Suppose a group of cattle ranchers each have $100 to spend. The farmers can eith
ID: 1117346 • Letter: S
Question
Suppose a group of cattle ranchers each have $100 to spend. The farmers can either purchase a steer for $100, and let it graze in a common grazing area, or they can buy a bond with the $100 which receives an interest rate of 6%. The table below gives the value of each steer after it has been grazing for one year.
# of steers
Price per steer
Total Value of the Steers
Marginal Value of This Steer
1
$133
2
$128
3
$123
4
$118
5
$113
6
$108
7
$102
a) Fill in the two blank columns above.
b) If the ranchers put their steers in the grazing area one at a time and act only in their self interest, how many steers will be put on the grazing area?
c) If the ranchers work together to maximize their total income, how many steers will be put on the grazing area?
# of steers
Price per steer
Total Value of the Steers
Marginal Value of This Steer
1
$133
2
$128
3
$123
4
$118
5
$113
6
$108
7
$102
Explanation / Answer
No. of steers Price per stees Total Value Marginal Value TC MC 1 133 133 133 106.0 106.0 2 128 256 123 112.4 6.4 3 123 369 113 119.1 6.7 4 118 472 103 126.2 7.1 5 113 565 93 133.8 7.6 6 108 648 83 141.9 8.0 7 102 714 66 150.4 8.5 b) He will put till the marginal benefit = 0. So, number of steers will be =7. c)Now ranchers will buy till Marginal beefit = Marginal Cost . So he will put 7 steers Marginal Cost is the interest foregone.
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