Show that in a parabolic potential well, the spacing between the energy levels is constant. In semiconductors, parabolic potential wells are often produced by using narrow square potential wells where the well to barrier width ratio gradually changes. Use the virtual crystal approximation to design a GaAs/AlAs parabolicwell where the level spacing for the electron is approximately 8meV. (Hint: This isthe harmonic oscillatorproblem.)

1. A firm’s annual revenues are $635,00 Its expenses for the year are $428,000, and it claims $129,000 in depreciation expenses. Due to recent (2018) tax law changes, use a flat 21% corporate tax rate to calculate taxes.
   1. Calculate Taxes owed
   2. Calculate after-tax income (aka AFIT Net Income)?
   3. Calculate after-tax cash flow. (AFIT Cash Flow)

Consider the Solow model economic production function,

Y = A * K^a * L^(1-a)

Assume the following initial conditions:

A = 1.2

a = 0.27

K = 16

L = 112

Additionally, you know that depreciation rate is 11 % and the savings rate is 12 %. Assuming no changes in any of the parameters, besides the change in K over time,

what is the long-run equilibrium level of output?

2. Answer the following questions regarding bond valuation.
   1. What is the price of a $1,000 par value bond with a 6% coupon rate paid semiannually, if the bond is priced to yield 4% and it has five years to maturity?
   2. Following a, what would be the price of the bond if the coupon is paid quarterly?
   3. Explain how the calculation changes, given semi-annual coupons in (a) versus quarterly coupons in (b).

Suppose you have a perfectly competitive industry and firms have positive profits. Explain the forces of change that will move the situation toward equilibrium (just as in the assignment on this chapter)

include what happens in the market diagram and then say how that changes the picture of the firm's diagram (what is the relationship between the firm's Demand and ATC after the adjustment?) be clear about how that picture looks

1(i). Derive the solution to mass balance equations for the nth-order reactions occuring in a CSTR and in a PFR at steady state.

(II) A first-order reaction A--- products (the long dash represents an arrow) is to be carried out in a CSTR. The reaction rate constant was determined to be 1.0/h. What is the residence time required for 90% conversion of the reactant provided there are no changes in temperature and density of the system?

Consider a project with a life of 3 years with the following information: initial fixed asset investment = $350,000; straight-line depreciation to zero over the 3-year life; zero salvage value; price = $34; variable costs = $12; fixed costs = $133,000; quantity sold = 59,850 units; tax rate = 22 percent. How sensitive is OCF to changes in quantity sold?

Use short-run supply demand analysis to indicate how equilibrium price and quantity will change if the following changes occur in the economy. Draw a supply and demand curve for each answer and provide a brief one sentence explanation.

c) Immigration policy leads to a sharp reduction in the in-migration of Mexican workers. What happens to the market for low-wage labor in Los Angeles?

For a number of years, pundits have predicted that the Social Security retirement system will fail at some future date. Explain why the current system is considered to be in trouble, noting the demographic and societal changes that have contributed to this situation. Outline a couple of modifications to the system that may stabilize it for the long run, so that current and future workers can confidently expect to receive benefits when they retire.