# Help with Deriving Hicksian Demand in the Monocentric City Model?

I have a fairly standard Alonso-Muth-Mills model, but struggling to derive the Hicksian demand.

Starting with the basic utility function:

And this Budget Constraint:

Housing Floor-space is subsequently added in:

My ask: Now this is where I am confused: How is U-bar, P(X) and H(X) derived?

I am following this guidance here, but seemingly cannot solve it algebraically.

Any help would be greatly appreciated and more than happy to shout a coffee, provide a donation!

Many Thanks!

• Try to assume that you are at the edge of the city. The differentiate profit with respect to k. The find expression for k is a function of price at edge and exogenous parameters. Backinsert this into profit expression and use that profit is equal to 0 and solve this for price at the edge as a function of exogenous parameters. Insert Marshall demands into utility function and get valuefunction. Insert price at edge in valuefunction to get utility at edge. Then use that utility is the same everywhere. Get (14) by setting valuefunction equal to u-bar and inverting valuefunction to solve for P(x). Commented Jun 26 at 23:38
• Then insert the expression for P(x) into expression for Marshall demand to get (15) ... try it ... if you can follow the instructions or I made mistake let me know :) good luck. Commented Jun 26 at 23:40
• @JesperHybel - Thank you so much for your contribution, I truly appreciate it. I am working on your solution now and hope to get back to you. Thanks again for being amazing! Cheers.
– GWY
Commented Jun 29 at 8:04