Consider an industry operating under monopolistic competition, in which each firm produces a unique differ- entiated product. Firms in this industry can sell their output in two markets, Home (H) and Foreign (F). The demand curves that firm i faces in each market are: 9tH 4F - Hom APH APIE (1) (2) where A is a measure of market size and o> 1 is the elasticity of demand. Each firm i has a productivity level that takes values over the interval (0, 0], and produces its output using the production function: 91 Oil, (3) where l denotes the labour used in production by firm i. In order for a firm based at Home to sell its output domestically it needs to incur a fixed cost fo, and if it chooses to export it needs to incur a fixed cost fx, both of them denominated in units of labour. Additionally, a firm based at Home that wishes to export its output to Foreign incurs an 'iceberg' transport cost 7 > 1. That is, in order to sell one unit of output in Foreign, it needs to ship 7 units from Home. (a) State the profit maximisation problem for a given firm i and find the optimal price the firm charges when selling their output in market k. [5 marks] (b) Explain what determines whether a given firm i chooses to export its output to Foreign or not. [3 marks] (c) Suppose that 70-jx > fp. Provide an economic intuition for this condition. What implications does this condition have for the size and productivity premium of exporters relative to firms that only sell domestically? Are these predictions supported by empirical evidence? [5 marks] (d) Suppose that Home and Foreign sign a free-trade agreement that significantly reduces the variable cost of trade, 7. Explain, without using equations, how this policy change will affect the intensive and extensive margins of exports.