4. You are given the following cost functions:

TC= 100+ 60Q- 3Q² + 0.1Q³

TC= 100+ 60Q+ 3Q²

TC= 100+ 60Q

a. Compute the average variable cost, average cost, and marginal cost for each function. Plot them on a graph.

b. In each case, indicate the point at which diminishing returns occur. Also indicate the point of maximum cost efficiency (i.e., the point of minimum average cost).

c. For each function, discuss the relationship between marginal cost and average variable cost and between marginal cost and average cost. Also, discuss the relationship between average variable cost and average cost.

PLEASE EXPLAIN EVERY STEP WITH DETAIL

Year   Project A   Project B
0 –$200   –$200   
1 80   100   
2 80 100   
3 80 100   
4 80      

a)   If the opportunity cost of capital is 10%, which of these projects is worth pursuing? Explain.

b)   Suppose that you can choose only one of these projects. Which would you choose? The discount rate is still 10%. Justify your reasoning.

c)   Which project would you choose if the opportunity cost of capital were 16%?

d)   What are the internal rates of return on projects A and B?

e)   In light of your answers to Problems a) – d), is there any reason to believe that the project with the higher IRR is the better project?

In R-Syntax, create a vector of 100 employees ("Employee 1", "Employee 2", ... "Employee 100")

[Hint: use the `paste()` function and vector recycling to add a number to the word "Employee"] then create a vector of 100 random salaries for the year 2017

[Use the `runif()` function to pick random numbers between 40000 and 50000] and finally create a vector of 100 salary adjustments between -5000 and 10000 [use runif() to pick 100 random #'s in that range]

You mix 100 mL of 1.0 M HCl with 100 mL of 1.0 M NaOH, both initially at 25.0°C, into a coffee-cup calorimeter. The temperature of the reaction raises to 34.2°C. The heat capacity of the coffee-cup is 132 J/°C. What is the heat of the total reaction? What is it per mole of H2O (l) formed?

Input price and input efficiency variances

The budgeted and actual data for direct materials and labor are as follows:

Actual sales volume is 100 units. Budgeted sales volume is 80 units.

Compute the input price and input efficiency variances for DM and DL.
As a preliminary step, compute actual input quantity (total pounds or hours we actually used) and flexible budget input quantity (total pounds or hours we should have used for actual output):
    actual input quantity for DM = ___________pounds
    flexible budget input quantity for DM = ________ pounds
    actual input quantity for DL = __________ hours
    flexible budget input quantity for DL = __________ hours
Next, compute the variances. Enter favorable variances as a positive number and unfavorable variances as a negative number. Do NOT enter F or U.
    input price variance for DM = $ ___________
    input efficiency variance for DM = $ ____________
    input price variance for DL = $ __________
    input efficiency variance for DL = $ ____________

1) A market’s demand curve

a. is the horizontal summation of individuals’ demand curves.

b. represents a relationship between the total quantity demanded for a good and the good’s price.

c. will shift out when the market includes more consumers.

d. all of the above.

2) Given a demand function Qd=100–5P and a supply function Qs=5P, find the equilibrium quantity and price. Answers are in numbers.

a. Q=20; P=16

b. Q=30; P=14

c. Q=40; P=12

d. Q=50; P=10

3) Given a demand function P=20–0.2Qd and a supply function P=0.2Qs. At the equilibrium price, the consumer surplus is

a. 300

b. 250

c. 200

d. 150

4) The own-price elasticity of demand for good x is -1.5 and there is a 10% increase in the good’s price.

a. The demand for good x is elastic.

b. The total spending on good x decreases.

c. The demand for x decreases by 15%.

d. All of the above.

5) The income effect

a. reflects the change in an individual’s real income as a result of a change in the price of the good.

b. is a movement from one point to another point on the same indifference curve.

c. reinforces the substitution effect for an inferior good.

d. all of the above.

A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon payments coming once annually). The bond sells at par value.

a. What are the convexity and the duration of the bond? Use the formula for convexity in footnote 7. (Round your answers to 3 decimal places.)

b. Find the actual price of the bond assuming that its yield to maturity immediately increases from 7% to 8% (with maturity still 10 years). Assume a par value of 100. (Round your answer to 2 decimal places.)

c. What price would be predicted by the modified duration rule ΔPP=−D*Δy?ΔPP=−D*Δy? What is the percentage error of that rule? (Negative answers should be indicated by a minus sign. Round your answers to 2 decimal places.)  

d. What price would be predicted by the modified duration-with-convexity rule ΔPP=−D*Δy+12×Convexity×(Δy)2?ΔPP=−D*Δy⁢+12×Convexity×(Δy)2? What is the percentage error of that rule? (Negative answers should be indicated by a minus sign. Round your answers to 2 decimal places.)

Gilbert Moss and Angela Pasaic spent several summers during their college years working at archaeological sites in the Southwest. While at those digs, they learned how to make ceramic tiles from local artisans. After college they made use of their college experiences to start a tile manufacturing firm called Mossaic Tiles, Ltd. They opened their plant in New Mexico, where they would have convenient access to a special clay they intend to use to make a clay derivative for their tiles. Their manufacturing operation consists of a few relatively simple but precarious steps, including molding the tiles, baking, and glazing. Gilbert and Angela plan to produce two basic types of tile for use in home bathrooms, kitchens, sunrooms, and laundry rooms. The two types of tile are a larger, single-colored tile and a smaller, patterned tile. In the manufacturing process, the color or pattern is added before a tile is glazed. Either a single color is sprayed over the top of a baked set of tiles or a stenciled pattern is sprayed on the top of a baked set of tiles. The tiles are produced in batches of 100. The first step is to pour the clay derivative into specially constructed molds. It takes 18 minutes to mold a batch of 100 larger tiles and 15 minutes to build a mold for a batch of 100 smaller tiles. The company has 60 hours available each week for molding. After the tiles are molded, they are baked in a kiln: 0.27 hour for a batch of 100 larger tiles and 0.58 hour for a batch of 100 smaller tiles. The company has 105 hours available each week for baking. After baking, the tiles are either colored or patterned and glazed. This process takes 0.16 hour for a batch of 100 larger tiles and 0.20 hour for a batch of 100 smaller tiles. Forty hours are available each week for the glazing process. Each batch of 100 large tiles requires 32.8 pounds of the clay derivative to produce, whereas each batch of smaller tiles requires 20 pounds. The company has 6,000 pounds of the clay derivative available each week. Mossaic Tiles earns a profit of $190 for each batch of 100 of the larger tiles and $240 for each batch of 100 smaller patterned tiles. Angela and Gilbert want to know how many batches of each type of tile to produce each week to maximize profit. In addition, they have some questions about resource usage they would like answered.

k. The kiln for glazing had to be shut down for 3 hours, reducing the available kiln hours from 40 to 37. What effect will this have on the solution? l. What are the reduced costs for larger and smaller tiles? Explain.

I don’t know how to do part l

Shrieves Casting Company is considering adding a new line to its product mix, and the capital

budgeting analysis is being conducted by Sidney Johnson, a recent business school graduate.

The production line would be set up in unused space in Shrieves's main plant. The machinery's

invoice price would be approximately $200,000, another $10,000 in shipping charges would be

required, and it would cost an additional $30,000 to install the equipment. The machinery has

an economic life of 4 years and would be in Class 8 with a CCA rate of 20%. The machinery is

expected to have a salvage value of $25,000 after 4 years of use.

     The new line would generate incremental sales of 1,250 units per year for 4 years

at an incremental cost of $100 per unit in the first year, excluding depreciation. Each

unit can be sold for $200 in the first year. The sales price and cost are both expected

to increase by 3% per year due to inflation. Furthermore, to handle the new line, the

firm's net operating working capital would have to increase by an amount equal to 12%

of sales revenues. The firm's tax rate is 28%, and its overall weighted average cost of

capital is 10%.

A) 1. Construct annual incremental project operating cash flows.

2. Estimate the required net operating working capital for each year and the cash flow due to investments in net operating working capital.

3. Calculate the present value of the CCA tax shield.

B)1. What is the after-tax salvage cash flows?

2. What is the projects NPV? Should the project be undertaken?

C) 1. What is sensitivity analysis

2. Perform a sensitivity analysis on the unit sales, salvage volume, and cost of capital for the project. Assume that each of these variables can vary from its base-case, or expected, value by +/- 10% and +/- 20%. Include a sensitivity diagram, and discuss the results.

3. What is the primary weakness of sensitivity analysis? What is its primary usefulness?

D)Assume that Sidney Johnson is confident of her estimates of all the variables that affect the project’s cash flows except unit sales and sales price. If product acceptance is poor, unit sales will be only 900 units a year and the unit price will be only $160; a strong consumer response will produce sales of 1,600 units and a unit price of $240. Johnson believes that there is a 25% chance of poor acceptance, a 25% chance of excellent acceptance, and a 50% chance of average acceptance (the best case).

1.What is scenario analysis?

2.What is the worst-case NPV? The best case NPV?

3.Use the worse-, base-, and best case NPVs and probabilities of occurrence to find the projects expect NPV, standard deviation, and coefficient of variation.

E)1.   Assume that Shrieves’s average project has a coefficient of variation in the range of 0.7 to 0.9. Would the new line be classified as high risk, average risk, or low risk? What type of risk is being measured here?

2.   Shrieves typically adds or subtracts 3 percentage points to the overall cost of capital to adjust for risk. Should the new line be accepted?

3.   Are there any subjective risk factors that should be considered before the final decision is made?

Problem 2: Consider a representative consumer whose preferences over consumption and leisure are given by the following utility function: U˜(C, l) = U(C) + V (l) (2) where U(.) and V (.) are twice differentiable functions (that is, their first and second derivatives exist). Suppose that this consumer faces lump-sum taxes, T, and receives dividend income, Π, from the 100% ownership of shares of the representative firm.

A) Write down the consumer’s optimization problem and the first-order conditions determining optimal consumption and leisure. B) Carefully explain the effect of a sudden boom in the stock market, which increases dividend income, on the optimal choice of consumption and leisure? Use the ABCDEF of Cramer’s rule to answer this question. Clearly state any assumptions you make. C) Using a carefully labeled diagram, describe the effects of this positive stock market shock characterized in (b).