general equilibrium theory discussed

Let's derive a few more results based on our ongoing white-collar / blue-collar, energy / food example (as covered in class last Wednesday and summarized further in the "Addendum" nibble in Coursework).

In answering the following questions, you may refer to your class notes and the Addendum. You don't need to do any calculus!

a) In the general competitive equilibrium we derived in class, how many units of labor will be employed by the food industry? By the energy industry? How many units of capital will be employed by each industry?

b) In this same general competitive equilibrium, what will be the utility level attained by each blue-collar household? By each white-collar household? What will be the profits earned in the food industry and in the energy industry?

Now suppose each of the 100 blue-collar households suddenly gains access to 10 units of capital, which they now are able to supply along with their 60 units of labor. Suppose, as before, that each white-collar household supplies 50 units of capital and 10 units of labor. Let's explore the effects of this infusion of capital on the general competitive equilibrium:

c) Write down new expressions for the market demands for energy and for food, XD(w, r, Ps) and YD(w, r, Pt). Write down expressions for the market equilibrium quantities of energy and food, in terms of w and r (just as in [Eq. 1] and [Eq. 2] of the Addendum).

d) Using the fact that labor supply = labor demand and that capital supply = capital demand, find the new equilibrium value of r, using the normalization m=$1.

e) In the new equilibrium, how much energy and how much food will be consumed by a typical blue-collar household? By a typical white-collar household? Is each type of household better or worse off after the influx of capital?

Does this make sense intuitively? Briefly explain.