1.)Assume that a producer has a budget of $4000 per growing season, that there are only two variable inputs (fertilizer and insecticide), and
that the price of one ton of fertilizer = the price of one barrel of insecticide = $400,
Maximum output could be achieved when fertilizer and insecticide are used in the following amounts:
Q(f)= ____ tons of fertilizer and
Q(i)= ____ barrels of insecticide
[Answer with two whole numbers separated only by a comma: no spaces]
2.)By using the inputs of fertilizer and insecticide in the optimal amounts (that you identified in the previous question), how much was added to total corn output?
Relative to a situation where no fertilizer and no insecticide were used, total product was ______ thousand bushels greater.
3.)Now if the price of both variable inputs to production increases to $500 (per ton of fertilizer and per barrel of insecticide), but the budget remains at $4000, maximum total product is achieved when inputs are used in the following amounts:
Q(f)= ____ tons of fertilizer, and
Q(i)= ____ barrels of insecticide.
[Again, answer with two whole numbers separated only with a comma]
4.) As the result of an "income effect" caused by the input prices rising, the use of fertilizer and insecticide can now only raise output by ____ thousand bushels of corn.
5.) Again assume a budget of $4000 and a that a barrel of insecticide still costs $400, but that the price for fertilizer was cut in half to only $200 per ton.
The optimal combination of inputs will now be
Q(f) = ____ tons of fertilizer and
Q(i) = ____ barrels of insecticide
6.) Now assume that the producer's budget is unlimited, and that the inputs are once again both $400 per unit, but that the producer will limit spending on inputs to avoid having the cost of one more unit of input exceed the dollar value of additional output produced (MRP). For this type of question, the dollar value of a thousand bushels of corn (output) must be given. Assume that it is $200 per 1000 bushels.
Under these conditions, the optimal amounts of inputs would be no more than 6 tons of fertilizer, but between ____ and ____ barrels of insecticide.
Since the price of fertilizer and insecticide are equal, set the MP's equal and spend as much as possible without going over budget. Steadily keep trying lower minimum MPs until the budget is approached. We know 400Q(f)+400Q(i)=4000, or Q(f)+Q(i)=10. MP=5 leads to Q(f)=4 and Q(f)=6. Since all money is spent, that must be the optimum (this approach works since both technologies are at diminishing marginal returns at these quantities).
The additional production is the sum of all the MPs of each barrel of insecticide and ton of fertilizer used. Thus, it is 10+9+8+6+8+10+11+9+7+5=83. Hence, the extra production is 83 1000's of bushels.
Again, use the same approach as in the first part and hope that diminishing marginal returns have set in. MP=7 exhausts the budget. Thus, Q(f)=3 and Q(i)=5. Since diminishing marginal returns have set in, we are done.
Use the same approach as #2. 10+9+8+8+10+11+9+7=72. Thus, the extra production is 72 1000's of bushels.
Now, the new budget constraint is 200Q(f)+400Q(i)=4000, or Q(f)+2Q(i)=20. Now, we set MP/P of both technologies equal. Taking the unit of currency to be bundles of $200, we have unchanged MP/P=MP for fertilizer and MP/P=MP/2 for insecticide. Now, we decrease MP/P until the budget is nearly exhausted or exhausted. MP/P here is 1.5 to exhaust the entire budget. Hence, Q(f)=6 and Q(i)=7 is the optimum. We are done due to diminishing marginal returns taking place.
Now, any unit such that MRP is greater than or equal to MP*C is purchased. The 6th ton of fertilizer has MRP $400 and the 7th barrel of insecticide is the last to have MRP over $400 ($400/200=2 thousand bushels of corn must be produced from a unit of input). Therefore, the optimum is Q(f)=6 and Q(i)=7.