The mathematics can be programed quite easily using fibonnacci algorithms. And this would be the half of the game thats still missing.
Editor Requirements
This requires an "Economical Improvement" Flag for buildings in the editor, programing that Improvement to have a stock name, editable possibly. The resource requirement choice box already exists in the Civ3 Editor, keep it in the Fourth but have it as a selection box. The "Economical Improvement" flag would just make the requirement city-radius specific. Also a "Produces Resource" selection box would be required. (The Economical flag has to already exist, otherwise the Smith's Trading Co. Wonder wouldn't do what it does, right?)
Introduction
Have a separate stock for each economicly related city improvement (i.e. Marketplace, Bank). The Stock Markets in each city would be one stock in unity, an example of your modern day NASDAQ, but each additional Stock Market in each city would strengthen it in price and stability. The Smith's Trading Co. Small Wonder would then become a civ related Small Wonder such as NYSE, AMEX, or NIKEI (a civ-specific Exchange); Strengthened(as in Weath & Growth) by the direct effect of the all Stock Market Improvements. The Individual Stock Markets in each city is strengthen by the collective strengths of the businesses in the relevant city (Explained below), and the population size & unemployment rate.
Multiple Exchanges for specific civs could become a civ specific strength or weakness. Civ's Exchange(s) in relation to each other would denote relative currency value and nothing more. A Candaian dollar doesn't always equal a German Mark, but it can be worth more & less. This has a direct effect on Gold when exchanged in diplomacy with other civs and importation & exportation.
Businesses & Stock
When a cartain technology that is researched, the ownership of resources is changed slightly. Each resource on the map changes to a ownership of a certain type, depending on government type. Democracy allows for a Capitalistic economy allowing for more wealth gaining, but more volatility. Communism would lead to a Marxist type economy, all businesses & corporations being owned by the state, and only directly affected by outside stock effects. One type has many stocks that are unstable, but few uberwealthy to strengthen the general economy, the other has mostly stable stocks but near to no wealthy ones.
Resources are under control of the city that is the closest, and is owned by the relevant business created by the improvement that is now available in that city's production window. Markets & Banks would basically be modern Wal-Marts & First National Banks; Airports & Harbours would become you Airline & Cargo companies, with their strengths coming from their city's population (everybody borrows & has money; businessmen travel & imports have to come somehow, right?). These are hard coded, and are the basis of your economic stability. Once an Economical Improvement is built the relevant stock is opened at a price & begins to fluctuate over time.
There are additional "Economical Improvements" that are available at there own relative technologies, which have already been suggested. Such as the Steel Mill, which takes Coal & Iron to produce Steel and allowing for Battleships & possibly an improvement; or the Refinery, which takes Oil and makes Gasoline, Lubricant and Chemicals. These have been explained and would be VERY useful in this way, along with their original purpose. And the mind can always come up with another one.
Also Science Improvements could become businesses that only consume resources to produce more science funding. And there effective pricing would be based on how much Science funding there is altogether, and the relevance of the Tech being researched to that Scientific Business. (Like Pharmecutical Business when researching Modern Medicine). Also allows for more relevant Techs to have a purpose.
Now each "Economical Improvement" that is built is a business and acts as one. They employ your population, and contribute to your unemployment rate & GNP (It has a Purpose Now!!!). Its price is affected by these two variables and can grow and prosper, or splatter like a marshmallow under a falling brick. How you govern has a direct effect, such as War Weariness & the additional Economic Legislation (How good your businesses, Exchange(s) & Index are doing). Which your action on raising tariff rates, taxes & the Interest Rate (all of which deposit into your treasury), along with your governing your importation and exportation.
Importation & Exportation
Civs could combine strengths for wealth by signing "Economic Pact" Treaties, agreeing to lower Tariffs on the partner civ to a certain level. "Tariffs" would contribute directly to your treasury and be hard-coded into the game as a part of the Tariff/National Interest slider choice much in the same way as the Tax\Science\Culture slider.
Lower the Tariffs and your Interest has to go higher, because of the increase of importation causes more jobs & more spending, thus more wealth, thus more borrowing, thus more wealth. When Tariffs are raised importation becomes expensive and more reliance is give to domestic business and loans aren't so hot right now & need to be encouraged. All much the same way as real life.
Your Importers would be first your Marketplaces which import luxuries & Foods, then the individual businesses that exist in your cities that are producers of refined reources, like that Steel Mill. The selections for these would be hard coded into the City Screen or the Right-Click window. You can choose your importer in a window for that importer that shows a listing, displaying the Exporters of the required resource, civ owner, and price. You can also choose to stop importation, and turn that importer "OFF" and pay a lower upkeep (gotta maintain it, sry).
Your exports generate wealth for the individual business that owns each resource you have in your control. You can divert exportation by right-click on a resource on a window appearing listing what business require it and at what price they'll buy it at or stop it all together. Your own businesses requiring that resource won't have the Tariff and will be lower priced, or course. Be careful not to change it alot because each time you do, your exporter under-bids the current supplier to that business (If there is one). You can turn off, and thus stop exportation of that resource
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Embargos have suddenly taken a more interesting approach).
I've read about the contracting of Units to other countries and this can have a direct effect on the selling civ in this manner. Each citiy's Production Window could become a business with a stock and their wealth is derived from the production. When Units are sold to foreign markets, the Contract is the decider of the growth; Domesticaly, it would be your government's military unit upkeep. Production of Improvements just adds to the population wealth and effects the Marketplace and Bank improvements.
Also, I wanted to think of the possibility of a cargo ships being built and designated for trade routes between harbors. I've posted about this before, jus' not sure where, but this really gives subs a REALLY good use. I'd use this as a way to create a cargo business with a harbour and then that cargo company owning each Trade Route connected to that city with cargo ships .
Auto-Govern
Your Economic Advisor would also be the one how could control the Imports & Exports based on your requirements, which is choosable in a drop-down window in that Advisor's Screen or the individual City Screen, but only if you choose not to directly control it. These would be Export(Wealth Effect), Import (Cultural Effect), War Economy (Which tries to be self-sufficient), and Growth (A combination of the Three). This would probabliy work best as a copy of the Tax/Science/Culture sliders
The Major Additional Screen
The final addition would be the Stock Listing screen where you can take your treasury and invest, buy low sell high. The added effect is that if you own the majority of a business' shares you control it (Import & Export) and get a dividend from any shares you hold (related to its Weath & Growth), even if its physically in another civ. The Buy/Sell drop box would be much the same as a Bid/Ask screen on a Level II system. Make money and control, only reason for this screen. This screen is where most of the coding would be.

<=== You doin it right?
The one thing that makes this work is the movement of stocks is directly linked to every civ's population in total & their relative wealth level. A Third world civ could hardly stand up to a economic beast. Since the Exchanges decide the currency ratios, it is possible to export something for cheaper than domestically selling it. Importation from a choice of multiple suppliers generates competition & simulates real life, while contributing to population happiness and culture value. Embargos would have a direct effect on related business, and could also be resource specific (No Uranium for You!!) Distances between Suppliers & Consumers effect the pricing and create some remarkably realistic situations. Also being able to own Cargo companies can lessen this effect. A state of War between you and a Civ would "freeze" assets that you control that is physically in that Civ.
Application
Economic War, Economic Opportunity and Economic Deception. Quick Funding for a impromptu war or the slow takeover of a belligerent. Control of your interests while staying peaceful. Endgame would become much more involved, and quite possibly never-ending. Also allows for a whole new way to use espionage & smuggling.
The Editor would allow for great expansion on this idea with jus' those editor abilities listed. Someone can find a use for a "Children's Charity Organization" improvement cominations, or a use for an Internet Common Market that imports everything cheaper.
The prices stated for in the Importation/Exportation windows for each business are not acutally exchanged, but effect the relevant business' wealth & growth. If you were buying supplies for the cheapest price and selling your product for the highest I'd say your growing, but how long have you done it? Their wealth is decided by the city's population & national unemployment rate and is reflected as a price & stable price range, this increasing is Growth and is reflected as the price climbing stably but if it stays increasing is up to you.
This ability, in its entirety, would become available in stages. The marketplaces & banking would come first, during the Ancient Age, and resources would be treated the usual way. Importing & Exporting would come second, during the Middle Ages (research Merchantilism), with resources coming under business control and help prepare them for the next step. During the Industrial Ages, Economics could be researched, changeing the businesses to stocks (they publish there own, when you build your Exchange(s)) and begin the Economic Revolution. Then in the Modern Times, tech & research business could be available at choice Techs, so as to diversify the choices and create more competition & volatiliy.