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Timed Statistics Quiz – 1.5 Hours

Hi, I’m looking for a tutor to take a timed statistics exam. The topics are attached below.It would be like 12-14 multiple choice and 5-7 short responseThe multiple choice questions are based on content like knowing definitions and concepts and applying them in situations. For the short response portion it would require written work to be shown.The exam can be taken any time between 11/18-11/19 and is 1.5 hours long with a 15 minute grace period to submit work separately. I would send the questions and would submit answers as they come in. At the end of the exam please send all work at once to be submitted during the grace period.Topics -Analysis of variance (anova)One way independent groups AnovaTwo tailed AnovaMultiple ComparisonsLinear contrasts

Make-Up Problem Set

November 11, 2020

Due Date: November 24

- Leverage: For the following question, assume the that bank’s balance

sheet has only 3 categories: assets, liabilities, and capital.

Suppose a bank has $5,000,000 in capital, and that it’s leverage ratio is

20.

(a) Draw the bank’s balance sheet. How much assets and liabilities does

this bank have?

(b) What is the bank’s capital ratio?

(c) Suppose that after one week, the bank’s assets depreciate by 3.5%.

How much capital does the bank have left, and is it solvent? If the

bank is insolvent, by how much is it insolvent?

(d) Suppose instead that after one week, the banks assets depreciate by

6%. How much capital does the bank have left, and is it solvent? If

the bank is insolvent, by how much is it insolvent?

(e) Describe the relationship between leverage, expected prots, and –

nancial fragility. You may nd it helpful to answer this question by

using examples of balance sheets with dierent leverage ratios, al-

though this is not required for a complete answer. (1-2 sentences is

ne).

1 - Okun’s Law: Assume Okun’s law is given by: ut ut 1 = 0:4(gy 0:03).

Suppose you are the head of the Council of Economic Advisors, and are at

a dinner with the President. The President asks you to roughly calculate

the following on the back of your napkin:

(a) The President remarks that due to unfavorable economic conditions,

growth this year will only be 1.5%.

i. By how much will the unemployment rate increase or decrease?

ii. Suppose instead that the President said that growth this year

would be 4%. By how much will the unemployment rate increase

or decrease?

(b) The President mentions that unemployment is too high, and needs

to be decreased by roughly 0.8 percentage points.

i. What level of growth would be needed to reduce the unemploy-

ment by this amount?

ii. Suppose that the best estimates place growth this year at 2%,

and the multiplier for scal policy at 1.5. How much scal stim-

ulus (as a percentage of GDP) would be required to bring unem-

ployment down to the desired level?

(c) What are the two reasons listed in your textbook that growth needs

to be equal to 3% to have no change in unemployment? - Deriving the Slope of the IS Curve with a Balanced Budget

Requirement:

1) Y = C(Y T)

+

- I(Y; i)

+ - G, with T = T(Y )

+

, 0 < TY < 1, and G

exogenous.

2) Y = C(Y T)

+ - I(Y; i)

+ - G , with T = T(Y )

+

, 0 < TY < 1, but now

G = T (i.e. there is a balanced budget requirement).

(a) For economy one, use the total derivative to derive an expression for

di

dY .

(b) For economy two, use the total derivative to derive an expression for

di

dY .

(c) Is the slope of the IS curve for economy one equal to, steeper than,

or atter than the slope for economy two? How do you know?

(d) What is the intuition for your result in part iii? (1-2 sentences is

ne).

- Suppose now that the production function is given by:

Y = 3K1=4N3=4

(a) Show that this production function characterized by constant returns

to scale.

2

(b) Show that there are decreasing returns to capital.

(c) Show that there are decreasing returns to labor.

(d) Transform the production function into the relation between output

per worker and capital per worker.

(e) For a given savings rate, s, and depreciation rate, , give an expres-

sion for capital per worker in the steady state.

(f) Give an expression for output per worker in the steady-state

(g) Solve for the steady state level of output per worker when s = :032

and = :08

(h) Suppose the depreciation rate remains constant at = :08 , while

the saving rate is reduced by half, to s = 0:16. What is the new

steady-state output per worker? - Derivation of the Phillips Curve

One version of the Phillips Curve is written:

e = m + z u

(a) Find the natural rate of unemployment, un

(b) Use the expression for un you derived above to rewrite the Phillips

Curve as:

e = (u un)

i.e., in terms of the deviation of unemployment from the natural rate

of unemployment.

(c) According to our production function, Y = L(1 u); so Yn = L(1

un).

Use these denitions to write u un in terms of Y Yn and L (i.e.

u un on the left hand-side, and all other variables on the right).

(d) Substitute the expression for u un you found in part c into the

expression for the Phillips Curve in part b, to rewrite the Phillips

Curve in terms of the output gap, Y Yn; as it is found in chapter

9: e =

L(Y Yn) - Begin with the graph of medium run equilibrium.

(a) What four conditions characterize medium run equilibrium? Write

these conditions in words and math. Describe the intuition for these

conditions

(b) Beginning in medium run equilibrium, use a graph to show the eects

of the following on 1) the output gap, 2) the deviation of ination

from expected:

i. An increase in the mark-up.

ii. An increase in z, the catch-all term for labor market conditions.

3

iii. An increase in the IS curve. A decrease in the IS curve.

iv. An increase in the LM curve. A decrease in the LM curve.

v. An increase in the natural rate of unemployment. A decrease in

the natural rate of unemployment.

vi. An increase in potential output. A decrease in potential output.

4

Lab Assignment 44

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