and capital? Use part (c) to substantiate your answer to this question. 4. USA debt (20 points) In class, I mentioned that the returns on investment were higher in foreign af filiates of US multinationals than in US affiliates of Foreign multinationals. This exercise proposes that the US comparative advantage in R&D may explain these patterns. Suppose that statistical agencies calculate the returns on investment of an establishment 1' as:1 yiPi Ci K,- + A, where y,- is the quantity produced, pi is the price, C,- is the total cost, K,- is the stock of capital invested in the establishment and A,- is the stock of R&D investments in the establishment. We refer to this return as the \"accounting returns\" (which is different from the returns on investment in the problem of the firm in part (c)). (a) (4 points) Use this expression to explain how investments in R&D in the USA headquarters may affect the accounting returns of affiliates of US firms in foreign countries. Specify which variables may change and why. (b) (4 points) Use the same expression to explain how investments in R&D in the USA affiliates of a foreign multinational affects its accounting returns. Again, specify which variables may change and why. (c) (7 points) Denote with K : (K1,K2, ..., K1) the vector of capital that a firm uses in each location of its establishments, 1' : 1, ..., I, and with A : (A1, ..., A1) as the vector of investments in R&D. Assume that the firm chooses its op- timal R&D investment and capital in each location solving the following problem: rpix Zyif'i * wiLi * er' * rAiAi subject to: 13,-(Li, 19A) : 3/:- Pi : D'1(yzuA) where P, is the production function of the firm in country 1', and D'1 is the inverse demand function that the firm faces. Interpret each line of the prob lem above. In particular, highlight and explain economically the difference between K,- and A,- in the problem. (d) (5 points) Do the different accounting returns in (a) and (b) imply that for- eign and US multinationals are not optimally allocating investments in R&D 1In reality the USA agency, Bureau of Economic Analysis (BEA) uses dividends. The expression above is simpler because you don't need to be concerned with the decision to retain profits or distribute them as dividends. It also disregards taxes on profits. 3