Solve the following: Intertemporal Rational Choice

Assume that your intertemporal endowment is made of M1=2500? available in the present period and M2 =4200? available in the future. The interest rate is 20%. Draw the intertemporal budget constraint and write its equation. What is the opportunity cost of present consumption?

Assume, moreover, that your utility function is U=C₁².C₂ . Identify your optimal choice about present and future consumption. Finally, show how the budget constraint changes when, ceteris paribus:

(i) the interest rate decreases to 10%;

(ii) present income increases to 3000? and show, graphically, how the rational consumer will change her choice when the above changes take place.

Utility Function:

U