True or false

1) Ricardian Equivalence does not hold in a closed economy, given that domestic agents cannot borrow or lend from abroad.
False. Ricardian Equivalence does hold in a closed economy, as long as private agents and the government can borrow and lend from each other. Given the equilibrium interest rate, a decrease in taxes simply means that agents will hold more government bonds, but they will not change their consumption choice - see also discussion in class.
2) If Ricardian Equivalence holds, for given time pattern of government spending (G) changes in the amount of outstanding public debt do not affect the equilibrium real interest rate (provided that the intertemporal budget constraint of the government is respected).
True. The equilibrium real interest rate is given by the first order condition, which states that the real interest rate is equal to the marginal rate of substitution between consumption today and consumption tomorrow. If Ricardian Equivalence holds, consumption does not depend on the choice between debt and taxes. Since changes in the amount of outstanding public debt do not affect the equilibrium consumption, therefore they do not affect real interest rate.
3) Consider an open economy where agents are borrowing constrained (are not allowed to borrow) and are currently consuming all their disposable income (C1=Y1-T1). The government is financing all of its spending by raising taxes (G1=T1). If the government decides to lower taxes, and therefore to finance part of its spending by issuing debt, consumption in period 1 (C1) will rise.
True. Or, more precisely, consumption will increase or stay constant, but certainly not decrease. If individuals are borrowing constrained, and are consuming all their disposable income, then either i) they are happy as they are, or ii) they would like to consume more and they cannot. If the government lowers taxes (and finances government spending by borrowing abroad), disposable income today will increase, so in case ii) they will consume more. This is a situation where Ricardian Equivalence does not hold. The government is effectively borrowing on behalf of the agents, who are borrowing constrained.
4)At the current real interest rate, say $r=5\%$, I am not a borrower nor a lender (so C1=Y1, C2=Y2). If the interest rate rises to $6\%$ I will become a lender [assume there is not government in this economy].
True. If I am not a borrower nor a lender, then there is no income effect. The substitution effect will induce me to lower today's consumption and, therefore, to become a lender.
5) With exogenous labor supply, and perfect capital mobility with respect to the rest of the world, preferences of domestic agents do not affect investment.
True. With exogenous labor supply, and with perfect capital mobility with respect to the rest of the world, investment is determined by the condition:

$$F_K(1,K)-\delta=r^w$$

and this condition is not affected by the preferences of domestic agents.
6) Countries which expect high government spending in the future will tend to run Current Account surpluses - other things being equal.
True. See permanent income: countries which expect to have low disposable resources (Y-G) in the future should ``save for rainy days''. In fact:

$$CA=Y-\bar{Y}-(G-\bar{G})$$

If government spending in the future will be higher than today, then

$$G-\bar{G}<0$$

and - other things being equal - the country will run a Current Account surplus.
7)Many developing countries are running current account deficits. This is consistent with permanent income theory.
True. See above. By definition of developing country (although this may not hold for all developing countries),

$$Y-\bar{Y}<0$$

as income will hopefully grow in the future.
8) If the production function is Cobb-Douglas, the return to capital in developing countries is higher than in developed countries.
True. Developing countries have a capital to labor ratio (capital per capita) which is lower than in the developed world. By the fact that the marginal productivity of capital is decreasing in the capital to labor ratio, F_K in developing countries is higher than in developed countries.
9)In order to compare living standards in Mexico and the U.S., all one has to do is to compute the per capita GDP in both countries, expressed in U.S.$, and compare them. This would be true only if all goods were tradables.
True. If all goods were tradables, than the CPI would be the same in all countries - this is if the Law of One Price holds, that is, the price in Pesos of a tradable good (ie, a CD) has to be the same as the price in US $ times the exchange rate. If all goods are tradables the relative prices of all goods are the same in both countries. So people will choose the same consumption basket and this consumption basket will cost exactly the same in both countries.
10) If all countries had a fixed exchange rate among each other (as during the Gold Standard), inflation should be the same across countries.
False. If all countries had a fixed exchange rate among each other, the price of tradables would change in the same way. However, inflation also depends on changes in the price of non tradables.