** (a) (i) What is Managerial Economics?

(ii) What is the scope of Managerial Economics?

(iii) As a CEO of a company, of what relevance is Managerial Economics to you?

(b) Define and give an example of each of the following demand terms and concepts and illustrate diagrammatically a change in each.

(i) Demand

(ii) Normal good

(iii) Inferior good

(iv) Substitute good

(v) Complementary good

(c) The market demand for brand X has been estimated as Qx= 1,500 – 3Px – 0.05I- 2.5Py + 7.5Pz, where Px is the price of the brand X, I is per-capita income, Py is the price of brand Y, and Pz is the price of brand Z. Assume that Px = $2, I = $20,000, Py = $4, and Pz =$4

(i) With respect to changes in per-capita income, what kind of good is brand X?

(ii) How are brands X and Y related?

(iii) How are brands X and Z related?

(iv) How are brands Z and Y related?

(v) What is the market demand for brand X?

Which of the following systems demonstrates the least deformation? i. A 10 mm diameter, 1 m long copper cable made of copper raising a wet statue ii. A 5 mm diameter, 1 m long steel cable raising a wet statue iii. A 10 mm diameter, 1 m long steel cable raising a dry statue iv. A 10 mm diameter, 1.5 m long steel cable raising a wet statue v. A 10 mm diameter, 1 m long steel cable raising a wet statue

why?   



c. Rank the following according to the amount of heat absorbed to heat from 20 – 100°C? Rank i. A 169 kg wet statue why?   


ii. A 230 kg wet statue why?   


iii. A 230 kg dry statue why?   


iv. A 230 kg dry, foil-covered statue why?   


v. A 230 kg limestone statue why?

Quantitative Behavior of RC Circuit

Task: You will be filling in the data table below with 10 rows of data that will track the time elapsed (the ‘Charging Time’), the voltage across the resistor, the voltage across the capacitor, the charge of the capacitor, and the current in the circuit.

Example table:

I only need clarification on these few questions:

1. “Make a graph of your voltage on the resistor as a function of current (in A).”
   Does this mean I have to change the current from mA to A, and put it in a graph with time (s) on the y axis and current on the x axis? Also, we were told to fit a trendline to the graph. What would the value of the slope of the trendline correspond to in the circuit?
2. “Make a graph of your charge stored on your capacitor (in C) as a function of voltage across the capacitor. Fit a trendline to your data.”
   And what would the value of the slope of this trendline correspond to?
   Thank you in advance!

One method for reducing the pumping work in throttled spark-ignition engines is early intake valve closing (EIVC). With EIVC, the inlet manifold is held at a pressure pi, which is higher than the normal engine intake pressure pi*. The intake valve closes during the intake stroke. The trapped fresh charge and residual is then expanded to the normal cycle (lower) intake pressure, pi*. You can assume that both cycles have the same mass of gas in the cylinder, temperature and pressure at state 1 of the cycle.

a) Sketch a p-V diagram including both the standard and EIVC cycle. On the p-V diagram, shade the area that corresponds to the difference of pumping work between the standard and EIVC cycles.

b) What value of intake pressure pi and VEIVC will give the maximum reduction in pumping work for the EIVC cycle?

c) Derive an expression for this maximum difference in pumping work between the normal cycle and the EIVC cycle in terms of pe, pi*, Vc and Vm. Justify any assumptions you make.

One method for reducing the pumping work in throttled spark-ignition engines is early intake valve closing (EIVC). With EIVC, the inlet manifold is held at a pressure pi, which is higher than the normal engine intake pressure pi*. The intake valve closes during the intake stroke. The trapped fresh charge and residual is then expanded to the normal cycle (lower) intake pressure, pi*. You can assume that both cycles have the same mass of gas in the cylinder, temperature and pressure at state 1 of the cycle.

a) Sketch a p-V diagram including both the standard and EIVC cycle. On the p-V diagram, shade the area that corresponds to the difference of pumping work between the standard and EIVC cycles.

b) What value of intake pressure pi and VEIVC will give the maximum reduction in pumping work for the EIVC cycle?

c) Derive an expression for this maximum difference in pumping work between the normal cycle and the EIVC cycle in terms of pe, pi*, Vc and Vm. Justify any assumptions you make.

Consider the Hamiltonian of a particle in one-dimensional problem defined by: H = 1 2m P 2 + V (X) where X and P are the position and linear momentum operators, and they satisfy the commutation relation: [X, P] = i¯h The eigenvectors of H are denoted by |φn >; where n is a discrete index H|φn >= En|φn > (a) Show that < φn|P|φm >= α < φn|X|φm > and find α. Hint: Consider the commutator [X, H] (b) Using the result from the previous part, and with the aid of the closure relation show that: X m (En − Em) 2 | < φn|X|φm > | 2 = ¯h 2 m2 < φn|P 2 |φn > (c) For an arbitrary operator A, prove the relation: < φn|[A, H]|φn >= 0 (d) In terms of P, X and V(X), find the commutators: [H, P], [H, X], [H, XP] (e) Show that < φn|P|φn >= 0 (f) Establish a relation between the mean value of the kinetic ene

The following data relates to Sephakor Ltd for the month of April 2020.
Names of Employees Rates per hour (GHS) units of job Bonus (GHS)
Adusei Poku 30 30 760
Kwame Bekoe 25 40 430
Samuel Ato 40 45 440
Serwaa Akoto 45 35 550
James Obli 30 25 450
Additional information:
NB - It takes 4hours to complete a unit job
i) Income tax is 10%
ii) Rent allowance is 15% of basic wages
iii) Risk allowance is at 5% of basic
iv) The SSF contribution is 15%.
(vi)Provident fund contribution is 13% of basic
v) SSF & Provident fund are non-taxable deductions

You are required to prepare payroll for the month showing;
i. Basic wages
ii. Gross wages
iii. Total deductions
iv. Net wages
v. State the reasons why SSF & Provident Fund are non-taxable (2marks)
(Total 16marks)

Two field generals, 1 and 2, are positioned to attack an enemy stronghold in the valley below. The two armies are separated by a treacherous canyon and communication between the two commanders is impossible. The generals know that if they coordinate their attack, both moving their troops into the valley at dawn, they will defeat the enemy, earning a value v > 0. If one of the two sides attacks alone, the other will not be able to re-enforce the attacker’s troops in time to prevent a defeat at the enemy’s hands, losing v. A stalemate where no general attacks is worth 0. Suppose all these elements of the strategic problem are common knowledge.

1. (5 pts) Solve for the (pure and mixed strategy) Nash equilibria.

2. (5 pts) Consider a modified version of this game. Suppose that General 1 must first decide whether or not to attack, and then General 2 decides whether or not to attack based upon General 1’s decision. Solve for the (pure) Nash equilibria and the Subgame Perfect Nash Equilibria (solve through backward induction).

4. Solve this mixing study case study using this reference information given below. Identify the missing coag factor(s).
AGED SERUM(AS): Rich in Factors VII, IX, X, XI, XII. Deficient in II, V, VIII.
ABSORBED PLASMA(AP): Rich in factors V, VIII, XI,XII. Deficient in II, VII, IX, X (vitamin K dependent factors)
(Both AS & AP have XI, XII, neither has II.)
Reference ranges: PT 11.0 -14.0 seconds   PTT 25.0 – 36.0 seconds (Note: You will need to know the reference ranges for the Lab final exam!)
Case study patient: PT = 20 seconds       PTT = 80 seconds

Mixing studies with aged serum and adsorbed plasma:

Aged serum mixed with patient plasma 1:1                                          PT = 14.0 seconds      PTT = 33 sec

Mixing studies with Absorbed plasma with patient plasma 1:1        PT = 20.0 seconds      PTT = 84 sec

Which factor is missing?

An individual faces the following to investment options:
Investment A: buy a stock fund that every year either earns 50% with a probability of 60% or loses -25% with a probability of 40%.
Investment B: buy a bond that returns 5% with a probability of 50% or 0% with a probability of 50%.
Assume that the returns of the two funds are independent and that returns from year to year are also independent. Also, assume an initial investment of £1.
The value function of the individual is specified as:
V(z)=z for z>0
V(z)= 3.5z for z<0
4.1) Which investment option would the investor choose if he looks at the investment once per year?

4.2) Which investment option would the investor choose if he looks at the investment once every two years?

4.3) Discuss the term “Myopic loss aversion”

4.4) Explain the equity premium puzzle. Why is it deemed to be a puzzle?

4.5) How can myopic loss aversion explain the equity premium puzzle?