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- Assume that an open economy with a floating exchange rate is described by the equations:C = 0.5(Y-T)T= 1000I= 1500 -250rG= 1500NX= 1000 – 250e(M/P)d = 0.5Y – 500rM= 1000S-I= 500 – 250rP= 2r* = 1 a. Solve for NX and e. b. Using the information from parts a. to be part d. above, graphically illustrate on aclearly labelled diagram, the short-run impact of contractionary fiscal policy on theexchange rate and level of output in this small open economy.c. Assuming that the economy adopted a fixed exchange rate system, illustrate on aclearly labelled diagram, the impact of contractionary fiscal policy.Suppose a renewable population grows logistically according to N = 778/ 1 + 5e−0.07t . According to the theory of maximum sustainable yield, what is the optimum harvesting level?Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100 pounds of salt is dissolved in the solution in tank A and 50 pounds of salt is dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in Figure 3.3.7.(a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1 (t) and x2(t) at time t in tanks A and B, respectively.(b) Find a relationship between the variables x1(t) and x2 (t) that holds at time t. Explain why this relationship makes intuitive sense. Use this relationship to help find the amount of salt in tank B at t = 30 min. FIGURE 3.3.7 Mixing tanks in Problem 9Chapter 3.3, Problem 9E, Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100
- The average number of customers in the system in the single-channel, single-phase model described in Section 12.4 is L=λ/(μ – λ) Show that for m = 1 server, the multichannel queuing model in Section 12.5, is identical to the single-channel system. Note that the formula for P0 (Equation 12-13) must be utilized in this highly algebraic exercise.You have an avocado tree, growing 100 avocados this year, 0 next year. Neighbor's tree grows 0 this year, 200 next year. Let's say you save s avocados, and nber borrows b avocados. a) Under agreement "1 this year = 1 next year": s=b s>b s<b b) Under agreement "1 this year = 3 next year": s=b s>b s<b c) In equilibrium, "1 this year = v next year". Solve for v. 1 2 3 4Two interacting populations of hares and foxes can be modeled by the recursive equations h(t + 1) = 4h(t) − 2 f (t) f(t+1)=h(t)+ f(t). For each of the initial populations given in parts (a) through (c), find closed formulas for h(t) and f (t). a. h(0)= f(0)=100 b. h(0)=200, f(0)=100 c. h(0)=600, f(0)=500
- The revenue per month earned by the Couture clothing chain at timetisR(t) =N(t)S(t),whereN(t) is the number of stores andS(t) is the average revenue per store per month. Couturereleases a statement to their investors saying that currently they have 50 stores with a total revenueof$7,500,000 and expect to increase the number of stores by about 2 stores per month and increasetotal revenue by about$250,000 per month. What does this statement imply about the current rateof change of the average revenue per store per month?29 A. Between these times, about 2,000 more megawatts of eletricity are used every hour. B. Between these times, about 500 fewer megawatts of electricity are used every hour. C. Between these times, about 500 or more megawatts of electricity are used every hour D. Between these times, about 2,00 fewer megawatts of electricity are used every hour.On the basis of how long he has until retirement and his comfort with investment risk, Connor has decided that he wants to allocate the money in his retirement account as follows: 70% to equities, 15% to fixed income, and 15% to cash. If Connor assumes that each asset class provides the low end of the rates of return shown in the table below, what overall rate of return would he expect to earn over the long term? Asset Class Degree of Risk Historical Average Rate of Return Equities High 8% - 12% Fixed Income Moderate 4% - 7% Cash Minimal 2% - 5% Group of answer choices 4.34% 6.50% 1.43% 7.25%
- a) What is the annual net level premium for a $100,000 fully discrete life insurance (only) 10-year term policy for a life age 45? b) What is the annual net level premium for a $100,000 fully discrete endowment/insurance 10-year term policy for a life age 45? Mortality follows the Standard Ultimate Life table at i = 0.05Please answer this question using the assumptions from the Solow Model In a country, the production function in terms of output per capita, y, and capital per labor, k, is y = k(12) The fraction of output saved, s, is 25% and the depreciation rate, δ, is 0.05. Assume that the population does not grow. What is the steady-state of capital per worker, k*, and output per worker, y*? What happens to the steady-state values if the population growth rate rises to 5%? By how much would the country have to increase its savings rate in b) in order to reach the same levels of steady-state values as in a)? Does the country’s growth rate increase in c) compared to a)? how?With data from the Social Security Trustees Report for selected years from 1950 and projected to 2030, the number of Social Security beneficiaries (in millions) can be modeled by B(t) = 0.00024t3 − 0.026t2 + 1.6t + 2.2