4. Suppose we have a two Department economy where Department 1 produces machines and Department 2 produces bread. Techno

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4. Suppose we have a two Department economy where Department 1
produces machines and Department 2 produces bread. Technology is
given by
Y1 = K =min(L1,2K1)
Y2 = min(L2, K2)
The wage is paid in bread and given by w = 1/2.
A) Calculate the value of machines (capital) and the value of
bread (Hint: value is equal to labor used in producing one unit of
output plus the value of non-labor inputs.)
B) What is the ratio of the output of department I to department
II in this model? (Hint: write an equation for total capital and
set this equal to Y1. Using the fact that Y1 = 2K1 and Y2 = K2, you
should be able to arrive at a function for Y1 in terms of Y2.)
C) What is the ratio of L1 to L2 in equilibrium? (Hint: write an
equation for total wages and set this equal to the output of
department 2. Then use the production function for Y2 to replace Y2
with L2 and simplify.)
D) Give an example of values for L1, K1, L2, K2, Y1, and Y2
which are compatible with your answers for b and c.
E) Assuming values are equal to prices, what is the price of the
machinery demanded by department 1 in your answer to d? What is the
price of the machinery demanded by department 2 in your answer to
d? Will this exchange between the departments take place in a
capitalist economy?