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Question 1

1.) Suppose that we have a standard two period endowment economy with no uncertainty. The representative household receives period utility U(Ct) from consuming the basket of goods Ct where U.(Ct) > 0 and Uce(Ct) 0, then we have that MRTe, = (1+ R)MRS., in equilibrium, resulting in too much leisure and too little consumption for the household compared to the efficient allocation. Assume that the nominal interest rate is about 6% per year (4% real interest rate at 2% inflation), and that the relevant period length for the cash-in-advance constraint is a month, resulting in a period interest rate of R=0.5%.We project unit sales for a new household laser-guided cockroach search and destroy system as follows: Year 1 2 3 4 5 Unit Sales 53,000 65,000 76,000 86,000 46,000 The new system will be priced to sell at $95 each. The cockroach eradicator project will require $585,000 in net working capital to start, and total net working capital will rise to 30% of sales. The net working capital will be zero at the end of the project. The variable cost per unit is $60, and total fixed costs are $25,000 per year. The equipment necessary to begin production will cost a total of $6.5 million. This equipment is mostly industrial machinery and thus qualifies for CCA at a rate of 20%, In five years, this equipment will actually be worth about 30% of its cost. The relevant tax rate is 40%, and the required return is 20%. Based on these preliminary estimates, what is the NPV of the project?(b) (2 points) The government collects a flat rate labor income tax with a tax rate, T =10%. If the tax revenue is not enough to cover the government spending the government will borrow abroad. If the tax revenue is more than government needs, the government lends out to foreigners. What is the representative household's optimal time allocation under this flat rate tax regime? How much is consumed and how much is produced? Calculate the welfare of the representative household in this case. (c) (1 point) In the previous question does the government need to borrow or lend abroad? If so, how much? In this case is it still true that c + g = Y?Macro_homework_4_2 Solve numerically the Soiow'e model based on the following information. Equlibriurn condition are\" = :12 JKt = e{K*)%{E)i e" = e Find the equilibrium values of capital, output, investment, and consumption, 117*, 1\