Question 1

The table below shows the cost and revenue information of a firm.

(a) Complete the table above.

(b) Determine the price and output at equilibrium.

[6 marks]

(c) Calculate the profit or loss at equilibrium.

[4 marks]

(d) Is this firm in the short-run or long-run? Explain your answer.

[5 marks]

(e) To what type of market structure does this firm belong? Why do you say so?

[6 marks]

​(Present

value of an uneven stream of

payments​)

You are given three investment alternatives to analyze. The cash flows from these three investments are as​ follows:

What is the present value of each of these three investments if the appropriate discount rate is

99

​percent?

a.  What is the present value of investment A at an annual discount rate of

99

​percent?

Cola is considering the purchase of a​ special-purpose bottling machine for$28,000.It is expected to have a useful life of 4 years with no terminal disposal value. The plant manager estimates the following savings in cash operating​ costs:

Calculate the following for the special purpose bottling​ machine:

Snow Geese lay 4 eggs in a nest. A field biologist wanted to know if there is a relationship between the order in which the eggs are laid and the sex of each egg. Please see the table below.

Is there a relationship between sex and laying order in snow geese?

1. What are the null and alternate hypotheses for the chi-square goodness of fit test?

2. What are the expected counts under the null hypothesis?

3. Use Minitab to determine a chi-square test statistic and P value

4. Do you accept or reject the null?

Mr. Brown the CEO of a corporate company wants to know if a new method of rewarding employees influences morale. He gives 12 employees an anonymous survey measuring morale, implements the new method, and then measures morale again after four weeks.

a. State the null and alternative hypotheses

b. State the rejection region

c. Conduct a sign test on the above data

d. What can you conclude?

THE CODE IN THIS QUESTION IS STORED IN THE MEMORY FROM ADDRESS 0X1FFF000. SO TAKE THIS INTO CONSIDERATION.

1.     In the following MIPS assembly code, translate all the instructions to their corresponding machine code in hexadecimal format. This code is stored in the memory from address 0x1fff0000.
Loop: sw $t1, 4($s0)
       addi $t1, $t1, -1
   sll $t1, $t1, 2
       bne $t1, $s5, Exit
   addi $s0, $s0, 4
         j Loop
Exit: …

********************************THE FOLLOWING QUESTION NEEDS TO BE CONVERTED TO MIPS ASSEMBLY LANGUAGE, WHERE i is stored in $s0 and the array is stored in $s1. ***********************************

2. Compile the following C code into MIPS:

i=0;  

        while (i<=100) do

            A[4*i]=0;  

        where integer i is in register $s0 and the base memory address of array A is in$s1.

Consider Cournot model of quantity competition between two firms, firm 1 and firm 2. Suppose the inverse demand for the firms product is given by ?=40(?+2)−(?+1)(?1+?2)p=40(A+2)−(B+1)(q1+q2), where ??qi denotes the quantity of firm ?i, ?=1,2i=1,2, ?A is 6 and ?B is 9. Each firm's average cost is equal to ?+2c+2, where ?c is 4.
a) Derive and accurately plot each firm's best response function.
b) Find the (Nash) equilibrium quantities, price, profits and consumer surplus.
c) Suppose next that each firm has a fixed cost equal to ?=20(?+1)f=20(A+1) where A is 6. Would the allocation you found in part (b) be an equilibrium? Explain.

6. Consider the initial value problem dy/ dt = t ^2 y , y(1) = 1 .

(a) Use Euler’s method (by hand) to approximate the solution y(t) at t = 2 using ∆t = 1, ∆t = 1/2 and ∆t = 1/4 (use a calculator to approximate the answer for the smallest ∆t). Report your results in a table listing ∆t in one column, and the corresponding approximation of y(2) in the other.

(b) The direction field of dy/dt = t ^2y is shown at right. In this figure, add a sketch of ◦ the exact solution y(t) to the given initial value problem, for t ∈ [1, 2] ◦ the numerical approximation using Euler’s method that you found above (indicate the solution obtained at each step, and a line showing how it is obtained)

Below market interest note

On January 1, Investor purchased a 9 year, $400,000; 4% note from Borrower. The yield

(market interest rate) at the time of issuance was 9%, compounded annually.

For Investor:

1. Record the journal necessary on January 1

2. Record the journal entry necessary on December 31.

(Assuming no additional entries were made since January 1)

3.Record the journal necessary on the following January 1.

For Borrower:

4. Record the journal necessary on January 1.

5. Record the journal necessary on December 31.

6. Record the journal necessary on the following January 1.

1. What is G if B = A × (1+G)^T and B = 4,916, A = 2,111, and T = 11? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

2.What is A if P = [A/(1+R)^L] + [B/(1+R)^M] and P = 6,087, B = 1,499, R = 0.138, L = 4, and M = 9?  Round answer to nearest whole number.

3.What is A if P = [A × (1+R)^L] + [B × (1+R)^M] and P = 8,004, B = 1,591, R = 0.137, L = 4, and M = 10? Round answer to nearest whole number.