Could there ever be conditions under which the equilibrium (real) prices for some assets are infinite? What would happen to an economy as it approached those conditions? Would those prices keep climbing to the skies heavens, then collapsing in waves of fear and panic? I'm trying to figure it out.

Start with an economy with technology and total factor productivity growing at rate g. Assume everything else (population, capital, etc.) is constant over time, so the growth rate of output, income, and consumption is also g. Assume intertemporal consumption preferences such that the equilibrium real rate of interest, r, is the same as g.

So far very standard.

Now add in an asset in fixed supply. Ocean-front land, maybe. There is a demand to rent ocean-front land. Assume that rental demand has a price elasticity, and income elasticity, both equal to one. That means total annual rents on ocean-front land are a constant fraction of real income. Given the fixed supply, that means rents per acre (or per metre of ocean-front) must be rising in real terms at rate g. The present value of the rents on one metre of ocean-front are therefore equal to (today's rent)/(r-g), which is infinite. If investors are rational, and there are no bubbles, either positive or negative, so prices reflect fundamental values, the equilibrium price of ocean-front land should equal the present value of the rents. So the equilibrium price should be infinite.

And if we assume instead that the income elasticity of demand exceeds one, rents per metre will be rising faster than g, and faster than r. So the equilibrium price of ocean-front land should exceed infinity (yes, I know).

Those assumptions about elasticities, interest rates, growth rates, don't seem totally implausible.

What have I got wrong?