Question

The production technology for corn seed requires water, engineers, and unskilled workers The production requirements for a metric ton of corn can be summarized by: a. fs(w, u, e) 120 (2 u+4 e)01 .w0.4 Monsanto's costs per input are as follows: $10 per ton ofwater, $10 per hour of unskilled labor, and $40 per hour of engineer labor. Compute the marginal productivity of investing in each of the inputs MPI of water MPI of engineer hours: Comparing the MPI of engineers to unskilled workers, you notice something about the relative productivity of investing in engineer hours vs unskilled labor hours (hint: would it ever be possible to set them equal?) and make the following decision about hiring unskilled vs engineer labor By comparing the MPI of unskilled labor to water, you determine that for every hour of unskilled labor, you should use tons of water Putting this all together, you are able to determine Monsanto's variable cost function. The first step is to substitute in the optimal input ratios you have just solved for into the production plan. How many metric tons of corn are produced when u hours of unskilled labor are used in the optimal combination with the other inputs? (at this step, and only at this step, you should round to the nearest integer) Rearrange to get the hours of unskilled labor required to produce q metric tons of corm.