Problem 4 - Costless Magical MacGuffin Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up the corporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) + Bu(C2) 1. Assume this consumer cannot borrow. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve. 2. Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraints such that for one of them consumer prefers to borrow and for the other - prefers to save. 3. Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin trades at P1 >0 in the first period and is expected to trade at P2 in the second period. Write down the new budget constraint. Would a consumer borrow a MacGuffin? What is the condition on the P,? Is P, a fair price of a MacGuffin? Could the consumer be better off with a MacGuffin?
Problem 4 - Costless Magical MacGuffin Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up the corporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) + Bu(C2) 1. Assume this consumer cannot borrow. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve. 2. Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraints such that for one of them consumer prefers to borrow and for the other - prefers to save. 3. Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin trades at P1 >0 in the first period and is expected to trade at P2 in the second period. Write down the new budget constraint. Would a consumer borrow a MacGuffin? What is the condition on the P,? Is P, a fair price of a MacGuffin? Could the consumer be better off with a MacGuffin?
Chapter1: Making Economics Decisions
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Transcribed Image Text:**Problem 4 - Costless Magical MacGuffin**
Consider a consumer that lives only for two periods. He works in period 1 (and gets income \( Y_1 \)) and moves up the corporate ladder in period 2 (and gets income \( Y_2 \)), where \( Y_1 < Y_2 \). This consumer has the usual preferences over time: \( u(C_1) + \beta u(C_2) \).
1. **Assume this consumer cannot borrow. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve.**
2. **Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraints such that for one of them consumer prefers to borrow and for the other prefers to save.**
3. **Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin trades at \( P_1 > 0 \) in the first period and is expected to trade at \( P_2 \) in the second period. Write down the new budget constraint. Would a consumer borrow a MacGuffin? What is the condition on the \( P_2 \)? Is \( P_2 \) a fair price of a MacGuffin? Could the consumer be better off with a MacGuffin?**
**Note:** The highlighted section pertains to the assumption that the consumer is now allowed to save or borrow, emphasizing the need to analyze new budget constraints and consumption patterns over the two periods.
Transcribed Image Text:**Problem 4 - Costless Magical MacGuffin**
Consider a consumer that lives only for two periods. He works in period 1 (and gets income \( Y_1 \)) and moves up the corporate ladder in period 2 (and gets income \( Y_2 \)), where \( Y_1 < Y_2 \).
This consumer has the usual preferences over time: \( u(C_1) + \beta u(C_2) \)
1. **Assumption 1:** The consumer cannot borrow. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve.
2. **Assumption 2:** Now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraints such that for one of them the consumer prefers to borrow, and for the other, prefers to save.
3. **Assumption 3:** Once again assume a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin trades at \( P_1 > 0 \) in the first period and is expected to trade at \( P_2 \) in the second period. Write down the new budget constraint. Would a consumer borrow a MacGuffin? What is the condition on the \( P_2 \)? Is \( P_2 \) a fair price of a MacGuffin? Could the consumer be better off with a MacGuffin?
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