Is the number of children a couple must have in order to insure that the population neither increases nor decreases?

I can only put away $2,000 a year toward retirement. I am 25 and plan on retiring at 65 and earning 5%. How much will I have at

Scorpion4ik [409]

Answer: $241,600

Explanation:

As this amount is a constant amount, it is an annuity. To find out the total amount after a certain period of time, use the future value of annuity formula.

Future value of annuity = Amount * [ {( 1 + rate) ^number of periods - 1} / rate]

Number of periods = 65 - 25 = 40

Future value of annuity = 2,000 * [ {(1 + 5%)⁴⁰ - 1} / 5%]

= 241,599.54

= $241,600

3 0

3 years ago

Select the correct answer.

valkas [14]

Answer: The answer would be C. Collective bargaining

4 0

3 years ago

Describe why most countries are described as having a mixed economy

Tamiku [17]

Explanation:

A mixed economic system is a system that combines aspects of both capitalism and socialism. A mixed economic system protects private property and allows a level of economic freedom in the use of capital, but also allows for governments to interfere in economic activities in order to achieve social aims.

8 0

3 years ago

The owner of an orange grove must decide when to pick one variety of oranges. She can sell them for $27 a bushel if she sells th

uysha [10]

Answer:

The oranges should be picked in 2 weeks for maximum return

Explanation:

We assume that the return of the owner is y ($)

Assume that the number of weeks the oranges should be picked to have maximum return is x (weeks). (x≥0)

If collect now, the price for each bushel is $27

As the price per bushel decrease by $1.50 per bushel each week

=> After x weeks, the price of a bushel decrease: 1.5x ($)

=> The price of 1 bushel after x weeks is: 27 - 1.5x ($)

If collect now, each tree can yield 7 bushels

As the yield increases by half a bushel per week for the next 5 weeks

=> After x weeks with x ≤ 5, each trees would yields: 7 + 0.5x (bushels)

The return = The price of each bushes × The quantity of bushels

=> $y = (27-1.5x)(7+0.5x)$

⇔ $y= 27 (7 +0.5x) - 1.5x(7+0.5x) = 189 + 13.5x - 10.5x - 0.75x^{2}$

⇔ $y = -0.75x^{2} +3x +189$

We have: if the equation has the form of $y =ax^{2} +bx +c$ with a≠0, its maximum value is: $max y = c - \frac{b^{2} }{4a}$

In the equation $y = -0.75x^{2} +3x +189$ , we have: a = -0.75; b = 3; c = 189

=> $max y = c -\frac{b^{2} }{4a} = 189 - \frac{3^{2} }{4.(-0.75)} = 189 - \frac{9}{-3} = 189 - (-3) = 189+3 = 192$

To look for the number of weeks, we should find x (0≤x≤5) with which y = 192

$192 = -0.75x^{2} +3x +189$

⇔ $-0.75x^{2} + 3x + 189 - 192 = 0$

⇔ $-0.75 x^{2} + 3x - 3 =0$

⇔ $-0.75x^{2} + 4*0.75x - 0.75*4 =0$

⇔ $x^{2} -4x + 4 = 0$

⇔ $(x-2)^{2} = 0$

⇔ x = 2

The oranges should be picked in 2 weeks for maximum return

7 0

3 years ago

We calculated the gains and losses from price controls on natural gas and found that there was a deadweight loss of $5.68 billio

Simora [160]

Answer:

Explanation:

1. If the price of oil were $70.00 per barrel, what would be the free-market price of gas?

The free-market price is defined by the equilibrium point: when the quantity demanded and the quantity supplied are equal.

QS = 15.90 + 0.72PG + 0.05PO

QD = 0.02 – 1.8PG + 0.69PO

15.90 + 0.72PG + 0.05(70.00) = 0.02 – 1.8PG + 0.69(70.00)

19.4 + 0.72 PG= 48.32-1.8PG

PG(0.72+1.8)=48.32-19.4

PG= 28.92/2.52

PG= $11.48

QS=QD= 15.90+0.72(11.48)+0.05(70.00)

QS=QD= 27.66

What would be the deadweight loss if the price of natural gas were regulated to be $4.00? The deadweight loss would be $___ billion. (Round answer to two decimal places)

If PG is $4.00

The quantity supplies will be less than the quantity demanded. The quantity supplied will be the quantity sold in the market.

QS= 15.90+0.72(4)+0.05(70.00)

QS= 22.28

To find the deadweight loss we must evaluate the quantity supplied in the demand curve:

22.28 = 0.02 – 1.8PG + 0.69(70.00)

1.8PG= 48.32-22.28

PG= 26.04/1.8

PG= 14.47

And now we calculate the area shown in the figure attached:

Base: 14.47-4= 10.47

Height: 27.66-22.28= 5.38

Deadweight loss: (10.47*5.38)/2

Deadweight loss: 28.1643

The deadweight loss would be $28.16 billion.

6 0

3 years ago