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 + c1, where = 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.

Solve the consumer's problem and find the optimal consumption in each period when r = 10%. Is the consumer a borrower or a lender?

Is the goods market in the equilibrium in the two periods when r = 10%? Explain.

What are the equilibrium values of (c0, c1) using goods market equilibrium?

Compute the equilibrium interest rate r ? .