Elasticity and share of subsidies

Firstly, elasticity of demand = %△Qd / %△P
and elasticity of supply = %△Qs / %△P

After the subsidies levied,
the production cost and the price immediately fall.
The quantity supplied stay at the initial level,
and the quantity demanded increased.
The excess demand induces competition.
Then the price will be bidden up.

When the price starts to be bidden up,
the Qd starts to decrease(MUV increases)
and Qs starts to increase(MC increases)
As the Ed of Demand is higher than the Ed of Supply
When Qd decreases and Qs increases,
MUV increases slighter than MC.
The rapid increase in MC bid up the price rapidly in the competition also
Therefore, the larger share of subsidies will be captured by the supplier.

If demand is more elastic, that means it's more responsive to price change than the supply.

When subsidy is given to the supplier, the supplier can lower down the price level which will then lead to increase in demand from the customer side. However, as the supply is less elastic than the demand, it means that the % of the price drop (say 10%) is less than the % increase of the demand (say 20%). When the suppliers don't decrease much of the price while the buyers increase lots of the quantity demanded, supplier benefit much more and buyers enjoy less of the subsidy.

When subsidy is given the the buyer, the demand for the goods will be boosted up leading to increase in price. However, as the demand is more elastic than the supply, the subsidy will only pay for a greater increase in price level as seller won't increase supply much even if there's huge increase in demand. As a result, supplier gain more than the buyer.

Please let me know if you think the explanation isn't clear enough.