3. (25 points} Consider two countries, Santa (Home) and Cruz (Foreign), that produce Skate- boards (S) and Cookies (C) with capital (K) and labor (L). Both factors freely move across sectors. The production technology in each sector demonstrates constant returns to scale with diminishing returns of marginal product of each factor and factor complementar ity. Consumers in this economy exhibit homothetic preferences. in and 1' denote nominal worker wages and nominal rental rate of capital, respectively. The production of cookies is labor intensive while skateboard production is capital intensive. Santa is relatively labor abundant, and Cruz is relatively capital abundant. (a) (5 points) What is the relationship between autarky relative prices (Pg/P0) and (Pg/Pg.) in the two countries? (b) (5 points) What is the pattern of trade that results from free trade between these two countries? (c) (5 points) Will capitalists (i.e. the owners of capital) in Santa be in favor of free trade with Cruz? Describe how their real income r/Pg and r/PC changes with trade. (d) (5 points) Suppose the two countries were trading freely for several years, do you expect to observe the same wages in Santa and Cruz? Explain why or why not. (e) (5 points} Suppose that Santa experiences a wild re that reduces Home's stock of capital. Using the box diagram below, demonstrate the change in factor allocations in Santa before and after the drought. ( L3 08 th