Question

Fred’s fennel farming costs and Rosie’s rhinoceros ranching costs are provided below. (Both Fred and Rosie continue to be price-takers.) Fred faces a market price of $130 per acre regardless of how many acres he plants and Rosie faces a market price of $320 per rhino regardless of how many she raises.

FARMING						RANCHING
Acres	MC		TC	TR	Profit	Rhinos	MC		TC	TR	Profit
1	50					1	60
2	75					2	120
3	100					3	180
4	125					4	240
5	150					5	300
6	175					6	360

(a) Complete the table.

(b) Year 1: Rosie goes to Africa on “work-related” business so she doesn’t ranch. Fred farms fennel. How many acres should he plant? How much profit can he expect?

(c) Year 2: Fred visits family in Finland so his farm is fallow while Rosie raises rhinos. How many rhinos should she raise? How much profit can she expect?

(d) Year 3: Both Fred and Rosie stay home and work. Unfortunately, Rosie’s rhinos rampage and the fennel farm suffers. Fred decides to enclose his land with fences. He pays $20 per acre for each acre that he decides to enclose with fences. What are the profit-maximizing levels of production for Rosie and Fred? What is their combined profit this year?

(e) Year 4: The local animal control officer warns Rosie that rampaging rhinos that damage anyone’s crops will be rounded up and transferred to a nearby wildlife preserve. Rosie is rather fond of her rhinos and decides that she’d prefer to work with Fred to prevent any damaging rampaging. Fred and Rosie have a long-standing friendship so negotiating should be relatively easy. What do you reccommend they do?

Answer 1

1st 4 parts are answered.

a) I have added an axtra column for MR (Marginal Revenue) in both the tables.

Farming

TC_i=TC_i-1+ MC_i where i represents Acres from 1 to 6. for example TC₃=TC₂+MC₃

TR= Price(acres), price=130, acres=1,2,3,4,5,6.

MR=price or MC_i= TC_i - TC_i-1

profit= TR- TC.

Acres	MC	TC	TR	MR	Profit
1	50	50	130	130	80
2	75	125	260	130	135
3	100	225	390	130	165
4	125	350	520	130	170
5	150	500	650	130	150
6	175	675	780	130	105

Ranching

TC_j=TC_j-1+ MC_j where j represents Rhinos from 1 to 6. for example TC₃=TC₂+MC₃

TR= Price(Rhinos), price=130, rhinos=1,2,3,4,5,6.

MR=price or MC_j= TC_j - TC_j-1

profit= TR- TC.

Acres	MC	TC	TR	MR	Profit
1	60	60	320	320	260
2	120	180	640	320	460
3	180	360	960	320	600
4	240	600	1280	320	680
5	300	900	1600	320	700
6	360	1260	1920	320	660

b) Fred should plant the area of land at which the profit is maximum. from part A we can see from the farming table that the profit is maximum if he plants 4 acres. At 4 acres he can expect $170 profit.

c)Rosie should raise that number of Rhinos at which profit is maximum. from part A we can see from the Ranching table that the profit is maximum if she raises 5 rhinos . At 5 rhinos she can expect $700 profit.

d) if fred fences his farm and per acre fenscing cost $20. then his total cost increases by $20 for each level. the first unit marginal cost also increases by 20, TR and MR remain same. the new profit level for each acre is showin the new farming table which is as follows

Acres	MC	TC	TR	MR	Profit
1	70	70	130	130	60
2	75	145	260	130	115
3	100	245	390	130	145
4	125	370	520	130	150
5	150	520	650	130	130
6	175	695	780	130	85

thus his optimal area planted is still 4 acres but his profit at this level is now $150.

there is no change in the ranching table and Rosie still raises 5 rhinos and makes $700 as before.

so Combined profit this year = $150 + $700 = $850.