1. in the Malthusian model, suppose that there is a technological advance that reduces deathrates. Using diagrams, determine the effects ofthis in the long-run steady state and explain your results. 2. Suppose that the economy is initially in a steady state and that some of the nation's capitalstock is destroyed because of a natural disaster or a war. (a) Determine the long-run effects of this on the quantity of capital per worker and on outputper worker. (b) In the short run, does aggregate output grow at a rate higher or lower than the growthrate of the labour force? (c) After World War ll, growth in real GDP in Germany and Japan was very high. How doyour results in parts (a) and (b) shed light on this historical experience? 3. Modify the Solow growth model by including government spending, as follows. The government purchases G units of consumption goods in the current period, where G = 9N and g is a positive constant. The government nances its purchases through lump-sum taxes on consumers, where T denotes total taxes, and the government budget is balanced each period, so that G = T. Consumers consume a constant fraction of disposable income that is, C = (1 ~ s](i' T), where s is the savings rate, with 0