In a private companys accounting system, inputs are _______________ and outputs are ________

Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital

shusha [124]

Answer:

Check the explanation

Explanation:

Yt = Kt + Nt

Taking output per worker, we divide by Nt

Yt/Nt = Kt/Nt + 1

yt = kt + 1

where yt is output per worker and kt is capital per worker.

a) With population being constant, savings rate s and depreciation rate δ.

ΔKt = It - δKt

dividing by Nt, we get

ΔKt/Nt = It/Nt - δKt/Nt ..... [1]

for kt = Kt/Nt, taking derivative

d(kt)/dt = d(Kt/Nt)/dt ... since Nt is a constant, we have

d(kt)/dt = d(Kt/Nt)/dt = (dKt/dt)/Nt = ΔKt/Nt = It/Nt - δKt/Nt = it - δkt

thus, Capital accumulation Δkt = i – δkt

In steady state, Δkt = 0

That is I – δkt = 0

S = I means that I = s.yt

Thus, s.yt – δkt = 0

Then kt* = s/δ(yt) = s(kt+1)/(δ )

kt*= skt/(δ) + s/(δ)

kt* - skt*/(δ) = s/(δ)

kt*(1- s/(δ) = s/(δ)

kt*((δ - s)/(δ) = s/(δ)

kt*(δ-s)) = s

kt* = s/(δ -s)

capital per worker is given by kt*

b) with population growth rate of n,

d(kt)/dt = d(Kt/Nt)/dt =

= $\frac{\frac{dKt}{dt}Nt - \frac{dNt}{dt}Kt}{N^{2}t}$

= $\frac{dKt/dt}{Nt} - \frac{dNt/dt}{Nt}.\frac{Kt}{Nt}$

= ΔKt/Nt - n.kt

because (dNt/dt)/Nt = growth rate of population = n and Kt/Nt = kt (capital per worker)

so, d(kt)/dt = ΔKt/Nt - n.kt

Δkt = ΔKt/Nt - n.kt = It/Nt - δKt/Nt - n.kt ......(from [1])

Δkt = it - δkt - n.kt

at steady state Δkt = it - δkt - n.kt = 0

s.yt - (δ + n)kt = 0........... since it = s.yt

kt* = s.yt/(δ + n) =s(kt+1)/(δ + n)

kt*= skt/(δ + n) + s/(δ + n)

kt* - skt*/(δ + n) = s/(δ + n)

kt*(1- s/(δ + n)) = s/(δ + n)

kt*((δ + n - s)/(δ + n)) = s/(δ + n)

kt*(δ + n -s)) = s

kt* = s/(δ + n -s)

.... is the steady state level of capital per worker with population growth rate of n.

3. a) capital per worker. in steady state Δkt = 0 therefore, growth rate of kt is zero

b) output per worker, yt = kt + 1

g(yt) = g(kt) = 0

since capital per worker is not growing, output per worker also does not grow.

c)capital.

kt* = s/(δ + n -s)

Kt*/Nt = s/(δ + n -s)

Kt* = sNt/(δ + n -s)

taking derivative with respect to t.

d(Kt*)/dt = s/(δ + n -s). dNt/dt

(dNt/dt)/N =n (population growth rate)

so dNt/dt = n.Nt

d(Kt*)/dt = s/(δ + n -s).n.Nt

dividing by Kt*

(d(Kt*)/dt)/Kt* = s/(δ + n -s).n.Nt/Kt* = sn/(δ + n -s). (Nt/Kt)

$\frac{sn}{\delta +n-s}.\frac{Nt}{Kt}$

using K/N = k

$\frac{s}{\delta +n-s}.\frac{n}{kt}$

plugging the value of kt*

$\frac{sn}{\delta +n-s}.\frac{(\delta + n -s)}{s}$

n

thus, Capital K grows at rate n

d) Yt = Kt + Nt

dYt/dt = dKt/dt + dNt/dt = s/(δ + n -s).n.Nt + n.Nt

using d(Kt*)/dt = s/(δ + n -s).n.Nt from previous part and that (dNt/dt)/N =n

dYt/dt = n.Nt(s/(δ + n -s) + 1) = n.Nt(s+ δ + n -s)/(δ + n -s) = n.Nt((δ + n)/(δ + n -s)

dYt/dt = n.Nt((δ + n)/(δ + n -s)

dividing by Yt

g(Yt) = n.(δ + n)/(δ + n -s).Nt/Yt

since Yt/Nt = yt

g(Yt) = n.(δ + n)/(δ + n -s) (1/yt)

at kt* = s/(δ + n -s), yt* = kt* + 1

so yt* = s/(δ + n -s) + 1 = (s + δ + n -s)/(δ + n -s) = (δ + n)/(δ + n -s)

thus, g(Yt) = n.(δ + n)/(δ + n -s) (1/yt) = n.(δ + n)/(δ + n -s) ((δ + n -s)/(δ + n)) = n

therefore, in steady state Yt grows at rate n.

5 0

4 years ago

An emphasis is placed on proper income statement item recognition under what approach under US GAAP?

Over [174]

Answer:

Revenue /expense approach

Explanation:

As we know that the income statement recognized only the revenues and the expenses and if the revenue is more than the expenses so the company is earning profit else it would suffered loss

So for proper income statement, the item recognized under US GAAP should be placed in revenue and expense approach as it comes under the income statement and the same is to be considered

3 0

4 years ago

At December 31, 2018, the financial statements of Hollingsworth Industries included the following: Net income for 2018 $ 590 mil

m_a_m_a [10]

Answer:

Basic EPS = $1.359 million

Diluted EPS = $1.195 million

Explanation:

For Basic EPS we need to calculate the number of shares outstanding

Shares as on Jan 1 = 450 million

Treasury shares on Sep 1 = 48 million × (4 months ÷ 12 months)

= 16 million

Number of shares o/s = Shares as on Jan 1 - Treasury shares on Sep 1

= 450 million - 16 million

= 434 million

Basic EPS = Net Income ÷ Number of shares o/s

= $590 million ÷ 434 million

= $1.359 million

For Diluted EPS,

Interest savings = 10% × $ 250 million

= $25 million

Adjusted Net Income = Net Income + After tax interest savings

= $590 million + [25 millions - 40(25million)]

= $590 million - $15 million

= $575 million

and weighted number of shares will include the bonds, that are convertible

Outstanding shares as computed = 434 million

Bond conversion Shares = 47 million

Total shares outstanding = Outstanding shares as computed + Bond conversion Shares

= 434 million + 47 million

= 481 million

Diluted EPS = Adjusted Net income ÷ Total shares outstanding

= $575 million ÷ 481 million

= $1.195 million

8 0

3 years ago

Consider the following data to answer the following questions: Country GDP Population A $32,000 1,500 B $20,000 1,000 C $10,000

polet [3.4K]

Answer: 4 times

Explanation:

GDP per capita is a way of measuring the wealth Distribution in a country. It is calculated by dividing the Gross Domestic Product by the population of the country. The aim usually is to see if the Country's economy is big enough considering the amount of people it has.

Country C has a GDP per capita of,

= 10,000/500

= $20

Country D has a GDP per capita of,

= 10,000/2,000

= $5

= 20/5

= 4

Country C has a GDP per capita that is 4 times that of C.

4 0

3 years ago

Calculate the price of a two-year bond with a face value of $100, a coupon rate of 5%, and a yield-to-maturity of 5%.

aalyn [17]

The price of the bond is $100.

The bond's price is the present value of the face value plus the present value of the interest accrued throughout the bond's term.

The coupon interest rate is 5% of 100, that is $5 per year. The yield to maturity is also 5%. Because the coupon rate is equal to the yield, the bond's present value will only be its face value.

Present value = 5(P/A, 5%, 2) + 100(P/F, 5%, 2)

= 5×1.85941+ 100×0.90703

= 100

Therefore, the price of the bond is $100.

To know more about price of the bond click here:

brainly.com/question/15567868

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6 0

2 years ago

In a private companys accounting system, inputs are _______________ and outputs are _________.

In a private companys accounting system, inputs are _______ and outputs are _.