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In 1974, it was a live question whether the exhaustion of natural resources, such as oil, would necessarily lead to the decline of economic activity. Solow showed that constant levels of consumption could be sustained if there is sufficient substitutability between produced and natural factors of production. Hartwick then proved that underpinning this result is a saving rule—set investment in produced capital equal to the value of resource depletion at each point in time. A large literature has shown that a comprehensive measure of the change in real wealth—net saving—plays a central role in determining whether current well-being can be sustained. The current composition of wealth serves to define the policy challenges that countries face in achieving sustainable development. If substitution possibilities are limited between natural and other factors of production, as one might expect, then technical progress is a necessary complement to policies for sustainability.

We set out and solve a static neoclassical model with a labor/leisure choice for agents and a government sector producing a Samuelsonian public good. Numerical solutions vary considerably with the elasticity of substitution for commodities in an agent's utility function. We focus on solutions with an income tax rate set by the government (second best solutions). Govern- ment revenue varies with the rate of income tax (expressed in a Laffer Curve) and we observe that such curves generally peak "internally" only for case of "high" elasticity values in the utility function of a representative agent. Inelastic substitution possibilities involve the peaking of the Laffer Curve at a corner with the rate of income tax tending to unity. We report on welfare analysis for small changes in the rate of income tax and on first best outcomes (agents charged Samuelson "prices" for the public good).

We set out dollar-valued net national product for an economy with a wasting essential stock (oil deposit). We take up `maintaining capital intact' and locally unchanging consumption. The percentage change in `net investment' or `genuine savings,' relative to the market rate of interest, denotes whether current consumption is rising, constant, or declining.

We set out a small, open economy model of a city, one with local housing, government production and a non-traded good. We observe that a positive shift in labor productivity in the export sector generally results in a larger, higher-wage and more densely settled city. Production of the local public good increases for the special case of the public good 'counting' small in the utility function of the representative resident. Similar results obtain for the case of a city experiencing an exogenous improvement in a local climate amenity.

We set out a simple four sector macro model of the economy of the Roman Empire during a period of considerable economic prosperity. Our focus is on gold coins as currency and the seignorage which the government used to fund its activities. We solve numerically for a balanced growth representation of the economy of the empire, a solution that captures the intricacies of money creation, currency expansion and seignorage. We subscribe to the view that the exhaustion of low-cost gold and silver deposits contributed significantly to the ending of the economic prosperity enjoyed by Roman Italy and its provinces during the so-called Pax Romana (31 BC to 165 CE) and we attempt to capture significant shifts in variables during the decline.

We set out a city as a price-taking exporter and importer with its own local structure (housing (land per household) and a local pure public good are produced endogenously). We improve labor efficiency in the export sector, observe a jump in the local wage, and trace the impact, particularly on production of the public good. In one case the population, output of the public good, and residential density expand (the law of urban growth) and in another, population, output of the public good and density contract.

KolstadÂ’'s (1994) model of intertemporal, competitive supply to a linear market from two distinct exhaustible resource deposits admits two different interior solutions - one with the low cost deposit "earning" the higher resource rent and the other with the low cost deposit "earning" the lower resource rent. This latter outcome turns on the initial size of the low cost deposit being significantly larger than the high cost deposit. We infer then that size can trump quality in the determination of the resource rent for a deposit, when geography is explicit.

We solve for an S-shaped schedule for market size for a new product that undergoes gradual widespread adoption. We hypothesize that the speed of market expansion is positively related to the current proÂ…t per unit being produced. In a mature market the unit profit is relatively low.

We take up a growth model with both skilled and unskilled labor, and a steady migration of some unskilled workers, who undertake apprenticing, to the skilled group of workers. Apprenticing involves a period of observing and thus labor output foregone. The time-out for observing represents a cost to the economy and this results in the rate of balanced growth being endogenous. We examine the balanced growth path and report on the stability of our dynamic system.

We set out a model of a two-good, small open economy exporting a traditional exportable in order to finance capital goods rental payments. We observe that the traditional export sector declines with an exogenous increase in the country's oil export earnings, while the local goods sector expands. For input price effects to emerge, land is needed as a third input. For the "large land" case, we can have imports of capital steadily decline as oil earnings expand. Earnings from oil sales are stationary under our annuitization construction.

We find that a discount rate of 3.8% allows us to derive the schedule of "value of life years" in Murphy and Topel [2006] from their schedule of "value of remaining years of life", this latter presumably being based on a "value of statistical life" of $6.3 million. We draw on the Makeham function for life expectancy in our calculation.

We back out an estimate of a personal discount rate of between 3 and 4 percent for a person with a life expectancy of 74 years who dies at age 30 (or 40) and has a value of statistical life of $6.3 million. Central to these calculations is the series generated by Murphy and Topel of value of life years (the dollar value of consumption plus the dollar value of leisure, with some smoothing for income in retirement). We employ the Makeham "model" of life expectancy in our calculations.

We set out an open, monocentric city with residential structures and reflect how changes to the amenity index affect the city. On the consumption side, an amenity is represented by an exogenous boost to the utility of a resident's current commodity bundle. The city's population, land rent and footprint expand, and its density rises. We test for an amenity effect in local wages with household data for the US in 1990 and discover that city density is much stronger in explaining local premia than is the city population. We test for amenity effects in local house prices with the same data set.

We consider a competitive extraction industry comprising many small firms, each with a slightly different quality of mineral holdings. With "rapidly" declining quality of holding per firm we observe rent declining over and interval. We do not work with the planning solution, commonly invoked in the study of firms with distinct qualities of stock.

We draw on Ricardian comparative advantage between distinct persons to map out the division of labor among proto-humans in a village some 1.7 million years ago. A person specialized in maintaining a cooking fire in the village is of particular interest (Ofek [2001]). We are also interested in modelling hunting by village males in teams. The large issue is whether and how specialization (division of labor) and interpersonal trade might have driven brain-expansion in early humans.

Beckmann's interaction model has each resident touching base in face-to-face activity with every other resident, per unit time, at the other's residence. We re-work his resulting "interaction city" with each resident "operating with" a Cobb-Douglas utility function. We then turn to a more satisfactory "technology" of residents interacting and solve for an interaction city with an explicit payoff to resident i for engaging in interaction.

We consider costly administration at the center of a farming community surrounding a fortified village. Land rent taxation is high cost mode of financing central administration in a tax incidence sense. Participatory administration by the governed is a lower cost alternative. We speculate why the low cost option has been out-competed by its higher cost alternative throughout history. We also take up constraints on predation on farmers by a landlord at the center.

Each extractor has a distinct quadratic extraction cost and faces a linear industry demand schedule. We observe that the open loop and closed loop solutions are the same if initial stocks are such that each competitor is extracting in every period in which her competitors are extracting.

In each period, we have an R&D race among N competitive R&D firms, each with probability π of discovering a successful new technique for producing an intermediate good used in producing the economy's final consumption good. The winner of a race earns a monopoly profit over a generally uncertain interval. Each R&D firm faces distinctive "lottery" and "duration" uncertainty in each period. Numerical examples illustrate the growth behavior of the economy linked to the R&D sector.

We take up the hypothesis that risk premiums on equities are embodying the costs incurred by equity holders in monitoring the firms which they have invested in. This idea is a key ingredient in our construction of a two sector neoclassical model with widget producing firms and commercial banks. So-called user costs or interest rate spreads are key prices of commercial bank services in the model. Commercial banks produce deposit services (check-writing services or transactions services) and lending services to widget producers.

Certain group VIIIB transition metal compounds were found to inhibit cell division in Escherichia coli , causing marked filamentous growth. Gram-negative bacilli were the most sensitive to this effect, whereas gram-positive bacilli responded only at near-toxic levels of the metal. None of the cocci tested showed any apparent effect. Cytokinesis (cross-septation) can be initiated by removal or decrease of platinum, but not by treatment with pantoyl lactone, divalent cations, or a temperature of 42 C.