Calculate the optimal consumption bundle for each scenario below, compare it to the baseline case solved on the previous page, and explain the intuition behind the change.

1. Income is higher (exactly double)

A consumers consumption-utility function for a two-period horizon is

U(C₁, C₂) = ln(C₁) + 0.7 * ln(C₂).

The income stream is $100,000 this year (Y₁) and $115,750 $115,500next year (Y₂).

The market interest rate is 5% per year.

1. The interest rate is lower

A consumers consumption-utility function for a two-period horizon is

U(C₁, C₂) = ln(C₁) + 0.7 * ln(C₂).

The income stream is $50,000 this year (Y₁) and $57,750 next year (Y₂).

The market interest rate is 2% per year.

2. The consumer is more patient (less impatient)

A consumers consumption-utility function for a two-period horizon is

U(C₁, C₂) = ln(C₁) + 0.9 * ln(C₂).

The income stream is $50,000 this year (Y₁) and $57,750 next year (Y₂).

The market interest rate is 2% per year.

3. Consider a share of stock in a company named BigFarmCo.

Each share of a stock delivers five units of food to the stockholder in period 1 and another five in period 2.

The law of one price says the value of the share of stock should equal the value of the food it supplies.

What is the value today of a share of the stock? Use the parameters and results from question 0 as solved in class?