Letter to Professor

The letter is about a small variation of the labour supply model,

"Dear Dr Chan,

I am writing to ask for clarification of an assumption introduced in the last class of Human Resources Economics.

In discussing the effect of the fixed time cost of working on the individual labour supply curve, you made the assumption that leisure is normal. What puzzle me is that the precise meaning of this assumption. I have tried to work out the reasoning in simple math, and discovered that the income elasticity of leisure is positive, as assume, but can never be greater than one, or the outcome is totally reversed. So what I want to ask is the assumption means, “Leisure is normal but not superior”.

I am not sure my calculation is correct, or am I thinking too much, or I have turned into a wrong direction. Anyway, please accept my apology for wasting your time if it turns out to be a silly question. Just to let you have an idea of who I am, still remember the one who answered, “It depends ……… but I don’t know it depends on what”, I am the one being asked about the leisure normal income effect.

Regards,

Cheng Ho Cheung
Becon, Year III "


The reply come as,

"Hi, what you said is correct. I should have stated that if both C and L are normal, then the hours of work will decrease. If the income elasticity of leisure is greater than 1, then hours of work will increase when there is a fixed time cost of working."


My letter is surely not as good as Vic's lengthy and detailed one about MRS and DMU. [You may find his work and some follow-up discussion here.] I choose not to include the working in the email, because the math is so simple, and I want intuition more than rigorous proof. It all start with an identity, T = L + H, then empolying some basic calculus to get the percentage change effect explicitly. The rest is just simple comparison, left hand side vs right hand side.

(Vesper has shown me the graphical solution this afternoon in the canteen, which is a bit confusing to put that here, as there are many curve moving, but the key is to consider also the vertical axis althought that is not the one representing the variable in question. It should be intersting to note that while we are discussing, there are some people talking econ stuff more seriously than we do over several table apart. I doubt if the prof. is receiving money, or he must have an illness that cannot stop teaching.)

I should be happy that I can use what learnt in MME correctly, and yet as a year 3 student in economics major, I can only ask a trivial question to fill in a small hole of the lecture material, should that be a sad thing?