ii)     Write the expression of the price, p*, charged by the foreign firm in H, as a function of σ, s, c, τ, when trade is allowed.

To derive the expression for the price $p^*$ charged by the foreign firm in country H as a function of $\sigma$, $s$, $c$, and $\tau$, we will follow these steps:

1. Break Down the Problem

We need to express the price in a way that incorporates the relevant parameters:

• $\sigma$: The elasticity of demand or a similar parameter.
• $s$: The supply function or a related cost measure.
• $c$: The cost of production for the foreign firm.
• $\tau$: The trade cost or tariff.

2. Relevant Concepts

In international trade and pricing:

• The price charged by a foreign firm can be influenced by production costs, trade costs, and market conditions.
• If we denote the price function by $p^*$, we can express it in terms of the parameters given.

3. Analysis and Detail

Assuming a linear pricing behavior where the firm aims for profit maximization, the price can be structured as follows:

$p^* = c + \frac{\tau}{\sigma} + \frac{s}{\sigma}$

Here, $c$ is the basic cost of production, $\frac{\tau}{\sigma}$ represents the added cost due to trade barriers, and $\frac{s}{\sigma}$ accounts for the supply dynamics in relation to demand elasticity.

4. Verify and Summarize

The resulting expression logically combines the influences of cost and trade barriers on the pricing strategy of the foreign firm. It reflects both production costs and market conditions.

Final Answer

Thus, the expression for the price charged by the foreign firm in country H when trade is allowed is given by:

$p^* = c + \frac{\tau}{\sigma} + \frac{s}{\sigma}$