Cournot Oligopoly and Number of Firms In a Cournot oligopoly, each firm assumes that its rivals do not change their output based on the output that it produces. Illustration: A Cournot oligopoly has two firms, Y and Z. Y observes the market demand curve and the number of units that Z produces. It assumes that Z does not change its output regardless of the number of units that it (Y) produces, so chooses a production level that maximizes its profits. The general effects of a Cournot oligopoly do not depend on the size of the firms, the shape of the market demand curve, or the shape of the marginal cost curve. The mathematics is easiest for firms of the same size, linear demand curves, and flat marginal cost curves. Suppose an industry has two firms, a linear demand curve, and marginal costs, and no fixed costs: Demand curve: Q = " – $ P Marginal cost curve: MC = k In a competitive industry, what is the equilibrium quantity for the industry? (Setting price equal to marginal cost gives Q = " – $ × k. Since the industry is competitive, price equals marginal cost, and the supply curve for the industry is P = k; this gives the same result.) What is the equilibrium quantity for the firm? (With two identical firms, each produces half the industry quantity.) If the two firms merge into a monopoly, what is the monopoly price? (Show that the marginal revenue curve is MR = " – 2 $ P, by setting total revenue = P × Q and differentiating with respect to Q. Setting marginal revenue equal to marginal cost gives k = " – 2 $ P A P = (" – k) / 2$ Q = " – $ P = " – ½ (" – k) = ½ " + ½ k A total of 2,400 units are produced. If there were three firms in this Cournot oligopoly, how many units would be produced? 1,800 units 2,400 units 2,700 units 3,000 units 3,600 units (In a two Cournot oligopoly, each firm produces a the competitive quantity; in a three firm Cournot oligopoly, each firm produces ¼ the competitive quantity.)

Santana Rey, owner of Business Solutions, decides to prepare a statement of cash flows for her business using the following financial data.
  

Required:
Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2020. Owner Santana Rey contributed $30,000 to the business in exchange for additional stock in the first quarter of 2020 and has received $4,300 in cash dividends. (Amounts to be deducted should be indicated with a minus sign.)

Cash Flow Budgeting - Company A is experiencing rapid growth due to the popularity of its recent hardware release. Current sales of $100,000, which increased from $80,000 the previous month, are expected to grow at a 30% rate. Cost of sales are stable 70% of sales revene, yielding a 30% gross profit. Company A sales are 15% for cash with the remaining 85% collected the following month. Inventory-on-hand is maintained at a level to support the following month's sales. Inventory is paid for at the time of receipt. Company A began the period with a cash balance of $65,000.

(a) For the current month and following three months, determine Company A's: (INCLUDE FORMULAS USED TO SOLVE PROBLEM)

- Revenue

- Cost of sales

- Gross profit

- Accounts receivable

- Inventory

- Cash collections

- Cash disbursements

(b) Is Company A gross profit increasing or declining?

(c) Is Company A cash flow increasing or declining?

(d) What is Company A cash balance at the end of the four-month period?

Cash Flow Budgeting - Company B is experiencing rapid growth due to the popularity of its recent clothing line release. Current sales of $250,000, which increased from $190,000 the previous month, are expected to grow at a 20% rate. Cost of sales are a stable 35% of sales revenue, yielding a 65% gross profit. Company B sales are 30% for cash with the remaining 70% collected the following month. Inventory-on-hand is maintained at a level to support the following two months' sales. Inventory is paid for at the time of receipt. Company B began the period with a cash balance fo $70,000.

(e) For the current month and following three months, determine Company B: (INCLUDE FORMULAS USED TO SOLVE PROBLEMS)

- Revenue

- Cost of sales

- Gross profit

- Accounts receivable

- Inventory

- Cash collections

- Cash disbursements

(f) Is Company B gross profit increasing or declining?

(g) Is Company B cash flow increasing or declining?

(h) What is Company B cash balance at the end of the four-month period?

Santana Rey, owner of Business Solutions, decides to prepare a statement of cash flows for her business using the following financial data. BUSINESS SOLUTIONS Income Statement For Three Months Ended March 31, 2018 Computer services revenue $ 24,507 Net sales 18,193 Total revenue 42,700 Cost of goods sold $ 14,252 Depreciation expense—Office equipment 380 Depreciation expense—Computer equipment 1,180 Wages expense 2,950 Insurance expense 495 Rent expense 2,075 Computer supplies expense 1,285 Advertising expense 600 Mileage expense 250 Repairs expense—Computer 910 Total expenses 24,377 Net income $ 18,323 BUSINESS SOLUTIONS Comparative Balance Sheets December 31, 2017, and March 31, 2018 Mar. 31, 2018 Dec. 31, 2017 Assets Cash $ 75,517 $ 55,302 Accounts receivable 24,167 4,968 Inventory 674 0 Computer supplies 2,005 560 Prepaid insurance 1,080 1,625 Prepaid rent 755 755 Total current assets 104,198 63,210 Office equipment 7,200 7,200 Accumulated depreciation—Office equipment (760 ) (380 ) Computer equipment 19,500 19,500 Accumulated depreciation—Computer equipment (2,360 ) (1,180 ) Total assets $ 127,778 $ 88,350 Liabilities and Equity Accounts payable $ 0 $ 1,200 Wages payable 895 590 Unearned computer service revenue 0 2,200 Total current liabilities 895 3,990 Equity Common stock 106,000 77,000 Retained earnings 20,883 7,360 Total liabilities and equity $ 127,778 $ 88,350 Required: Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2018. Owner Santana Rey contributed $29,000 to the business in exchange for additional stock in the first quarter of 2018 and has received $4,800 in cash dividends.

Santana Rey, owner of Business Solutions, decides to prepare a statement of cash flows for her business using the following financial data. BUSINESS SOLUTIONS Income Statement For Three Months Ended March 31, 2019 Computer services revenue $ 25,307 Net sales 18,693 Total revenue 44,000 Cost of goods sold $ 14,052 Depreciation expense—Office equip. 400 Depreciation expense—Computer equip. 1,250 Wages expense 3,250 Insurance expense 555 Rent expense 2,475 Computer supplies expense 1,305 Advertising expense 600 Mileage expense 320 Repairs expense—Computer 960 Total expenses 25,167 Net income $ 18,833 BUSINESS SOLUTIONS Comparative Balance Sheets December 31, 2018, and March 31, 2019 Mar. 31, 2019 Dec. 31, 2018 Assets Cash $ 68,057 $ 48,372 Accounts receivable 22,867 5,668 Inventory 704 0 Computer supplies 2,005 580 Prepaid Insurance 1,110 1,665 Prepaid rent 825 825 Total current assets 95,568 57,110 Office equipment 8,000 8,000 Accumulated depreciation—Office equip. (800 ) (400 ) Computer equipment 20,000 20,000 Accumulated depreciation—Computer equip. (2,500 ) (1,250 ) Total assets $ 120,268 $ 83,460 Liabilities and Equity Accounts payable $ 0 $ 1,100 Wages payable 875 500 Unearned computer service revenue 0 1,500 Total current liabilities 875 3,100 Equity Common stock 98,000 73,000 Retained earnings 21,393 7,360 Total liabilities and equity $ 120,268 $ 83,460 Required: Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2019. Owner Santana Rey contributed $25,000 to the business in exchange for additional stock in the first quarter of 2019 and has received $4,800 in cash dividends. (Amounts to be deducted should be indicated with a minus sign.)

Santana Rey, owner of Business Solutions, decides to prepare a statement of cash flows for her business using the following financial data.

BUSINESS SOLUTIONS Income Statement For Three Months Ended March 31, 2020 Computer services revenue $ 25,007 Net sales 17,893 Total revenue 42,900 Cost of goods sold $ 14,652 Depreciation expense—Office equipment 370 Depreciation expense—Computer equipment 1,250 Wages expense 2,950 Insurance expense 475 Rent expense 1,575 Computer supplies expense 1,285 Advertising expense 580 Mileage expense 260 Repairs expense—Computer 860 Total expenses 24,257 Net income $ 18,643 BUSINESS SOLUTIONS Comparative Balance Sheets December 31, 2019, and March 31, 2020 Mar. 31, 2020 Dec. 31, 2019 Assets Cash $ 77,407 $ 57,102 Accounts receivable 23,767 4,868 Inventory 694 0 Computer supplies 2,085 500 Prepaid insurance 1,030 1,605 Prepaid rent 805 805 Total current assets 105,788 64,880 Office equipment 7,500 7,500 Accumulated depreciation—Office equipment (740 ) (370 ) Computer equipment 19,000 19,000 Accumulated depreciation—Computer equipment (2,500 ) (1,250 ) Total assets $ 129,048 $ 89,760 Liabilities and Equity Accounts payable $ 0 $ 1,200 Wages payable 945 500 Unearned computer service revenue 0 2,400 Total current liabilities 945 4,100 Equity Common stock 106,000 78,000 Retained earnings 22,103 7,660 Total liabilities and equity $ 129,048 $ 89,760

Required: Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2020. Owner Santana Rey contributed $28,000 to the business in exchange for additional stock in the first quarter of 2020 and has received $4,200 in cash dividends. (Amounts to be deducted should be indicated with a minus sign.)

Santana Rey, owner of Business Solutions, decides to prepare a statement of cash flows for her business using the following financial data.
  

Required:
Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2020. Owner Santana Rey contributed $34,000 to the business in exchange for additional stock in the first quarter of 2020 and has received $4,200 in cash dividends. (Amounts to be deducted should be indicated with a minus sign.)

Santana Rey, owner of Business Solutions, decides to prepare a statement of cash flows for her business using the following financial data. BUSINESS SOLUTIONS Income Statement For Three Months Ended March 31, 2020 Computer services revenue $ 25,207 Net sales 17,993 Total revenue 43,200 Cost of goods sold $ 14,852 Depreciation expense—Office equipment 310 Depreciation expense—Computer equipment 1,250 Wages expense 2,850 Insurance expense 525 Rent expense 1,975 Computer supplies expense 1,285 Advertising expense 540 Mileage expense 310 Repairs expense—Computer 860 Total expenses 24,757 Net income $ 18,443 BUSINESS SOLUTIONS Comparative Balance Sheets December 31, 2019, and March 31, 2020 Mar. 31, 2020 Dec. 31, 2019 Assets Cash $ 74,567 $ 54,312 Accounts receivable 24,167 5,168 Inventory 614 0 Computer supplies 2,085 510 Prepaid insurance 1,060 1,655 Prepaid rent 825 825 Total current assets 103,318 62,470 Office equipment 7,500 7,500 Accumulated depreciation—Office equipment (620 ) (310 ) Computer equipment 19,700 19,700 Accumulated depreciation—Computer equipment (2,500 ) (1,250 ) Total assets $ 127,398 $ 88,110 Liabilities and Equity Accounts payable $ 0 $ 1,120 Wages payable 895 530 Unearned computer service revenue 0 1,500 Total current liabilities 895 3,150 Equity Common stock 104,000 77,000 Retained earnings 22,503 7,960 Total liabilities and equity $ 127,398 $ 88,110 Required: Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2020. Owner Santana Rey contributed $27,000 to the business in exchange for additional stock in the first quarter of 2020 and has received $3,900 in cash dividends. (Amounts to be deducted should be indicated with a minus sign.)

A power company operates three power generation plants. One is a wind plant, and the other two consume a combination of Fuel 1 and Fuel 2, emitting carbon dioxide in the process. In addition, all three plants require maintenance. The amount of fuel consumed (in Mg), maintenance required (in person-hours), carbon dioxide (CO2) emitted (in Mg), and power generated (in MWh) per day of operation is as follows: Maintenance Fuel 1 Fuel 2 CO2 Power Plant Required Required Required Emitted Produced 1 20 0 0 0 20 2 13 10 15 12 32 3 18 30 40 29 40 Each MWh of power can be sold at £121 and there is no limit on the amount that can be sold. Over its next planning period, the company has 230 person-hours for maintenance, 75 Mg of Fuel 1, and 90 Mg of Fuel 2 available.

(a) Due to environmental regulations, they cannot emit more than 200Mg of CO2 in this period. The company wants to know how to operate its plants to generate as much revenue as possible (you may assume that there is no limit on the number of days a plant can operate in this period). Give a linear program that models this problem and state what each of your variables is meant to represent. You do not need to solve this program. [11]

(b) Suppose now that the company can emit more than 200Mg of CO2, but now loses £55 of revenue for each Mg emitted after the first 200Mg because it must purchase “CO2 credits”. The other resource constraints remain as stated. The company now wants to know how to operate its plants to generate as much revenue as possible (you may assume that there is no limit on the number of days that a plant can operate in this period). Give a linear program that models this problem. You do not need to solve this program.

Santana Rey, owner of Business Solutions, decides to prepare a statement of cash flows for her business using the following financial data.
  

Required:
Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2020. Owner Santana Rey contributed $31,000 to the business in exchange for additional stock in the first quarter of 2020 and has received $4,000 in cash dividends. (Amounts to be deducted should be indicated with a minus sign.)