Problem 3 Consider an economy with one nonperishable physica

Problem 3: Consider an economy with one non-perishable physical good. There are two points in time, now 0) and the future (t-1). At t-1 there are two possible states of the world, 1 and 2. There are two assets available in the economy. Each unit of asset 1 pays 5 in state 1 and 1 in state 2, while each unit of asset 2 pays 3 in state 1 and 1 in state 2. Thus, the return matrix is . The time 0 asset price vector is An investor has endowments of the physical good of X:50 at t=0 and Y = at t-1. ,1 2 His utility function is EU(x,yM)-y, + ie, the investor gets no utility of consuming the good att-0, only from consumption at t-1.You will have to solve the investor\'s problem of choosing his optimal portfolio =-11 of the two assets What will be the investor\'s consumption at t-0? (Look at his utility function, and think about it intuitively, you shouldn\'t need calculations to answer this.) Write down the investor\'s time-zero budget constraint. (Keep in mind your answer to part a.) what is the investor\'s optimal portfolio? Le, what are the optimal amounts , and 6, he should buy of the assets? (Hint: write down the Lagrangian and solve. You can use the substitutions we made in class to make it less messy.) a. b. c.

Solution

Now let’s add an aisle. To meet municipal code almost anywhere you go, (and to fit a scissor lift between the rows, necessary for harvesting) you’ll need a four-foot aisle.

So now you have an 8 x 8 area (64 square feet) and a 4 x 8 area (32 square feet). The ratio of growing space to total space is 1:2. You can also say that you have .5 growing space for every 1 foot of total space.

Now let’s look at the 8 x 8 foot bed. Add a four-foot aisle, and you’re looking at 8 x 12 total space (96 sq ft) and 8 x 8 growing space (64 sq ft). Now you have a better ratio, 2:3, or .66 growing space to every square foot of total space.

Of course you’re thinking, “stack the beds on top of each other; that’s where the efficiency happens!”

Let’s assume there are four tiers (above fours tiers you start losing money) stacked. Each tier is about three or four feet tall.

Now your growing space to total space ratios have changed again, and you’re looking at 2.0 and 2.64 growing space for your two options. Not bad, right? You can double the amount of production that you began with.

Sounds pretty good.