Question

Question 6 (9 points) In a two sector economy, production of a dollar's worth of agriculture output requires an input of $0.40 from agriculture and $0.20 from manufacturing industry. Production of a dollar's worth of manufacturing output requires an input of $0.15 from agriculture and $0.30 from manufacturing industry. a. Find the necessary levels of output (in $ billions) by agriculture and manufacturing industries if there is also a surplus (final demand) of $16 billion for agriculture and $36 billion for manufacturing. (7 points) b. If there is a reduction in the surplus (final demand) for manufacturing output by $6 billion while the surplus (final demand) for agriculture remains the same, what would be the outputs that should be produced by the two sectors to meet the total demand? (2 points)

Answer 1

Solution: Page No. 1 We have two sectors here, 1) Agriculture. 2) Manufacturing lets consider output of Agriculture as a Mammfachire as y Accordingly, for & & of Agriculture require &$x0.4 of Agricultore t x$ x 0.2 of Mamfacture. we can rewrite it as 0.4x & 0.22 Accordingly, for y units of Manufacture it is o. 15 y t 0.304 (A) (M) 30, along with suaplus demand given, we. require. (given in a) as 16 for Agri & 36 for Mamb.) x = 0.4x + o.15y + 16 - y = 0.2x + 0.30y +36 -

a -0.40 -0.154 – 16 y 0.2x - 0.304 - 36 0.6x-o.1sy -16 0.74-0.22 - 36 Solving equations G ①. x2 & 0.62 - 0.1sy - 16 x3 = -0.6% 2.104-108 – +1.950 - 124 1.95y = 124 ya 63.59 Subcriitting y value in any equation we can get a value. 0.6x= 0.15 (63.59) + 16 0.6x= 25.54 Page No 2 For the probleus (ca), Solution is 42.56 $ (Billion) in Agriculture & 63.59 $ (Billions) in Manufachre x= 42.56.

(6) for reduction in swaphus demand of output by $6 (billion) in Manfachding output de 36 becomes 30 now. Subsitute 30 in equation , Accordingly. 0. Bx - oisy - 16 - v. ty - 0.22-30 – solve equation, a ©* 1 - 0-62 - o.1sy - 16 ② 3 « – 0.6x + 2.104-90 - 1.954-100 y = 54.35 Accordingly a value will be For 0.6 r = 0.15 (54.35 +16 & - 40.25 the proslens (6) Solution is 40.25 $ (Billion) in 54.35 $ (Billion in Agriculture & Manufacture. Page No.3
Summary: The problem is related to Input-Output operations, as only two variables are involved it is advisable to solve using linear equation model so the solution can be obtained without iterations

The solution to the problem is

(a) Output for agriculture is $42.56 Billion and manufacturing is $63.59 Billion

(b) Output for agriculture is $40.25 Billion and manufacturing is $54.35 Billion