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Consider a two period model, populated by a representative consumer and a government. The consumer’s preferences can be described by the utility function: u(c0, c1) = √(c0)+β√(c1), where β = 0.95 captures the consumer’s preference for the future. The consumer has an income y0=20 in the current period and expect a future income y1 = 25. The government plans to spend G0 = 5 in the current period and G1 = 7. The interest rate is r = 10% in the economy. (a) If the government decides to impose a tax of T0 = 7, what will be the value of T1? (b) Is it optimal for the consumer to consume his disposable income in each period? Explain. (c) Solve the consumer’s problem and find the optimal consumption in each period when r = 10%. Is the consumer a borrower or a lender? (d) Is the goods market in the equilibrium in the two periods when r = 10%? Explain. (e) What are the equilibrium values of (c0, c1) using goods market equilibrium? (f) Compute the equilibrium interest rate r ?
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