This question requires you to make use of the appropriate price-equals-unit equation in a simple closed Smithian economy with two outputs, beaver and corn, corn being the numraire, and the total amount of labor (all of which is productive and fully employed) being exogenously fixed. Neither the production of beaver nor that of corn requires costly land (land is abundant and available at zero rents), but only the production of beaver is instantaneous (thus requiring merely labor and no wage advance by capitalists); by contrast, the production of corn is time-consuming, hence necessitates a corn wage advance to workers out of a corn wage fund owned by capitalists:

(a) (10 points) Show that in such an economy, and if (by analogy to Smith) it takes twice the amount of time to kill a beaver as it takes to produce a pound of corn, the price of a beaver in terms of corn will not be two pounds of corn per beaver, but less than two pounds of corn per beaver.

(b) (10 points) Show why, despite the breakdown of the labor theory of value under (a), the long run price of beaver in terms of corn is entirely independent of the demand for beaver.

(c) Explain how this long run price invariance to demand changes is the result of the dynamic adjustment of the economy -- namely through capital (wage fund) accumulation or decumulation -- whenever there is a change in the demand for beaver that manages, on impact (thus, at a given capital stock), to temporarily raise or lower the market price of beaver above or below the invariant long run price:

(i) (10 points) In particular, what happens to the uniform corn wage rate entrepreneurs in the two sectors face on impact of an increase in the demand for beaver? (Hint: use the price-equals-unit cost equations in the two sectors.) What, in consequence, happens to the economy's short run profit rate, as determined by the price-equals-unit cost equation in the corn sector?

(ii) (20 points) How does your answer to (i) allow you to infer that a process of wage fund decumulation and consequent reversal of the wage increase - hence of the beaver price increase that triggered the latter - will ensue, thereby producing the long run price invariance claimed under (b)? (Hint: ask yourself what must happen, on impact, to the labor allocation between the two sectors, given that the wage rate jumps but the wage fund -- used as, we recall, exclusively in the corn sector -- is as yet unchanged.)