Exercise 5.3 (Relative Prices of Investment Goods and the Current Account} We assumed that households consume goods different from those produced by firms (food and oil, for example) and analyzed the effects of changes in the terms of trade. Specifically, we assumed that consumer and investment goods are imported and that the relative price of capital goods to consumer goods is always 1. Now we consider the following scenario. Assume that the country produces only consumer goods and that the output is available for the country's consumption and exports. The country does not produce capital goods, so capital goods must be imported. The relative price of capital goods is PK, . The country is a small economy, so it cannot influence this price. The production function of domestic firms is ++1:- I , where t = 'l, 2 and at (0, 1) and I-idenotes investment, measured by the quantity of capital goods. Qt) expressing the investment expenditure curve in period 1 as a function of consumption goods, i.e., deriving an equation similar to L:I(r, rm except that the lefthand side of the equation is replaced by ' 4' spending on capital goods (instead of the quantity of capital goods), and the right-hand side should contain PKI in addition to rI and A 3'. How does a rise in PK1 affect the investment curve? Q2. Write the savings curve for period 1, Le, derive an equation similar tog\" = Sfr. . t1 ,+2) + . will a rise in PK. shift the savings curve to the left or right? Or does it stay the same? 03. Write the current account curve for period 1, i.e., derive an equation similar to C+|:C'pf(t.;'}('l'h1 4' cf .I does a rise in PK, shift the current account curve to the left or right? Or will it remain unchanged? 04. Assuming that the country is a small economy and is open to trade in goods and assets, i.e., capital is free to move, what is the effect of a rise in PK,on savings, investment, and the current account in equilibrium? 05)What would be the difference in the answer to the fourth question if the country only allowed trade in goods and did not allow cross-border trade in assets