Urgent Help Please :( Maths Problems

[Jackass]

Hi, really struggling with some revision questions that I have to have done tonight and struggling quite significantly. Could anyone help please? On a side note, if I'm sturggling with this kind of maths, is an Economics degree a bad idea??

Would really really appreciate help.

Thank you so much for help lads, so lost, so bummed right now, and need this done tonight.

Question 1

1.Given the consumption function C = 20 + 3Y0.4 , the equation for the marginal propensity to Consume (MPC) can be written as

Answer
A. – (19 + 3Y0.4)
B. None of these
C. 1 – 1.2Y – 0.6
D. 1.2Y –0.6 – 1
E. 1.2 Y – 0.6

Question 2

1. If the Average Cost function is AC = 4Q + 9 + 3/Q then the Marginal Cost can be written as:
Answer
A. 4Q3 + 9Q2 + 3Q
B. 8Q + 9
C. 12Q2 + 18Q + 3
D. 4Q2 + 9Q +3
E. None of these

Question 3

1.Differentiating the function y = (3x3+2x2 + x + 5)2 with respect to x gives the first derivative:
Answer
A. 2(3x3+2x2 + x + 5)
B. None of these
C. 2(3x3+2x2 + x + 5)2
D. 2(3x3+2x2 + x + 5) (9x2+4x + 1)
E. (9x2+4x + 1)

Question 4

1. Given the demand function: Q = 100 – 2P, the elasticity of demand when P = 10 is given as
Answer
A. – 1/2
B. –2
C. – 0.8
D. – 1/5
E. None of these

Question 5

1.The first derivative, dy/dx of the function y = ln (2x+1 ) is
Answer
A. 1 / (2x + 1)
B. 2 / (2x + 1)
C. 2x + 1
D. (2x + 1) / 2
E. None of these

Thanks for help.

noodler

[Jackass] wrote: »

Hi, really struggling with some revision questions that I have to have done tonight and struggling quite significantly. Could anyone help please? On a side note, if I'm sturggling with this kind of maths, is an Economics degree a bad idea??

Would really really appreciate help.

Thank you so much for help lads, so lost, so bummed right now, and need this done tonight.

Question 1

1.Given the consumption function C = 20 + 3Y0.4 , the equation for the marginal propensity to Consume (MPC) can be written as

Answer
A. – (19 + 3Y0.4)
B. None of these
C. 1 – 1.2Y – 0.6
D. 1.2Y –0.6 – 1
E. 1.2 Y – 0.6

Question 2

1. If the Average Cost function is AC = 4Q + 9 + 3/Q then the Marginal Cost can be written as:
Answer
A. 4Q3 + 9Q2 + 3Q
B. 8Q + 9
C. 12Q2 + 18Q + 3
D. 4Q2 + 9Q +3
E. None of these

Question 3

1.Differentiating the function y = (3x3+2x2 + x + 5)2 with respect to x gives the first derivative:
Answer
A. 2(3x3+2x2 + x + 5)
B. None of these
C. 2(3x3+2x2 + x + 5)2
D. 2(3x3+2x2 + x + 5) (9x2+4x + 1)
E. (9x2+4x + 1)

Question 4

1. Given the demand function: Q = 100 – 2P, the elasticity of demand when P = 10 is given as
Answer
A. – 1/2
B. –2
C. – 0.8
D. – 1/5
E. None of these

Question 5

1.The first derivative, dy/dx of the function y = ln (2x+1 ) is
Answer
A. 1 / (2x + 1)
B. 2 / (2x + 1)
C. 2x + 1
D. (2x + 1) / 2
E. None of these

Thanks for help.

Q2: You have Average Cost....

To get total cost multiply everything by Q..

=> TC=4Q2 +9Q +3

You want Marginal, so differentiate the above with respect to Q:

MC= 8Q + 9



Always remember Average Cost is Total Costs Divided By Q

Marginal Cost is Total Cost differentiated with respect to Q

andrew

What exactly are you having trouble with? Is It with getting derivatives, or is It with actually understanding why you've to get them in the first place?

[Jackass]

No I understand the concept, just not the maths part. Struggling again with more revision questions.

Ugggh, I'm so screwed in this subject and desperate, just fallen so far behind. Maybe someone would be kind enough to run through some of these questions and give explenations?? I would really really appreciate it and am freaking out over not being able to understand these.

Question 1

Find the second cross-partial derivative for the following function:
y = xz-2

Answer

-2z-3

z-2

2xz-2

None of these

-2xz-1

I think the answer to this one is the first differentiation is the second option based on x being dropped after the first differentiation with no power (sorry, not really able to type my calculations)

Question 2

Suppose the utility of consuming goods x and y is given by U = x0.25y0.25
What is the marginal utility of consuming x?
Answer

x-0.75y0.25

0.25x-0.75

None of these

xy

0.25x-0.75y0.25

I think the last one is the answer, but couldn't get exact answer for any of these

Question 3

Suppose the utility of consuming goods x and y is given by U = x1/4y1/4
How does the marginal utility of x change as x increases?
Answer


The marginal utility of x is the same at all levels of x

None of these


The marginal utility of x gets smaller at higher levels of x


The marginal utility of x gets larger at higher levels of x

I have no idea about this one

Question 4

Suppose the output of a firm is given by Y = KL where K denotes the number of units of capital, L denotes the number of units of labour, and Y denotes the number of units of output
What is the first derivative of Y with respect to K?


Answer

0

None of the above

L

K

KL

I think the answer is 1 (i.e. none of these) as none of the units are to a power of anything

Question 5

Suppose the output of a firm is given by Y = KL where K denotes the number of units of capital, L denotes the number of units of labour, and Y denotes the number of units of output
What is the second derivative of Y with respect to K? How would you interpret this?
Answer

Second derivative of Y with respect to K is KL.
This means that the marginal product of output with respect to capital increases as capital increases.

Second derivative of Y with respect to K is K.
This means that the marginal product of output with respect to capital increases as capital increases.

Second derivative of Y with respect to K is L.
This means that the marginal product of output with respect to capital increases as capital increases.

Second derivative of Y with respect to K is 0.
This means that the marginal product of output with respect to capital does not vary as capital increases.

None of these

Based on my previous answer, I have to go with none, but doubting I understand this part either...

---

Sorry, some of those numbers are to the power of, but couldn't type properly.

ANY help would be massively appreciated in explaining some or all of these...

andrew

[Jackass] wrote: »

No I understand the concept, just not the maths part. Struggling again with more revision questions.

Ugggh, I'm so screwed in this subject and desperate, just fallen so far behind. Maybe someone would be kind enough to run through some of these questions and give explenations?? I would really really appreciate it and am freaking out over not being able to understand these.

Question 1

Find the second cross-partial derivative for the following function:
y = xz-2

Answer

-2z-3

z-2

2xz-2

None of these

-2xz-1

I think the answer to this one is the first differentiation is the second option based on x being dropped after the first differentiation with no power (sorry, not really able to type my calculations)

Question 2

Suppose the utility of consuming goods x and y is given by U = x0.25y0.25
What is the marginal utility of consuming x?
Answer

x-0.75y0.25

0.25x-0.75

None of these

xy

0.25x-0.75y0.25

I think the last one is the answer, but couldn't get exact answer for any of these

Question 3

Suppose the utility of consuming goods x and y is given by U = x1/4y1/4
How does the marginal utility of x change as x increases?
Answer


The marginal utility of x is the same at all levels of x

None of these


The marginal utility of x gets smaller at higher levels of x


The marginal utility of x gets larger at higher levels of x

I have no idea about this one

Question 4

Suppose the output of a firm is given by Y = KL where K denotes the number of units of capital, L denotes the number of units of labour, and Y denotes the number of units of output
What is the first derivative of Y with respect to K?


Answer

0

None of the above

L

K

KL

I think the answer is 1 (i.e. none of these) as none of the units are to a power of anything

Question 5

Suppose the output of a firm is given by Y = KL where K denotes the number of units of capital, L denotes the number of units of labour, and Y denotes the number of units of output
What is the second derivative of Y with respect to K? How would you interpret this?
Answer

Second derivative of Y with respect to K is KL.
This means that the marginal product of output with respect to capital increases as capital increases.

Second derivative of Y with respect to K is K.
This means that the marginal product of output with respect to capital increases as capital increases.

Second derivative of Y with respect to K is L.
This means that the marginal product of output with respect to capital increases as capital increases.

Second derivative of Y with respect to K is 0.
This means that the marginal product of output with respect to capital does not vary as capital increases.

None of these

Based on my previous answer, I have to go with none, but doubting I understand this part either...

---

Sorry, some of those numbers are to the power of, but couldn't type properly.

ANY help would be massively appreciated in explaining some or all of these...

Note: when you want to denote an X to the power of something, type x^<number>. So x-squared is X^2

Question 1

In this question, you're differentiating with respect to X right? So just differentiate the X. What happens to a solitary X when you differentiate it? It turns into a 1. So yeah, the answer is z-2

Question 2

So the Utility function is X^0.25Y^0.25

Again, just differentiate with respect to X, Ignoring the Y. If you can differentiate X^0.25 on it's own, then you should be able to see why 0.25X^-0.75 Y^0.25 is indeed the correct answer

Question 3

So the utility function is U= X^0.25Y^0.25

Do you understand what the idea of marginal utility is? You can go to www.wolframalpha.com to get a better idea of this. Lets look at just X; since that's what the question cares about. Go to wolframalpha and type in:

plot X^0.25 from x=1 to x=10

See the shape of the graph, how it's concave? As X increases, the graph gets flatter. This is a visual representation of diminishing marginal utility.

For the lol, you could also type in:

plot X^1 from x=1 to x=10

note how the graph is a straight line. Then if you type in:

plot X^1.25 from x=1 to x=10 [maybe try X^2, so to see the curve better. The important thing is that X>1]

you'll get an upward curving line. So if the power is less than one, the graph is falling, if it's 1 the graph is constant, and if it's greater than 1 the graph is increasing. When it's straight you've got constant marginal utility, and when it's convex you've got increasing marginal utility

Question 4

Remember, Y = KL is the same as Y = K^1 L^1

Question 5

Again, see the answer to Question 4, and see how you get on. Since the power is 1 in this case, remember also the graph which I mentioned in question 3, in which the power is 1 and the slope is constant.




Hope this helps, if you've any more questions ask. Good luck.