Export Subsidy - Large Country

Free Trade
Under free trade, where the world price is P_W: This economy consumes X₁, [1] produces X₂, [2] exports (X₂ - X₁), [3] consumer surplus is AP_WC, [4] and producer surplus is BP_WD. [5]
Subsidy
If the government promises to pay a subsidy to exporters to encourage exports, exporters will export this good up to the point where the domestic price exceeds the foreign price by the amount of subsidy. If this economy is large, the increase of production by subsidy will decrease the world price to P'_W. [1] Domestic producers receive (P'_W + S) per unit that they export, [2] where S is the amount of subsidy per unit of X exported. Therefore, producers: produce X₄ [3] reduce domestic supply to X₃, [4] and export (X₄ - X₃). [5] The producer surplus increases to B(P'_W+S)F, [6] and the consumer surplus decreases to A(P'_W+S)E. [7] For this policy, the government must pay [P'_W + S) - P'_W] x (X₄ - X₃) = S(X₄ - X₃)
Questions: What if the government asks producers to receive P'_W in the domestic market? How much is the price of X in the foreign market? Who will receive benefits from this policy?

Free Trade