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7. (15 points) Consider the following static version of the Mortensen-Pissarides model. Labor force is normalized to 1. There is a large number of firms who can enter the market and search for a worker. Firms who engage in search first have to pay a fixed cost k. If a measure v of firms enters the market, a CRS matching function m(1, v) gives us the total measure of matches in the economy. Within each match, the firm and worker bargain for the wage, w, with # denoting the bargaining power of the worker. If they agree, they can move on to production, which will deliver output equal to y. If they disagree both parties get nothing. Assume that k/y