Consider the following utility function U(X,Y) = X^1/4Y^3/4

Initially
PX = 2

PY = 4

I = 120
Suppose the price of X changes to PX = 3. Perform a decomposition and fill in the table

Problem 13-4 Various liabilities [LO13-1, 13-2, 13-3, 13-4] The unadjusted trial balance of the Manufacturing Equitable at December 31, 2018, the end of its fiscal year, included the following account balances. Manufacturing’s 2018 financial statements were issued on April 1, 2019.

Accounts receivable $ 90,000

Accounts payable 46,600

Bank notes payable 654,000

Mortgage note payable 1,253,000

Other information:

The bank notes, issued August 1, 2018, are due on July 31, 2019, and pay interest at a rate of 15%, payable at maturity. The mortgage note is due on March 1, 2019. Interest at 14% has been paid up to December 31 (assume 14% is a realistic rate). Manufacturing intended at December 31, 2018, to refinance the note on its due date with a new 10-year mortgage note. In fact, on March 1, Manufacturing paid $252,000 in cash on the principal balance and refinanced the remaining $1,001,000. Included in the accounts receivable balance at December 31, 2018, were two subsidiary accounts that had been overpaid and had credit balances totaling $15,350. The accounts were of two major customers who were expected to order more merchandise from Manufacturing and apply the overpayments to those future purchases. On November 1, 2018, Manufacturing rented a portion of its factory to a tenant for $31,800 per year, payable in advance. The payment for the 12 months ended October 31, 2019, was received as required and was credited to rent revenue.

Required: 1. Prepare any necessary adjusting journal entries at December 31, 2018, pertaining to each item of other information (a–d). 2. Prepare the current and long-term liability sections of the December 31, 2018, balance sheet.

Exercise 2: Using the Relativistic Energy Momentum relationship ?² = ?²?² + ?²?⁴ and the de-Broglie relationships ? = ℏ? and ? = ℏ? with ? the angular frequency and ? the wave number, find the group ?_? and the phase velocity ?_?ℎ of the de-Broglie waves and show that their product is equal to ?².

Ehrenberg and Smith Chapter 2 Problems 2 and 4

2. Suppose that the supply curve for schoolteachers is L_S = 20,000 + 350W, and the demand curve for schoolteachers is L_D = 100,000 - 150W, where L = the number of teachers and W = the daily wage.

a. Plot the supply and demand curves.

b. What are the equilibrium wage and employment levels in this market?

c. Now suppose that at any given wage, 20,000 more workers are willing to work as schoolteachers. Plot the new supply curve, and find the new wage and employment level. Why doesn't employment grow by 20,000?

4. Suppose the adult population of a city is 9,823,000 and there are 3,340,000 people who are not in the labor force and 6,094,000 who are employed.

a. Calculate the number of adults who are in the labor force and the number of adults who are unemployed.

b. Calculate the labor force participation rate and the unemployment rate.

Suppose that ? is the intersection of the plane ?+?+3?=4 and the surface ?^2−?^2=?^2−8 . Note that this intersection contains the point (3,4,−1) . Verify the assumptions of the implicit function theorem at this point; then if ?(?)=(?,?) φ ( x ) = ( y , z ) be the function from ℝ→ℝ2 R → R 2 verifying the conclusion of the implicit function theorem, compute ??(3) J φ ( 3 ) using the theorem. Verify your conclusion by explicitly solving for (?,?) ( y , z ) in terms of ? x and differentiating.

Required information

[The following information applies to the questions displayed below.]

Tony and Suzie see the need for a rugged all-terrain vehicle to transport participants and supplies. They decide to purchase a used Suburban on July 1, 2022, for $15,400. They expect to use the Suburban for five years and then sell the vehicle for $6,200. The following expenditures related to the vehicle were also made on July 1, 2022:

• The company pays $2,650 to GEICO for a one-year insurance policy.
• The company spends an extra $6,400 to repaint the vehicle, placing the Great Adventures logo on the front hood, back, and both sides.
• An additional $2,850 is spent on a deluxe roof rack and a trailer hitch.

The painting, roof rack, and hitch are all expected to increase the future benefits of the vehicle for Great Adventures. In addition, on October 22, 2022, the company pays $2,100 for basic vehicle maintenance related to changing the oil, replacing the windshield wipers, rotating the tires, and inserting a new air filter.

Required:

1. Record the expenditures related to the vehicle on July 1, 2022. Note: The capitalized cost of the vehicle is recorded in the Equipment account. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field.)

2. Prepare a depreciation schedule using the straight-line method.

3. Record the depreciation expense and the expiration of prepaid insurance related to the vehicle on December 31, 2022

Consider the matrix A = [2, -1, 1, 2; 0, 2, 1, 1; 0, 0, 2, 2; 0, 0, 0, 1]. Find P, so that P^(-1) A P is in Jordan normal form.

At December 31, 2020, RB Company has outstanding three long-term debt issues. The first is a $2,120,000 note payable which matures June 30, 2023. The second is a $6,840,000 bond issue which matures September 30, 2024. The third is a $12,580,000 sinking fund debenture with annual sinking fund payments of $2,516,000 in each of the years 2022 through 2026.

Prepare the required note disclosure for the long-term debt at December 31, 2020.

Discuss 2 of the 4 elements of an Insurable Risk (peril). Choose one of the 4 elements, and describe how, if it is missing, an manager might deal with that risk (peril).

David Palmer identified the following bonds for investment: 1) Bond A: A $1 million par, 10% annual coupon bond, which will mature on July 1, 2025. 2) Bond B: A $1 million par, 14% semi-annual coupon bond (interest will be paid on January 1 and July 1 each year), which will mature on July 1, 2031. 3) Bond C: A $1 million par, 10% quarterly coupon bond (interest will be paid on January 1, April 1, July 1, and October 1 each year), which will mature on July 1, 2026. The three bonds were issued on July 1, 2011. (Each Part is Independent)

(a) If Bond B is issued at face value and both Bond B and Bond A are having the same yield to maturity (EAR), calculate the market price of Bond A on July 1, 2011. [Note: Full mark would only be given to correct answer of which the values of those variables not provided in the question directly are derived.]

(b) David purchased the Bond C on January 1, 2014 when Bond C was priced to have a yield to maturity (EAR) of 10.3812891%. David subsequently sold Bond C on January 1, 2016 when it was priced to have a yield to maturity (EAR) of 12.550881%. Assume all interests received were reinvested to earn a rate of return of 3% per quarter (from another investment account), calculate the current yield, capital gain yield and the 2-year total rate of return (HPY) on investment for David on January 1, 2016. [Hint: Be careful with how many rounds of coupons has David received during the holding period and thus how much interests (coupons and reinvestment of coupons) he has earned in total during the 2-year holding period.]

(c) David purchased Bond B on a coupon payment day. Bond B is priced to have a yield to maturity (EAR) of 12.36% and its market value is $1,101,058.953 on the date of purchase. Find the remaining life until maturity (in terms of 6-month period or year) of Bond B.