Makroökonomie Dr, WS 2009, LV1
Review: Math and model building
Let’s assume we want to build a (simple) Marxist model! (How many Marxist model have
you done in your undergraduate econ education?). The model should be simple, it should
capture the idea profit-driven accumulation process and the idea of the industrial reserve army
depressing wages.
1. In Marx capitalists want to (and they have to, because of competitive pressures)
accumulate. Profits therefore, by and large, get reinvested. Let’s assume that demand is a
positive function of the profit share. To keep things simple, let’s only do linear functions for
now. Write a linear demand (y) function that is a positive function of the profit share (p).
2. To keep things simple, let’s assume a constant productivity of labor. Write employment (e)
as a (linear) function of output.
3. The relative position of workers in class struggle will depend (negatively) on
unemployment. Inversely, the profit share will depend positively on unemployment. Write the
profit share as a function of employment.
4. How many equations do we now have? It would really be neat to have a two-dimensional
analysis. How can we get 2 meaningful equations out of this?
5. Let’s substitute the employment function into the distribution function, i.e. let’s write the
distribution function as a function of output.
6. Now solve for the equilibrium values (of y and p)!
(6a. Compare the denominator of y* and p*. Are they similar? Are they the same? Is this by
chance?)
7. Let’s do a graphical analysis of this.
Comparative statics
8. Assume there is a stock market boom and the euphoria affects investment expenditures.
What happens to income distribution if there is an exogenous increase in capital
accumulation?
8.a Do a graphical analysis
8.b Solve analytically
9. Assume there have been cut back in the welfare state. How would this affect distribution
and demand?
9.a Do a graphical analysis
9.b Solve analytically
10. Is this equilibrium stable? Analyze it by means of a phase diagram.
11. Is this equilibrium stable? How would you analyze this analytically? (What are the
stability conditions? Any idea what this is about? Don’t worry if not)
Economic policy. (an optimization exercise)
12. A Keynesian/social democratic state. Assume that workers have control over the state and
that the state can determine (by means of fiscal policy) autonomous demand. What level of
output would a workers-dominated state set? (no analytical solution required)
13. Assume that capitalists (1) capitalists want to maximize profits (not the profit share or the
profit rate!), (2) have complete control over the state, and (3) that the state can determine (by
means of fiscal policy) autonomous demand. What level of demand would a state dominated
by capitalists set? What is the level of the profit share that is implied? Solve analytically and
graphically.
Note. There are different ways of doing this. The analytical solution can actually be quite
simple.
Hint 1. What is profits (R)? What is the definition of the profit share? R/Y! Therefore R = …
Hint 2. You will find that the solution is a lot easier, if you think about what level of y rather
than which level of y0 they would choose. And then calculate y0.