microecon,,,

It is intuitive to think that the presence of more agents in the economy "shrinks" its core, since there are more coalitions that can object a given allocation. You will understand in this question why this is indeed the case.

Fix a standard, two-person exchange economy E = ((u', w'), (u, w')). Define its replica as the four-person exchange economy

= {(u, w). (u,w), (u', w). (u.w')}.

where (u", w) = (u, w) and (u", w) = (u,w).

1. Argue that if (p.x, x) is a competitive equilibrium for E, then (p.x,x, x, x') with x = x and x = x, is an equilibrium for .

2. Argue that if both utility functions are strictly quasi-concave, and (p.x,xx, x') is a competitive equilibrium for E2, then, x = x and x = x.

3. Argue that if both utility functions are strictly quasi-concave, and (x, xxx) is in the core of E2, then, x'=x' and x = x

4. Argue that if both utility functions are monotone and strictly quasi-concave, and (p. x, x) is a competitive equilibrium for E, then (x,x x, x) is in the core of .

5. Suppose that

u'(x) = x(x)=x

Rearden Metal is considering the purchase of a new blast furnace costing a total of $5 million dollars. This furnace will qualify for accelerated depreciation: 20% can be expensed immediately, followed by 32%, 19.2%, 11.52 %, 11.52 % and 5.76% over the next five years. Rearden has substantial tax loss carry forwards and estimates that its marginal tax rate will be only 10% over the next five years. Since Rearden will get very little tax benefit from the depreciation expense, it considers leasing the furnace instead. Suppose that Rearden and the lessor face the same 8% borrowing rate, but the lessor has a 40% marginal tax rate. Assume that the furnace is worthless after five years, the lease term is five years, and a lease would qualify as a true tax lease. What is the minimum acceptable upfront lease payment for the lessor? [Hint you must compute the upfront lease payment for which the NPV of "Buy and Lease" is zero for the lessor], (10 points)

Wyatt Oil has 8 million shares outstanding and is about to issue 10 million new shares in an IPO. The IPO price has been set at $15 per share, and the underwriting spread is 6%. The IPO is a big success with investors, and the share price rises to $35 at the end of the first day of trading.

a) What is the amount of money raised by Wyatt Oil with the IPO? (5 points)

b) Compute the post-IPO market value of Wyatt Oil, that is, its market value at the end of the first day of trading after the IPO. (5 points)

c) Suppose now that the post-IPO market value of Wyatt Oil represents a fair valuation. of the firm. Based on this assumption, what would have been a fair valuation of each of its shares of stock before the IPO? (5 points)

In this question you must show detailed reasoning. The probability that Paul's train to work is late on any day is 0.15, independently of other days. (i) The number of days on which Paul's train to work is late during a 450-day period is denoted by the random variable Y. Find a value of a such that P(Y > a) = [3] In the expansion of (0.15 + 0.85)50, the terms involving 0.15 and 0.15+1 are denoted by T, and T respectively. r+1 (ii) Show that T r 17(r+1) = T 3(50-r)* r+1 [3] (iii) The number of days on which Paul's train to work is late during a 50-day period is modelled by the random variable X. (a) Find the values of r for which P(X=r) P(X=r+1). [4] (b) Hence find the most likely number of days on which the train will be late during a 50-day period. [2]

Question: Garden Sales, Incorporated, sells garden supplies. Management is planning its cash needs for the second quarter. The company usually has to borrow money during this quarter to support peak sales of lawn care equipment, which occur during May. The following information has been assembled to assist in preparing a cash budget for the quarter:

Budgeted monthly absorption costing income statements for April-July are:

April May June July Sales $ 660,000 $ 830,000 $ 540,000 $ 440,000 Cost of goods sold 462,000 581,000 378,000 308,000 Gross margin 198,000 249,000 162,000 132,000 Selling and administrative expenses: Selling expense 84,000 103,000 65,000 44,000 Administrative expense* 47,000 63,200 39,800 42,000 Total selling and administrative expenses 131,000 166,200 104,800 86,000 Net operating income $ 67,000 $ 82,800 $ 57,200 $ 46,000 *Includes $26,000 of depreciation each month.

Sales are 20% for cash and 80% on account. Sales on account are collected over a three-month period with 10% collected in the month of sale; 70% collected in the first month following the month of sale; and the remaining 20% collected in the second month following the month of sale. February's sales totaled $250,000, and March's sales totaled $265,000. Inventory purchases are paid for within 15 days. Therefore, 50% of a month's inventory purchases are paid for in the month of purchase. The remaining 50% is paid in the following month. Accounts payable at March 31 for inventory purchases during March total $120,400. Each month's ending inventory must equal 20% of the cost of the merchandise to be sold in the following month. The merchandise inventory at March 31 is $92,400. Dividends of $33,000 will be declared and paid in April. Land costing $41,000 will be purchased for cash in May. The cash balance at March 31 is $55,000; the company must maintain a cash balance of at least $40,000 at the end of each month. The company has an agreement with a local bank that allows the company to borrow in increments of $1,000 at the beginning of each month, up to a total loan balance of $200,000. The interest rate on these loans is 1% per month and for simplicity we will assume that interest is not compounded. The company would, as far as it is able, repay the loan plus accumulated interest at the end of the quarter.

Required: 1. Prepare a schedule of expected cash collections for April, May, and June, and for the quarter in total. 2. Prepare the following for merchandise inventory: a. A merchandise purchases budget for April, May, and June.

5. Kansas Company uses a standard cost accounting system. In 2020, the company produced 28,000 units. Each unit took several pounds of direct materials and 1.6 standard hours of direct labor at a standard hourly rate of $12.00. Normal capacity was 50,000 direct labor hours. During the year, 117,000 pounds of raw materials were purchased at $0.92 per pound. All materials purchased were used during the year. Instructions (Show all of your work.... No credit for just an answer) variance was $3,510 favorable, what was the standard materials a. If the materials price price per pound? b. If the materials quantity variance was $4,750 unfavorable, what was the standard materials quantity per unit? C. What were the standard hours allowed for the units produced? d. If the labor quantity variance was $7,200 unfavorable, what were the actual direct labor hours worked? e. If the labor price variance was $9,080 favorable, what was the actual rate per hour? f. If total budgeted manufacturing overhead was $360,000 at normal capacity, what was the predetermined overhead rate? What was the standard cost per unit of product? h. How much overhead was applied to production during the year? i. Using one or more answers above, what were the total costs assigned to work in process?

Rearden Metal is considering the purchase of a new blast furnace costing a total of $5 million dollars. This furnace will qualify for accelerated depreciation: 20% can be expensed immediately, followed by 32%, 19.2%, 11.52 %, 11.52 % and 5.76% over the next five years. Rearden has substantial tax loss carry forwards and estimates that its marginal tax rate will be only 10% over the next five years. Since Rearden will get very little tax benefit from the depreciation expense, it considers leasing the furnace instead. Suppose that Rearden and the lessor face the same 8% borrowing rate, but the lessor has a 40% marginal tax rate. Assume that the furnace is worthless after five years, the lease term is five years, and a lease would qualify as a true tax lease. What is the minimum acceptable upfront lease payment for the lessor? [Hint you must compute the upfront lease payment for which the NPV of "Buy and Lease" is zero for the lessor], (10 points)

Question 4

Wyatt Oil has 8 million shares outstanding and is about to issue 10 million new shares in an IPO. The IPO price has been set at $15 per share, and the underwriting spread is 6%. The IPO is a big success with investors, and the share price rises to $35 at the end of the first day of trading.

a) What is the amount of money raised by Wyatt Oil with the IPO? (5 points)

b) Compute the post-IPO market value of Wyatt Oil, that is, its market value at the end of the first day of trading after the IPO. (5 points)

c) Suppose now that the post-IPO market value of Wyatt Oil represents a fair valuation. of the firm. Based on this assumption, what would have been a fair valuation of each of its shares of stock before the IPO? (5 points)