A college student has a utility function given by U = In(c1) + Bin(c2) where c1...

 

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A college student has a utility function given by U = In(c1) + Bin(c2) where c1 and c2 are her consumption during college and after graduation, and ß is her discount factor (0 <ß < 1). She earns zero income during college and income I after graduation. Assume that she can borrow money during college with an interest rate of r and will repay the loan after graduation. (a) Show that we can write her budget constraint as c1 + (1/1+r) c2 = 1. Draw the budget constraint in a coordinate where c1 is on the x-axis. How will the budget constraint change if the government lowers the interest rate for student loans? (b) Define the utility maximization problem and solve c1, c2 as functions of exogenous variables. (c) How will she change c1, c2 and the amount of loan she borrows if the government lowers the interest rate? Discuss the income and substitution effects. (d) The discount factor ß provides a measure of how patient an individual is, e.g. higher ß implies that she values future consumption versus current consumption, and hence she is more patient. How will c1, c2 change if one becomes more patient? Will she be better off when becoming more patient? A college student has a utility function given by U = In(c1) + Bin(c2) where c1 and c2 are her consumption during college and after graduation, and ß is her discount factor (0 <ß < 1). She earns zero income during college and income I after graduation. Assume that she can borrow money during college with an interest rate of r and will repay the loan after graduation. (a) Show that we can write her budget constraint as c1 + (1/1+r) c2 = 1. Draw the budget constraint in a coordinate where c1 is on the x-axis. How will the budget constraint change if the government lowers the interest rate for student loans? (b) Define the utility maximization problem and solve c1, c2 as functions of exogenous variables. (c) How will she change c1, c2 and the amount of loan she borrows if the government lowers the interest rate? Discuss the income and substitution effects. (d) The discount factor ß provides a measure of how patient an individual is, e.g. higher ß implies that she values future consumption versus current consumption, and hence she is more patient. How will c1, c2 change if one becomes more patient? Will she be better off when becoming more patient?

Answer rating: 100% (QA)

a We can write the budget constraint as c 1 1 1 r c 2 I This budget constraint can be represented gr... View the full answer