ISI 2005.. Utility function?

[Spiti]

[Dreyfus]

Consider.....vegetable being single good x....now when Laxmi's income is very low she can only afford rice not veggies... this represents the case of quasilinear preference b/w good x nd rice that is U(x,r)= v(r) +x
Now When she can afford veggies she will only prefer to buy either potato or cabbage depending on its price but she will never buy both so it can't represent perfect substitutability b/w veggies, therefore the preferences she have amongst veggies is concave ie x=max{c,p}
The final utility function for luxmi becomes U(r,c,p)= v(r) + max{c,p}

[Spiti]

Thanq

[The Villain]

Vaibhav i didnt get the max part..max denotes larger quantity of the 2??

[Dreyfus]

Ron, yes max presents the maximum of the two....consider when price of potato > price of cabbage now when u exhaust all ur income on potato u'll only get fewer no. of units compated to cabbage when u exhaust all ur income on cabbage.
Therefore max function represents the concave preference as when u exhaust income on both of the veggies u will get comparatively lesser units as when u buy only 1 type of veggie that is extremes are preferred over averages!
also when prices of two veggies are same the consumer will only buy only 1 type of veggie not both!

[mrittik]

This problem would be solved more easily....for the second part of cabbage and potato it means it is working as a perfect substitute b/w each other or take a concave function.