Consider a Sraffa system that describes production with a surplus. Assume that the whole of the wage is variable. The number of commodities in the system is n. Some are non-basic commodities. a. Write the price equations in matrix notation. (Make sure to mention the dimensions of the vectors and matrix in your equation). b. Explain the economic meaning of the A matrix and l vector. c. Identify the unknown and known variables of your system. d. How can you make the system determinate, i.e., make the number of equations equal to the number of unknowns? e. State the economic meaning of the viability condition and express it mathematically. f. Assume that the viability condition is satisfied and the rate of profit is given exogenously at a level that is lower than the maximum rate of profit. Explain, with the help of the relevant theorem, why the solution for prices must be nonnegative. NOTE: You need to use only three equations, one for specifying the numeraire, the second for expressing the final solution of the price equations, and third for expressing the condition for nonnegative prices.
Consider a Sraffa system that describes production with a surplus. Assume that the whole of the
wage is variable. The number of commodities in the system is n. Some are non-basic
commodities.
a. Write the price equations in matrix notation. (Make sure to mention the dimensions of the
vectors and matrix in your equation).
b. Explain the economic meaning of the A matrix and l vector.
c. Identify the unknown and known variables of your system.
d. How can you make the system determinate, i.e., make the number of equations equal to
the number of unknowns?
e. State the economic meaning of the viability condition and express it mathematically.
f. Assume that the viability condition is satisfied and the rate of profit is given exogenously
at a level that is lower than the maximum rate of profit. Explain, with the help of the
relevant theorem, why the solution for prices must be nonnegative.
NOTE: You need to use only three equations, one for specifying the numeraire, the
second for expressing the final solution of the price equations, and third for expressing
the condition for nonnegative prices.
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