b)

The parameter ? represents the utility elasticity of of consumption.

Basically if we take the natural logarithm on both sides of the utility function,

ln(U) = ? lnC + (1-?)lnL

Taking the partial differential wrt C we get,

dU/U = ?dC/C

Hence ? = (dU/U) / (dC/C)

This function provides ? as the percentage change in utility wrt a percentage change in C, hence it is named as the utility elasticiy of consumption.

Rahul Sunny answered 1 month ago

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