1 answer part a-d for the following formulas i

Question

1) Answer part a-d for the following formulas.

 i) y=e^1/x

ii) ln(y)=sin(x)  (calculate in Radians, not degrees, for d and f)

a) Calculate dy/dx

b) Calculate d²y/dx²  (simplify ii)

c) Calculate elasticity (simplify i and ii)

d) Calculate elasticity at x = 5, 10.  Are these points elastic or inelastic?

e) Calculate growth (simplify i and ii)

f) Calculate growth at x = 2, 4

2) You are putting together a costume for Halloween, and you wonder if you should spend more or fewer hours (H) than you usually do.  Costume awesomeness (C) is expressed as :

 C = H³ - 6H² - 63H

a) Maximize awesomeness. Show all steps.

b) Graph this equation, showing all steps.

3) Assume that your % midterm mark depends on hours spent studying (H) as expressed by:

Mark = -15 +10H

a) What functional form is this?

b) What are issues in this choice of functional form?

c) What would be an alternate functional form that avoids these issues?

d) If an error term were added to this formula, explain what 3 roles it would take.  Include examples.

4) Indicate whether the following statements are true, false or uncertain.  Justify your responses.

a) If consumers are sensitive to price changes, they are on the elastic portion of the demand curve.

b) Constant growth is graphed using a nonlinear function.

c) If a reciprocal model has increases that are too drastic, you can always use a log-log model to show smooth, gradual increases.

d) If you are modeling the effect of caffeine on studying, the error term would include intelligence.

5) From the following equations, calculate the direct, indirect, and total effects of a change in research and development (R) on quantity demanded (Q).  (Note: D = durability)

Q^D = R² + 2RD + D/4

D = 2√R

6) The great philosopher Rogers once said that you need holding knowledge (H), folding knowledge (F), and economics knowledge (E).  Therefore, overall knowledge (K) can be expressed as: 

K=  3HF + 2E³ + 17

a) Interpret this equation. (Ignore derivatives that are zero and ignore elasticity.)

b) Use this equation to show and explain Young's Theorem.