Example 9b_1 ($MODEL:M1_2I): Consider the following SAM, where sectors have symmetric intermediate demand on own products

		supply					total cost			expenditures
		PX	PY	PW	PL	PK	X	Y	W	CONS
demand	PX						20		100
	PY							20	100
	PW									200
	PL						40	60
	PK						60	40
total revenue	X	100+20
	Y		100+20
	W			200
income	CONS				100	100

Alternative representation of SAM:

Production Sectors Consumers

Markets | X Y W own | CONS

------------------------------------------------------

PX | 100+20 -100 -20 |

PY | 100+20 -100 -20 |

PW | 200 | -200

PL | -40 -60 | 100

PK | -60 -40 | 100

own demand | -20 -20 40 |

------------------------------------------------------

where 40 represents the total value of intermediate demand.

********************************************************************************

Example 9b_2 ($MODEL:M1_2II): Consider the following SAM, where sectors contribute to intermediate demand in a non-symmetric way

Alternative representation of SAM:

                 Production Sectors               Consumers
   Markets  |    X       Y        W       own |       CONS
   ------------------------------------------------------
       PX   |  100+20+5          -100-5 -20|
       PY   |  -5        100+20  -100+5 -20|
       PW   |                     200         |       -200
       PL   |  -40      -60                   |        100
       PK   |  -60      -40                   |        100
own demand  |  -20  -20   40 |
    ------------------------------------------------------

********************************************************************************

Example 9b_3 ($MODEL:M1_2III): Consider more complicated case, where both sectors contribute to intermediate demand 

		supply					total cost			expenditures
		PX	PY	PW	PL	PK	X	Y	W	CONS
demand	PX						20	7	100+5-7
	PY						5	20	100-5+7
	PW									200
	PL						40	60
	PK						60	40
total revenue	X	100+20-7	5+7
	Y	5+7	100+20-5
	W			200
income	CONS				100	100

Alternative representation of SAM:

  Production Sectors               Consumers
   Markets  |    X       Y        W       own |       CONS
   ------------------------------------------------------
       PX   |  100+20+5 -7  -100-5+7 -20|
       PY   |  -5        100+20+7  -100+5-7 -20|
       PW   |                      200          |       -200
       PL   |  -40      -60                   |        100
       PK   |  -60      -40                   |        100
own demand  |  -20  -20     40 |
    ------------------------------------------------------

$ONTEXT

$MODEL:M1_2III

$SECTORS:

        X       ! Activity level for sector X

        Y       ! Activity level for srctor Y

        W       ! Activity level for sector W (Hicksian welfare index)

$COMMODITIES:

        PX      ! Price index for commodity X

        PY      ! Price index for commodity Y

        PL      ! Price index for primary factor L

        PK      ! Price index for primary factor K

        PW      ! Price index for welfare (expenditure function)

$CONSUMERS:

        CONS    ! Income level for consumer CONS

$PROD:X s:0.5   va:1

        O:PX    Q:125

        I:PX    Q:20

        I:PY    Q:5

        I:PL    Q:40    va:    

        I:PK    Q:60    va:    

$PROD:Y s:0.75  va:1

        O:PY    Q:127

        I:PX    Q:7

        I:PY    Q:20

        I:PL    Q:60    va:

        I:PK    Q:40    va:

$PROD:W s:1

        O:PW    Q:200

I:PX    Q:98

        I:PY    Q:102

$DEMAND:CONS

D:PW    Q:200

        E:PL    Q:100

        E:PK    Q:100

$OFFTEXT

$SYSINCLUDE mpsgeset M1_2III

*Benchmark replication

        M1_2III.ITERLIM = 0;

$INCLUDE M1_2III.GEN

        SOLVE M1_2III USING MCP;

******************************************

*Exercises:

*

*(a). Implement a separate nest for the model M1_2III between inputs X and Y in the same way as between K and L.

*(b). Implement the same tax as in EXAMPLE 9a into the model M1_2III and into its modified version from (a). Compare the results using algebraic solution.

*(c). Revise the model M1_2III by using another calibration point (see EXAMPLE 1 on Lecture 2b)