Frank Cowell: Microeconomics Exercise 5.7 MICROECONOMICS Principles and Analysis Frank Cowell March 2007

Frank Cowell: Microeconomics Ex 5.7: Question purpose: Illustration of labour supply model with very simple preferences purpose: Illustration of labour supply model with very simple preferences method: Consumer optimisation with endogenous budget constraint method: Consumer optimisation with endogenous budget constraint

Frank Cowell: Microeconomics Ex 5.7: Worker’s problem Basic constraints on worker are Basic constraints on worker are  x is consumption   y is non-labour income  w is wage rate  ℓ is labour supply Worker’s problem can therefore be written as Worker’s problem can therefore be written as  found by substituting from above into utility function

Frank Cowell: Microeconomics Ex 5.7: Worker’s optimum Take log of maximand to get Take log of maximand to get   log(wℓ +  y) + [1   ] log(1  ℓ) Differentiate with respect to ℓ Differentiate with respect to ℓ This is zero if This is zero if   wℓ +  w + [1   ]  y = 0  which implies ℓ =  + [1   ]  y / w But this only makes sense if ℓ is non-negative But this only makes sense if ℓ is non-negative  requires w ≥ [1   ]  y /   so optimal labour supply is

Frank Cowell: Microeconomics Ex 5.7: Interior maximum   (leisure, consumption)-space   Max value of leisure   Non-labour income   Budget constraint x 1  ℓ 0   Indifference curves 1 yy   Optimum 1  ℓ * slope = w   w ≥ [1   ]  y /    0 < ℓ * < 1

Frank Cowell: Microeconomics Ex 5.7: Corner solution   Non-labour income   Budget constraint x 1  ℓ 0   Indifference curves as before 1 yy   Optimum   w < [1   ]  y /    ℓ * = 0

Frank Cowell: Microeconomics Ex 5.7: Points to note Treat leisure as a conventional good Treat leisure as a conventional good Has a natural upper bound Has a natural upper bound  where labour is zero Have to all for corner solution Have to all for corner solution  where person chooses not to work Type of equilibrium depends on Type of equilibrium depends on  wage rate  non-labour income