I have this indirect utility function:
with constraint Y = c + pq
I have posted before about getting the utility function from it, but I was not able to get it. I only needed that as a preliminary step to get price and demand functions similar to here: How do I get to this demand function in the monocentric city model?
Maybe it's possible to get the demand directly as a function of income and utility (but not as a function of c) without having the direct utility function first?
I thought of solving for c in the resulting demand function:
$$lnq= lnc-\beta lnp+ \gamma lny$$
And then substituting that into v and solving for q and p, but that doesn't seem right.
Any help with
- how to solve for c from the two first
- how to get demand function for q as function of income and utility (without c)
- how to get the direct utility function
Would be greatly appreciated.