Assume that GDP (Y ) is 5,000 in a closed economy. Consumption (C) is given by the equation C = 1,200+0.3(Y −T)−50r, where r is the real interest rate, in percent. Investment (I) is given by the equation I = 1, 500 − 50r. Taxes (T ) are 1,000, and government spending (G) is 1,500.

(a) What are the equilibrium values of C, I, and r?

(b) What are the values of private saving, public saving, and national saving? (

(c) For the given consumption function, what does the relationship between consumption and the interest rate imply about the saving schedule?

A mass of m = 1 Kg of an ideal gas (gas constant R= 278 J/KgK) undergoes two polytropic processes. During the first process temperature increases from 27 ⁰C to 237 ⁰C and volume decreases from 1 m³ to 0.3 m³. During the second process temperature increases to 473 0C and volume is constant. The isentropic exponent of the gas is 1.4. Determine (a) Polytropic exponents (b) missing properties of the gas (c) heat and work of the first process and (d) draw the processes in p-V diagram

You will need to read through the lab procedure and background information to solve this question. Need help? See a TA or your instructor in office hours. CaCrO4 is a slightly soluble solid. In the lab, you find that addition of 357.73 µL of 1 M H2CrO4 to 7.924 mL of 0.3 M Ca(NO3)2 results in formation of a persistent precipitate. Addition of water (1.878 mL) just dissolves the precipitate. What is the experimental value of Ksp for CaCrO4 according to the information above? Provide your response to 4 digits after the decimal.

Glass Science -- Stress Relaxation : please show calculation in detail or with explanation:

1] a) Show, by calculation, how much time is required to relax 90% of the stress in a glass at the annealing point; the initial stress is 300 MPa, the temperature is 535C, the elastic modulus is 55 MPa, the shear modulus is 10 GPa and Poisson’s ratio is 0.3

b) What about at the strain point ?

c) What about at the softening point where tempering is often initiated ?

*You should understand how these kinetics play a role in annealing, tempering and glass/metal/ceramic sealing.

A stock's returns have the following distribution:

Assume the risk-free rate is 4%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places.

Stock's expected return:   %

Standard deviation:   %

Coefficient of variation:

Sharpe ratio:

The performance and fees of 4 share classes of the same fund are in following table:

                                      Class Inst                Class Inv               Class A                  Class B

Expense ratio                     1%                          1%                        1%                       1%

12b-1 fee                                                            0.3%                     0.1%

Front-end load                                                                                 4%

Back-end load                                                                                                           start at 6%

                                                                                                                                    and ↓ 1%/year

All share classes have the same annual rate of return of 10.0%. If you have $10,000 to invest

in each of these share classes, how much will you get if you plan to sell them after 2 and 8

years?

Q: In MATLAB, make time-domain graphs of a Conventional DSB AM signal u(t) = A_c[1 + am(t)]cos(2×π×f_c×t), with A_c = 1, m(t) = cos(2×π×f_m×t), f_c = 1 kHz, f_m = 50 Hz, for four cases of AM modulations: a = 0, a = 0.3, a = 1, a = 1.3. Your graphs should be over four periods of the message (i.e., 0 < t < 4/fm). Include your code in your solution as well as the four graphs.

Assuming that the tax rate is 30%, Working Capital and Fixed Capital investments are Zero, Calculating FCFF from Net Income shows the following:

FCFF = Net Income + Interest Expense (1-T) + Depreciation Expense

FCFF = 107.28 + 17.25 (1-0.3) + 49.50

FCFF = $ 168.85

Required: Why do you add back the after-tax interest but the before-tax depreciation in the calculation of FCFF?