Answers
Crowding out is an effect of dampening multiplier effect of increased Governments spending on National Income. As you know, one dollar extra investment by Government has a multiplier effect on national income. It is known as expansionary fiscal policy. Mathematically this multiplier effect is shown as-
Here 'b' is marginal propensity to consume, T is tax rate and G and Y are government Investment and National Income respectively. The crowding out effect is shown with the help if IS and LM model.
In IS curve you will get different combinations of interest rate and National Income, that will equalise total demand and supply of commodities. So commodity market will be equilibrium. Similarly Money market will indicate different combinations of national Income and interest rate that will maintain equilibrium in the money market. Intersection of these two curves will maintain overall equilibrium of the two markets. Consider the diagram of IS-LM below to show crowding out effect.
In the above diagram, initial equilibrium combination of i and Y was (i0,Y0) at point e.
Now Government has increased investment by 
. It should increase National Income by 
. It is indicated by point e2 in the diagram. So Y should increase by Y0Y2. But it has not happen.
Due to increase in G, IS curve will shift to the right from IS1 to IS2. Thus general equilibrium point e will move to e1. As a result interest rate will rise from i0 to i1. This increase in interst rate will reduce private investment (I) as it is more costly now. This decrease in private investment will have multiplier effect on Y but in opposite direction.
Thus actual increase in Y will be Y0Y1 only. So Y1Y2 portion of expected expansion in national Income will be dampened off. It is known as crowding out effect.
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In order to judge severity of crowdng out effect causing frm money market supply curve. It is represented by the slope of LM curve. Consider extreme severity of this impact.
Suppose LM curve is vertical. In that situation, supply of money for investment is constant.Due to a very high interest rate, all investible fund have been already invested. So o further increase is possile. If it happens, then crowding out effect will totally dampen the multiplier effect of increase in investment on Y. So Y will rermain static at Y0.
It is shown below:
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B. Investment demad curve effect is shown by IS curve. If it is flat, then Investment is highly sensitive to interest rate. So damening effect of crowding out theory will e more severe. But id IS is steap, then the effect is low.
Consider Green line IS curve.
It is steaper than other blue line IS curve. So dampening of Y is less severe . Here effectively Y has dampened by Y0Y3 only instead of Y0Y2 found earlier.
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As already explained, Expansioary fiscal policy, shifts IS right side. So interest rate will rise. It will reduce private Ivestmet.
So Y will increase less. It will cause lower growth rate in the ecoomy. It will happe since due to less growth in Y, savings chage will be low. So increase in I expected will fall. Result is lowering of economys growth rate.