1. Given the input-coefficient matrix for a hypothetical economy made up of only two (2) industries as A = 0.1 0.5 , provide an economic interpretation for each of the elements 0.3 0.2 in matrix A. 2. Suppose there are only two industries in an economy, producing two outputs (1 and 2). To produce one monetary unit worth of output 1, it requires 0.5 monetary units of output 1 and 0.4 monetary units of output 2. Similarly, to produce one monetary unit of output 2, it requires 0.3 and 0.6 monetary units of outputs 1 and 2 respectively. Write out the matrix of the technical coefficients. 3. Consider an economy divided into agricultural sector, ?, and service sector, ?. To produce one unit in sector ? requires 1/6 units from ? and 1⁄4 units from ?. To produce a unit of ? requires 1⁄4 units from ? and 1⁄4 units from ?. Suppose final demands in each of the two sectors are 50 units. Let ? and ? denote total production in industries ? and ? respectively. What is the Leontief system for this economy? 4. The equilibrium levels of income ?, consumption ?, disposable income ? , and taxation ? ?, for a three-sector macroeconomic model satisfy the structural equations: ? = ? + ?? + ?0 ?=?+?? (00) ? ? =?−? ? ?=??+? (00) ?? i. Express this system in the form ?? = ? ii. Using Cramer’s rule, find the equilibrium levels of consumption (?∗), disposable income (? ∗) and taxation (?∗)
1. Given the input-coefficient matrix for a hypothetical economy made up of only two (2) industries as A = 0.1 0.5 , provide an economic interpretation for each of the elements
0.3 0.2 in matrix A.
2. Suppose there are only two industries in an economy, producing two outputs (1 and 2). To produce one monetary unit worth of output 1, it requires 0.5 monetary units of output 1 and 0.4 monetary units of output 2. Similarly, to produce one monetary unit of output 2, it requires 0.3 and 0.6 monetary units of outputs 1 and 2 respectively. Write out the matrix of the technical coefficients.
3. Consider an economy divided into agricultural sector, ?, and service sector, ?. To produce one unit in sector ? requires 1/6 units from ? and 1⁄4 units from ?. To produce a unit of
? requires 1⁄4 units from ? and 1⁄4 units from ?. Suppose final demands in each of the two sectors are 50 units. Let ? and ? denote total production in industries ? and ?
respectively. What is the Leontief system for this economy?
4. The equilibrium levels of income ?, consumption ?, disposable income ? , and
? ?, for a three-sector
? = ? + ?? + ?0
?=?+?? (0<?<1, ?>0) ?
? =?−? ?
?=??+? (0<?<1,? >0) ??
i. Express this system in the form ?? = ?
ii. Using Cramer’s rule, find the equilibrium levels of consumption (?∗), disposable
income (? ∗) and taxation (?∗)
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