If we consider more than three industries in an input-output model, it is cumbersome to represent all thedemands in a diagram as in Exercise 39. Supposewe have the industries
The consumer demand vector is
where
where
a. Find the four demand
b. What is the meaning in economic terms of
c. What is the meaning in economic terms of
d. What is the meaning in economic terms of the equation
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Linear Algebra with Applications (2-Download)
- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forward23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forwardSuppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.arrow_forward
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- 6. The covariance between X and Y is calculated and recorded as SXY (and sxy is a negative number). A linear transformation is performed on X. The linearly transformed variable is called W, where W; = 5 + Xi. The covariance between W and Y is calculated and recorded as sWY. Which statement is correct? A) В) In this example, swy would be less than sxY. In this example, swY Would be equal to sxY. In this example, swy would be greater than SXXY. 7. The covariance between X and Y is calculated and recorded as sxy (and sxy is a positive number). A linear transformation is performed on X. The linearly transformed variable is called W, where W; = (4)X;. The covariance between W and Y is calculated and recorded as sWY. Which statement is correct? In this example, sxY would be less than swy. In this example, sxY Would be equal to swy. In this example, sxY would be greater than sWY. A) B) 8. The correlation between X and Y is calculated and recorded as rxY (and rxy is positive). A linear…arrow_forwardVII.2. Let X = {1, 2, 3, 4} and Y = {a,b, c}. Let R C X × X be a relation on X given by T Ry if, and only if, x < y. Let S C X × Y be a relation between X and Y given by %3| the matrix: 1 0 0 0 0 1 0 1 0 1 0 0 Ms = (a) Represent R as a set of ordered pairs; (b) Represent S as a set of ordered pairs; (c) Represent S in graphical form; (d) Find the matrix MR representing the relation R (e) Use Boolean matrix multiplication to find the matrix MsoR representing the composition S o R.arrow_forward3. | Let us consider an arrival and a service processes of customers in a Q system. (unit: minutes) lat (A): 0, 40, 0, 40, 0, 40, . St (S): 15, 15, 15, 15, 15, . Determine E[A), V[A], E[S], V[S] and mean waiting time of the customers. Also, determine A and u per hour. Also calculate the server utilizationarrow_forward
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