3. (Bustos (2011)) There are two symmetric countries. Heterogeneous firms compete monopolistically. There is free entry. A large mass of entrepreneurs may pay a fixed cost fe to enter the market and draw a productivity o from a cumulative distribution function G() = 1 -4*, with k > 1. Firms choose to exit or to produce. If a firm produces, it chooses between two technologies: High (h) and low (1). Labor is the unique input into production, and wage w is the numeraire. The total cost of producing q units for a firm with productivity y using technologies 1 and h is, respectively, TC(9,0) = f +g/4 TC(2,4)= fn+g/(10) where 17,7 > 1 To export, firms pay a fixed cost fa, iceberg cost T. Demand is qw) = EP-p(w)]- 1/(1-0) P= = ["p(W)- du where P is the price index, E is total spending, and M is the mass of firms. 2 (a) Combining the discrete choice of technologies h and I with the choice of ex- porting or not, a firm that does not exit has four discrete choices. Derive the profit of the firm under each discrete choice. (b) Argue that the choice to export and to produce with a high technology are complementary 3. (Bustos (2011)) There are two symmetric countries. Heterogeneous firms compete monopolistically. There is free entry. A large mass of entrepreneurs may pay a fixed cost fe to enter the market and draw a productivity o from a cumulative distribution function G() = 1 -4*, with k > 1. Firms choose to exit or to produce. If a firm produces, it chooses between two technologies: High (h) and low (1). Labor is the unique input into production, and wage w is the numeraire. The total cost of producing q units for a firm with productivity y using technologies 1 and h is, respectively, TC(9,0) = f +g/4 TC(2,4)= fn+g/(10) where 17,7 > 1 To export, firms pay a fixed cost fa, iceberg cost T. Demand is qw) = EP-p(w)]- 1/(1-0) P= = ["p(W)- du where P is the price index, E is total spending, and M is the mass of firms. 2 (a) Combining the discrete choice of technologies h and I with the choice of ex- porting or not, a firm that does not exit has four discrete choices. Derive the profit of the firm under each discrete choice. (b) Argue that the choice to export and to produce with a high technology are complementary