Exercise 19.23. * Consider the model with labor in Section 19.4. Suppose that countries can invest in order to create new varieties that they will be able to sell to the world. Suppose that if a particular firm creates such a variety, it can charge a markup equal to the monopoly price to all consumers in the world. (1) Show that the optimal monopoly price for a firm in country j at time t is: pj (t) = (εrj (t)) / (ε − 1). Interpret this equation. (2) Suppose that a new variety can be created by using 1/η units of labor. Show how this changes the labor market clearing condition and specify the free entry condition. (3) Derive the world income distribution and show that it is stable, so that the same forces as in the model with exogenous distribution of products across countries apply in this model. (4) What happens if new products can be produced using a combination of labor and capital?