Question

A purely competitive wheat farmer can sell any wheat he grows for $10 per bushel. His five hectares of land show diminishing returns, because some are better suited for wheat production than others. The first hectare can produce 1000 bushels of wheat, the second hectare 900, the third 800, and so on. Fill in the table given below to answer the following questions. How many bushels will each of the farmer’s five hectares produce? How much revenue will each hectare generate? What are the TR and MR for each hectare?

Hectare #	That Hectare's Yield	That Hectare's Revenue	TR	MR
0	na	$0	$0	na
1	?	$ ?	$ ?	$ ?
2	?	$ ?	$ ?	$ ?
3	?	$ ?	$ ?	$ ?
4	?	$ ?	$ ?	$ ?
5	?	$ ?	$ ?	$ ?

If the marginal cost of planting and harvesting an hectare is $7,000 per hectare for each of the five hectares, how many hectares should the farmer plant and harvest?

_________hectares

Answer 1

The table would be as below. The product of each Hector is basically the marginal product, since , and since change in H is always 1, we have , and for , we have or . Supposing that at H=0, the TP=0, we have generated a column for TP. The each H's revenue yield would be the marginal revenue product, which is , and since P=10, we have . The total revenue would be or , and marginal revenue would be , and since , we have .

H	MP	TP	MRP($)	TR	MR
0	-	0	-	0	-
1	1000	1000	10000	10000	10
2	900	1900	9000	19000	10
3	800	2700	8000	27000	10
4	700	3400	7000	34000	10
5	600	4000	6000	40000	10

The MC=MR equality would be obtained if MC would have been stated per product (per bushel), not per input (Hectare). In this case, the optimal input would be where MC=MRP, which is where H=4, since at that input, the marginal revenue produt is $7000. Note that in this case, the MC per hectare is basically the input price of each input (H).

Hence, the farmer should plant in 4 hectares.

The reason being that, if the farmer employs 3 hectares or less, the farmer can still increase the revenue by employing more H, which would be less than or equal to the marginal cost of that hectare. If the farmer employs 5 hectares or more, the farmer would face loss, since the revenue yielded by each hector is less than the cost of that hectare (MC of each hectare), and hence must reduce the H. Only at H=4, the farmer is at equilibrium.