Consider the real intertemporal model with investment that we studied in class.

• (5pts) State the current, future, and inter-temporal budget constraints of the representative consumer. State the consumer's problem. Characterize its solu- tion and explain.
• (5pts) State the current, future and the present value of profits for the repre- sentative firm. Assume that at the end of the future period remaining capital can be sold at priceq. State the firm's problem. Characterize its solution and explain.
• (10pts) Construct the output supply curve if labor supply does not respond to a change in the interest rate. Next, suppose investment demand increases for ex- ogenous reasons. Explain the effects on output, the interest rate, consumption and investment.
• (10pts) Suppose the government increases government purchasesG. Carefully explain using diagrams and math the size of the partial government expen- diture multiplier assuming the consumption function is linear. In a diagram show the total government expenditure multiplier and carefully comment on its magnitude. What does the Ricardian equivalence theorem have to say about the size of the government expenditure multiplier?