l. |Consider our general equilibrium trade model with perfect competition. We mentioned how this model could be extended to multiple countries and multiple products. This question wants to demonstrate that with trade there should be a positive correlation between net exports and the difference in free trade and autarky prices. In equation form: 2:- (Pl' -P']Tr E D [1] Where T} denotes net exports of good i under free trade [equal to production in free trade. F - - - F ~ ~= [- . mmus consumpnon 1n free trade. E!- J. and there are N goods, indexed by r I, ...,.-"-.t. pfis the price of good i with free trade and pfis the price of good i in antarky. a] Letls start with our simple model of two goods and two countries. The two goods in our Home country are kayaks {K} and diamonds {D}. Making kayaks is laborintensive and Home is labor abundant. Initially in antarky explain why j}: E}? andQ = C5\". b] Explain why using intuition or a diagram that we would expect this equation to hold true. area PSI-'25. = P+ FEES c] Now let's open up to trade. Do you expect TH to be positive or negatiye?I What abont TD? :1] From the introduction. equation [I] can be rewritten for our simple case as equation [2]. Explain why equation [2] should be true. using your answer from part c). (115 PSJTD + (pl? palm E 0 [2] e) Equation [2] can be rearranged into three major terms shown by a, B, and y, in equation [3]. Show how to derive equation [3] from equation [2]. [PETK + p5To] -[(PROK + PBQ5) - (PACK + PBC5)] > 0 [3] (B) (V) f) Take term (a), why would you expect this term to be equal to zero? Explain your intuition. g) Taking term (B) answer using intuition why equation [4] must be true. Demonstrate your intuition using a graph. Hint: use a PPF with two goods and show that revenues are higher with autarky prices at the autarky production level compared to revenues with autarky prices at the free trade production level. PROK + PROB S PROA + PBQB [4] h) Taking term (y) answer using intuition why equation [5] must be true. Demonstrate your intuition using a graph. Hint: use a PPF with two goods and compare the value of consumption under free trade and autarky (with autarky prices) PACK + PBC > PACK + PBCA [5] i) Using your answers from b), g), and h), show why the following set of equations must be true. [(PROK + PBQB) - (PACK + PACE)] S [(PRQR + PBQB) - (PACK + PBCB)] j) Combining f) and i), how have we shown that equation [3] is true in part e)? What does this mean for equation [2]? k) Bernhofen and Brown (2004) in the Journal of Political Economy investigate Japan's trade liberalization in the 1860s. The y-axis below plots the change in prices from autarky to free trade. The x-axis shows net exports under free trade in 1869. Discuss if the graph is consistent with the theory we are trying to demonstrate?COMPARATIVE ADVANTAGE 63 100 Silk 80 Silkworm Eggs 60 40 Cotton Copper(Mfc) 20 Legumes Change in Price since 1851-1853 Rice Sake Wax 0 Fish Tea -20 White Sugar . Charcoal Brown Sugar * -40 . Pig Iron Cotton Cloth -60 - Cotton Yarn Candy Iron(Mfc) -80 - -1.25 -1 -,75 -.5 -.25 0 .25 .5 .75 1.25 Net Exports in 1869 FIG. 4.-Net exports and price changes for 1869. Source: Japan Bureau of Revenue (1893) for trade data and Kinyu Kenkyukai (1937), Miyamoto (1963), Ono (1979), Ya- mazaki (1983), and Mitsui Bunko (1989) for price data