In the context of imports and exports, there are two types of subsidies:

1. Production subsidies.
2. Export subsidies.

Production subsidies

Subsidies where government gives payments to domestic firms competing with imports in order to encourage them to produce more and protect them.

Diagram

Observing the diagram, before the subsidy, the economy is in free trade and operates at the world price $P_w$ which is below the domestic price $P_d$ that existed without free trade.

1. The quantity supplied by domestic producers is $Q_1$ and quantity demanded by consumers is $Q_2$.
2. The excess demand $Q_2 - Q_1$ is the initial quantity of imports.
3. The government sets a subsidy $s$ per unit, causing the supply curve to shift down by $s$ from $S_{d1}$ to $S_{d2}$
4. This indicates an increased supply since the firm gets a subsidy for each unit it produces.
5. Therefore, this subsidy increases the price that producers receive from world price $P_w$ to world price plus subsidy $P_w + s$ per unit.
6. However the price paid by consumers still stays at $P_w$.

Hence after the production subsidy:

1. The quantity supplied is $Q_3$ and the quantity demanded is still $Q_2$.
2. Hence the excess demand fall, thus the imports have fallen and producers earn an extra $s$ per unit.

The effects of a production subsidy

Winners

Domestic Producers

1. Domestic producers are supplying more ($Q_3$ instead of $Q_1$) at a higher price ($P_w + s$), earning higher revenues.
2. Producer surplus increases by the area marked as $a$, indicating the gain from the new prices and trade restriction.

Workers

As domestic producers now produce and sell a larger quantity, the employment in the industry would be protected and increase as well.

Neutral

Unlike the the restrictions before, consumers don't face a higher price since they still purchase at $P_w$ and the same quantity $Q_2$.

Losers

Government

1. The government has to pay for the subsidy negatively affecting their budget.
2. This can be seen by the area of the subsidy $s$ multiplied by the quantity supplied $Q_3$.
3. Also creates an opportunity cost as the tax money could've been used elsewhere.

Inefficiency of production

1. The reason world price $P_w$ is smaller than domestic price without trade $P_d$ is because foreign producers are more efficient.
2. The increase in quantity supplied from $Q_1$ to $Q_3$ represents the increase in domestic production that is inefficient as there is a waste of scarce resources by producing at $P_w + s$ instead of $P_w$.

Foreign producers

Foreign producers now supply fewer goods ($Q_2 - Q_3$ instead of $Q_2 - Q_1$), causing their quantity sold to decrease.

Welfare effects

After the subsidy was imposed:

1. The producer surplus increased by $a$ due to the higher price $P_w + s$ they earn and higher quantity $Q_3$ they sell.
2. The consumer surplus remains unaffected.
3. Therefore the government expenditure on subsidy increased by $a + b = s \times Q_3$.
4. Resultantly, the change in social surplus is a decrease of: $a + b - a = b$.
5. This change leads to a welfare loss of the area $b$ due to the inefficient production created by the subsidy.

Export subsidy

Subsidies where governments make payments to firms for each unit exported to increase export competition.

Diagram

Observing the diagram, before the export subsidy, the economy is in free trade and operated at the world price $P_w$ which is above the domestic price $P_d$ that existed without free trade.

1. The quantity demanded by consumers is $Q_1$ and quantity supplied by domestic producers is $Q_2$.
2. The excess supply $Q_2 - Q_1$ is the initial quantity of exports.

Unlike before, the domestic country is now more efficient in production.

1. The government sets a export subsidy $s$ per unit, causing the supply curve to shift down by $s$ from $S_{d1}$ to $S_{d2}$
2. This indicates an increased supply since the firm gets a subsidy for each unit it produces.
3. The intersection of $S_{d2}$ and the world price $P_w$ determines the new quantity supplied $Q_4$