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yawa3891 [41]
2 years ago
5

There are two firms in an industry. The industry demand curve is given by p = 3,600 - 4q. Each firm has one manufacturing plant

and each firm i has a cost function C(q_i) = q^2_i, where q_i is the output of firm i. The two firms form a cartel and arrange to split total industry profits equally.
Required:
a) Under this cartel arrangement, they will maximize joint profits if ___________.
Business
1 answer:
Natasha_Volkova [10]2 years ago
8 0

Answer:

Under this cartel arrangement, they will maximize joint profits if each of the firms produces 257.14 units and sells at $1,542.88 per unit.

Explanation:

p = 3,600 - 4q ..................................................... (1)

C(q_i) = q_i^2 ………………………………… (2)

MC_i = dC(q_i)/dq = 2q_i ……………………. (3)

Since q = q_1 + q_2, we have:

p = 3,600 - 4(q_1 + q_2)

p = 3,600 - 4q_1 - 4q_2 .................................... (4)

For Firm 1:

TR_1 = p * q_1 = (3,600 - 4q_1 - 4q_2)q_1

TR_1 = 3,600q_1 - 4q_1^2 - 4q_2q_1

MR_1 = dTR_1/dq_1 = 3,600 - 8q_1 - 4q_2

From equation (3), MC_1 = 2q_1

Since at the optimum MC_1 = MR_1, we have:

2q_1 = 3,600 - 8q_1 - 4q_2

10q_1 = 3,600 - 4q_2

q_1 = (3,600 - 4q_2)/10

q_1 = 360 - 0.4q_2 .......... (5)

For Firm 2:

TR_2 = p * q_2 = (3,600 - 4q_1 - 4q_2)q_2

TR_2 = 3,600q_2 - 4q_2q_1 - 4q_2^2

MR_2 = dTR_2/dq_2 = 3,600 - 4q_1 - 8q_2

From equation (3), MC_2 = 2q_2

Since at the optimum MC_2 = MR_2, we have:

2q_2 = 3,600 - 4q_1 - 8q_2

10q_2 = 3,600 - 4q_1

q_2 = (3,600 - 4q_1)/10

q_2 = 360 - 0.4q_1 .......... (6)

a. Calculation of Cournot equilibrium quantities

Substituting equation (6) for q_2 into equation (5), we have:

q_1 = 360 - 0.4(360 - 0.4q_1)

q_1 = 360 – 144 + 0.16q_1

q_1(1 – 0.16) = 216

q_1 = 216 / 0.84

q_1 = 257.14 <------------- Cournot equilibrium quantity for firm 1

Substitute for q_1 in equation (6), we have:

q_2 = 360 - 0.4(257.14)

q_2 = 360 – 102.86

q_2 = 257.14 <------------- Cournot equilibrium quantity for firm 2

b. Calculation of Cournot equilibrium price

Substitute for q_1 and q_2 into equation (4), we have:

p = 3,600 – 4(257.14) – 4(257.14)

p = 1,542.88

Therefore, under this cartel arrangement, they will maximize joint profits if each of the firm produces 25.14 and sells at $1,542.88 per unit.

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Thoro Clean, a firm providing house-cleaning services, began business on April 1. The following accounts in its general ledger a
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April 2

Cash $11,500 - $2,850+ Accounts Receivable + Supplies + Prepaid Van Lease $2,850 + Equipment = Accounts Payable + Notes Payable + Common Stock $11,500 + Retained Earnings

April 3

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April 3

Cash $11,500 - $2,850 + $10,000 - $3,500 + Accounts Receivable + Supplies + Prepaid Van Lease $2,850 + Equipment $5,500 = Accounts Payable $2,000 + Notes Payable $10,000 + Common Stock $11,500 + Retained Earnings

April 4

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April 7

Cash $11,500 - $2,850 + $10,000 - $3,500 - $4,300 - $350 + Accounts Receivable + Supplies $4,300 + Prepaid Van Lease $2,850 + Equipment $5,500 = Accounts Payable $2,000 + Notes Payable $10,000 + Common Stock $11,500 + Retained Earnings - Advertising Expense $350

April 21

Cash $11,500 - $2,850 + $10,000 - $3,500 - $4,300 - $350 + Accounts Receivable $3,500 + Supplies $4,300 + Prepaid Van Lease $2,850 + Equipment $5,500 = Accounts Payable $2,000 + Notes Payable $10,000 + Common Stock $11,500 + Retained Earnings - Advertising Expense $350 + Cleaning Fees Earned $3,500

April 23

Cash $11,500 - $2,850 + $10,000 - $3,500 - $4,300 - $350 - $1,500 + Accounts Receivable $3,500 + Supplies $4,300 + Prepaid Van Lease $2,850 + Equipment $5,500 = Accounts Payable $2,000 - $1,500 + Notes Payable $10,000 + Common Stock $11,500 + Retained Earnings - Advertising Expense $350 + Cleaning Fees Earned $3,500

April 28

Cash $11,500 - $2,850 + $10,000 - $3,500 - $4,300 - $350 - $1,500 + $2,300 + Accounts Receivable $3,500 - $2,300 + Supplies $4,300 + Prepaid Van Lease $2,850 + Equipment $5,500 = Accounts Payable $2,000 - $1,500 + Notes Payable $10,000 + Common Stock $11,500 + Retained Earnings - Advertising Expense $350 + Cleaning Fees Earned $3,500

April 29

Cash $11,500 - $2,850 + $10,000 - $3,500 - $4,300 - $350 - $1,500 + $2,300 + $1,000 + Accounts Receivable $3,500 - $2,300 + Supplies $4,300 + Prepaid Van Lease $2,850 + Equipment $5,500 = Accounts Payable $2,000 - $1,500 + Notes Payable $10,000 + Common Stock $11,500 + Retained Earnings - Advertising Expense $350 + Cleaning Fees Earned $3,500 + Dividends $1,000

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DATE    DESCRIPTION                 DEBIT     CREDIT

April 1    Cash Account                $11,500

             Common Stock                              $11,500

To record Randy Storm's investment of cash

April 2  Prepaid Van Lease        $2,850

            Cash Account                                $2,850

To record payment for six months' lease on a van.

April 3  Cash Account             $10,000

            Notes Payable                              $10,000

To record the borrowing of $10,000 from a bank.

April 3   Cleaning Equipment  $5,500

             Cash Account                              $3,500

             Accounts Payable                       $2,000

To record purchase of cleaning equipment.

April 4  Cleaning Supplies      $4,300

            Cash Account                              $4,300

To record the purchase of cleaning supplies.

April 7  Advertising Expense    $350

            Cash Account                                $350

To record the payment for advertisements.

April 21 Accounts Receivable      $3,500

            Cleaning Fee Earned                     $3,500

To record the cleaning fees earned.

April 23 Accounts Payable        $1,500

             Cash Account                               $1,500

To record the payment on account.

April 28 Cash Account           $2,300

              Accounts Receivable                 $2,300

To record the receipt from customers on account.

April 29 Cash Account         $1,000

             Dividends                                   $1,000

To record the receipt of dividends.

April 30 Wages Expense        $1,750

             Cash Account                            $1,750

To record the payment of wages for April.

April 30 Gasoline Expense    $255

              Cash Account                         $255

To record the payment for gasoline used during April.

Explanation:

The accounting equation is given as Assets = Liabilities + Equity.  This equation is always in balance with each transaction affecting at least one or two accounts in either side of the equation.  This equation explains that the assets owned by a company are made up of either owings to creditors or owners of the business.

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$30 / $0.50 = 60

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