Use the two sector model shown below to mathematically...

Use the two-sector model shown below to mathematically derive the slope of the IS curve. Interpret each of the determinants of this expression and provide an economic explanation to defend the inclusion of these parameters. c = c0 + c1y (1) i = i0 + i1y + i2r (2) ad = c + i (3) as = y (4) as = ad (5)

Transcript

00:01 The problem we have part first.

00:03 So here, in part first, for the given graph, the slope at x equal 4 and y equal 0, that is given as y dash 4 .0, which is equal to 1.

00:20 So let's check the options.

00:22 So we have option b here, that is y -dash equal cost y.

00:27 So y -daz at the given point that is 4 comma 0 become cause 0 this is equal to 1 so the answer for part first of the problem is option b now we have the part second in part second for the given graph the slope at x equal 0 and y equal 4 is equal to that is given as y dash at 0 .4 this is given as 0 so let's verify the options that is first one is white as is equal to y into 4 minus y so we have the y dash add 0 comma 4 this is equal to 4 into 4 minus 4 so this is equal to 0 so we have the option this one and other option is y dash equal to x into 3 minus x so here this y -daz at the given point which is 0 .4 that equals to 0 into 3 minus 0 this is equal to 0 hence we have the option for part second as the d and f so this is the answer for part second of the problem now we have part third of the problem here for the given graph we have the slope at x equal 4 and y equals equal 0 this slope lies between minus infinity and minus 1 so this is 4 comma 0 and this lies between minus infinity and minus 1 so let's verify the differential equations so we have option f which is y -d -d -as equal x into 3 minus x so y -daz at the point which is 4 .0 equal to 4 .0 3 minus 4 this is equal to minus 4 so we have this minus 4 lies between minus infinity to minus 1 hence the option for part third of the problem is f so this is the option now we have part 4 of the problem in part 4 we have the slope at x equal minus 4 and y equal 0 so this corresponds to the slope at 4 .0 corresponds to minus 1 so let's check the options so we have option see here why does equal cost 4 minus y so y dash at the point 4 comma 0 equal to cost 4 minus 0 this is equal to cost 4 and this corresponds to minus 0 .65 so this equals to minus 1 so we have the answer for part 4 of the problem as c now we have the last which is part 5th and part 6th so for part 5th we have the slope at x equals 0 and y equal 4 therefore the slope is equal to y -daz 0 and 4 this is given as 1 so let's verify the differential equations we have part a here y -d -d -as is equal to e -t power minus x squared so y -d -daz at 0 and 4 equal to e -t to 0 that is equal to 1 and also we have part c of the problem so here this option c is y -d -as equal cost 4 minus y.

04:26 This is y -d -d -as at 0 .4...

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