To segment markets means to distinguish customers or markets according to common characteristics.

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

3 years ago

______ effect happens when the place a product was manufactured influences how consumers perceive the product.

stiks02 [169]

Effect happens when the place a product was manufactured influences how consumers perceive the product. Country of Origin

What benefits do consumer product firms derive by marketing internationally?

Competition with other companies can be maintained. Sales and profits can be enhanced. Life cycles of products can be extended.

Country of origin:

Country of origin represents the country or countries of manufacture, production, design, or brand origin where an article or product comes from. For multinational brands, CO may include multiple countries within the value-creation process.

Learn more about country of origin:

brainly.com/question/19048062

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8 0

1 year ago

Suppose that $2000 is loaned at a rate of 11.5% , compounded semiannually. assuming that no payments are made, find the amount o

Zolol [24]

This problem is solved by using the compound interest formula:
A=P(1+(I/period))^(number of periods)
Where A = amount accumulated and P = amount loaned and I = Interest
A = ? P = $2, 000, I = 0.115, Period = 2 (semi annually) Number of period = 2
*7 (I. e paid twice over a 7 yrs span)
So we have
A = 2000 ( 1 + 0.115/2)^(14)
A = 2000 ( 1 + 0.0575)^(14)
A = 2000 (1.0575)^(14)
A = 2000 (2.1873851765154) = 4374.77035
So we have 4374.80 to the nearest cent.

6 0

3 years ago

g Robert Hitchcock is 40 years old today and he wishes to accumulate $500,000 by his 65th birthday so he can retire to his summe

Mariana [72]

Answer:

The correct answer is $6934.48.

Explanation:

According to the scenario, the given data are as follows:

Time period ( 41 - 64 years) (n)= 24 years

Rate of interest (r) = 8%

Future value (FV) = $500,000

Annual deposit amount = P

So, we can calculate the annual deposit amount by using following formula:

FV = P × (1+r) × [{ (1+r)^n - 1} ÷ r]

By putting the value, we get

$500,000 = P × ( 1 + 0.08) [{ (1+0.08)^24 - 1} ÷ 0.08]

$500,000 = P × ( 1.08) [{ (1.08)^24 - 1} ÷ 0.08]

$500,000 = P × ( 1.08) [{ 6.34118073724 - 1} ÷ 0.08]

$500,000 = P (72.1035)

P = $500,000 ÷ 72.1035

P = 6934.48

8 0

3 years ago

Assuming periodic inventory procedure, what effect would an understatement of ending inventory have on the different items on th

Serjik [45]

Answer:

The understatement of the ending inventory balance would result in an overstatement of the cost of goods sold. This will in turn result in an understatement of the gross and net profits for the year in the p/l.

Explanation:

The relationship between the elements of inventory in a financial statement is as shown below,

Opening balance + purchases - cost of goods sold = closing balance

As such, the understatement of the ending inventory balance would result in an overstatement of the cost of goods sold. This will in turn result in an understatement of the gross and net profits for the year in the p/l.

5 0

3 years ago