1. (30 marks total) Consider a modification of the search and matching model of the labour market from LN2. In that model, we assumed that all firms were identical. Suppose instead that firms differ in how much they have to pay to search for a worker. That is, let's index the firms by je [0, co) (i.e., j can take on any real number between 0 and co), and suppose that firm j must pay search cost k(), where k(.) is a continuous and strictly increasing function (i.e., k'(j) > 0) with k(0) = 0 and limj-+x k(j) = co. In every other respect, the model set-up is the same. (c) (4 marks) The worker's surplus in the match from (b) is given as usual by $, = w - b. The total surplus in the match is then s() = $w + sy(). Assuming Nash bargaining where the worker receives share / of the total surplus in the match, solve for the Nash wage in this match. How does it depend on j? Explain your answer intuitively. (d) (2 marks) Given the wage from (c), let R(j, 0) denote firm j's expected value of searching, conditional on the level of tightness being 0. Write down an expression for R(j, 0). (e) (2 marks) Under what condition will firm j decide to search for a worker? (HINT: The answer should take the form of a weak inequality (i.e., a "greater than or equal to" condition).)