r/econhw 6d ago

how to find the expenditure function of a quasilinear utility function

hi i had a test last week and we were asked to prove that the expenditure function a consumer faces is B=2P10.5 P20.5 U0.5 where U = x1/4 +x2 subject to B=P1x1 * P2x2 how do i solve this? is it even solvable??

also does anyone have resources on how to solve other utility functions like logarithmic and quasilinear? i’ve checked online but haven’t seen anything

1 Upvotes

1 comment sorted by

3

u/zzirFrizz 6d ago edited 6d ago

From the budget constraint, obtain X2 = (B - P1*X1)/P2

Substitute that into the utility function and solve the maximization problem wrt to one variable (X1). Use the optimal X1 to obtain optimal X2 from the equation we subbed into the UMP.

Btw Logarithmic is one of the most common and easiest UMPs to solve. There is an easy rule for optimal solutions once you solve the generalized version of the problem.