government bond, solow model, economics homework help

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(b) A village has six residents, each of whom has £1000. Each resident may either invest his money in a government bond, which pays 11 percent/year, or use it to buy a year- old steer, which will graze on the village commons. Year-old steers and government bonds each cost exactly £1000. Steers require no effort to tend and can be sold for a price that depends on the amount of weight they gain during the year. Yearly weight gain, in turn depend on the number of steers that graze on the commons. The price of 2 year old steers are given in the table as a function of the total number of steers. Number of Steers 1 Price per 2-year old steer $1200 $1175 2 3 $1150 4 $1125 5 $1100 6 $1075 (1) If village residents make their investment decisions independently, how many steers will graze on the commons? (ii) How many steers would graze on the commons if investment decisions were made collectively? 5. Consider the Solow model with population growth. Assume a positive rate of depreciation for capital, 8 >0, and a positive population growth rate, 1 > 0. Denote capital per worker and output per worker by k = K/L and y = Y/L, respectively, where L denotes the population. Start off with the basic equation of motion for capital AKSF (K, D) -8K where s is the saving rate and F denotes the production function. Derive the equation of motion in per-worker terms (i.e., with Ak on the left-hand side). Explain in words the meaning of the terms on the right-hand side, in particular when the left-hand side is zero.
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Running head: Solow model & government bonds

Solow model & government bonds:
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1

Solow model & government bonds

2

Q1
I.

The number of steers that will grave on the commons

NO. of steers

Price /2yr-old

Income /steer

Total gain in the

Marginal gain

steer

($)

herd value ($)

in the herd

(Row 2-1000)

value ($)

1

$1200

1200-1000=200

1*200=200

200

2

$1175

1175-1000=175

2*175=350

350-200=150

3

$1150

1150-1000=150

3*150=450

450-350=100

4

$1125

1125-1000=125

4*125=500

500-450=50

5

$1100

1100-1000=100

5*100=500

500-500=0

6

$1075

1075-1000=75

6*75=450

450-500=-50

An interest of $100 per year is earned whenev...


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