Question

uestion 10 (8 points) You are considering planting a garden to get fresh lettuce during the pandemic. You get $3 of happiness from every bag of lettuce you get from your garden. Your discount rate is 5% per week. It costs you $5 to plant lettuce. To simplify the math, assume that you must harvest all of your lettuce at once. In week 3 you have 1 bag of lettuce in your garden. It will grow by 25% between week 3 and 4. What is the value to you of lettuce if you harvest in week 3? What is the value if you harvest in week 4? Should you plant the garden if these are your only two choices of when to harvest?

Answer 1

In week three we have 1bag of lettuce in garden. Cost of this will be 5(e^-0.0031)=4.9845 Happiness obtained $3. Value at end of third week is -1.9845$ .Now if it grows 25% from week 3 to week 4.happines will ncrease from $3 to 3.75$. Cost of lettuce will be 5(e^-0.0042)=5.0210. Thus value of lettuce at the end of fourth week will be =-5.0210+3.75=-1.2710 Yes i should plant the garden as value of harvesting lettuce to me has increased from -1.98 to -1.27 in week 4.