1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ede4ka [16]
3 years ago
11

If the supply function for a commodity is p = q2 + 6q + 16 and the demand function is p = −7q2 + 2q + 436, find the equilibrium

quantity and equilibrium price.
Business
1 answer:
adell [148]3 years ago
4 0

Answer:

equilibrium quantity = 7

equilibrium price = 107

Explanation:

Data provided in the question:

supply function, p = q² + 6q + 16  ........(1)

demand function is p = −7q² + 2q + 436

Now at equilibrium

Demand = Supply

Thus,

q² + 6q + 16 = −7q² + 2q + 436

or

q² + 6q + 16 + 7q² - 2q - 436 = 0

or

8q² + 4q - 420 = 0

or

2q² + q - 105 = 0

on solving for the roots of q

using the Quadratic Formula where

a = 2, b = 1, and c = -105

[ x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }]

a = 2, b = 1, and c = -105

Thus,

[ q = \frac{ -1 \pm \sqrt{1^2 - 4(2)(-105)}}{ 2(2) }]

[ q = \frac{ -1 \pm \sqrt{1 - -840}}{ 4 }]

[ q = \frac{ -1 \pm \sqrt{841}}{ 4 }]

The discriminant ( b² - 4ac > 0)

so, there are two real roots.

Therefore,

q = [\frac{ -1 \pm 29}{ 4 }]

[ q = \frac{ 28 }{ 4 } \; \; \; q = -\frac{ 30 }{ 4 }]

[ q = 7 \; \; \; q = -\frac{ 15}{ 2 }]

since,

Quantity cannot be negative

Thus,

q = 7

therefore, substituting q in (1)

p = 7² + 6(7) + 16

or

p = 49 + 42 + 16

or

p = 107

You might be interested in
Where do you think the biggest hole is in the registration statement?
Alex17521 [72]
In the United States, a registration statement is a set of documents, including a prospectus, which a company must file with the U.S. Securities and Exchange Commission before it proceeds with a public offering.

Not that sure though
Best luck with your studying
8 0
2 years ago
You would like to borrow money three years from now to build a new building. In preparation for applying for that loan, you are
zysi [14]

Answer:

Option "D" is the correct answer to the following statement.

Explanation:

The cash coverage ratio helps find the available cash in hand or cash at the bank to pay for the expenditure of a loan. The ratio must be considerably higher to 1: 1, it shows our potential to pay interest. In this situation Option "D" has the highest Cash coverage ratio.

The debt-equity ratio is used to find the firm's credibility.

5 0
3 years ago
What three factors influence the value of a country’s currency?
kondor19780726 [428]

Economics conditions, political stability and balance of payments 3

7 0
3 years ago
Read 2 more answers
The following transactions are for Kingbird Company.1. On December 3, Kingbird Company sold $450,000 of merchandise to Blossom C
SpyIntel [72]

Answer:

Kingbird Company or Mack Company

Journal Entries:

Dec. 3:

Debit Accounts Receivable (Blossom Co.) $450,000

Credit Sales Revenue $450,000

To record the sale of goods on account, terms 1/10, n/30.

Debit Cost of Goods Sold $310,000

Credit Inventory Account $310,000

To record the cost of goods sold.

Dec. 8:

Debit Sales Allowance $22,000

Credit Accounts Receivable (Blossom Co.) $22,000

To record the allowance granted.

Dec. 13:

Debit Cash Account $423,720

Debit Cash Discount $4,280

Credit Accounts Receivable (Blossom Co.) $428,000

To record the settlement of account.

Explanation:

Journal entries are used to record transactions that occur on a daily basis.  They are usually the first set of records made in the accounting books.  They show the accounts to be debited and the accounts to be credited.  Each transaction is usually debited in one account and credited in another to reflect the double entry system of accounting and to keep the accounting equation in balance.

7 0
2 years ago
Air Destinations issues bonds due in 10 years with a stated interest rate of 11% and a face value of $500,000. Interest payments
olga nikolaevna [1]

Answer: $471,324.61

Explanation:

Price of a bond = Present value of coupon payments + Present value of face value at maturity

Coupon payments = 500,000 * 11% * 1/2 years = $27,500

Periodic yield = 12%/ 2 = 6% per semi annual period

Periods = 10 * 2 = 20 semi annual periods

Coupon payment is constant so it is an annuity.

Price of bond = Present value of annuity + Present value of face value at maturity

= (Annuity * Present value interest factor of Annuity, 6%, 20 years) + Face value / (1 + rate) ^ number of periods

= (27,500 * 11.4699) + 500,000 / (1 + 6%)²⁰

= $471,324.61

8 0
2 years ago
Other questions:
  • Julio purchased a stock one year ago for $27. The stock is now worth $32, and the total return to Julio for owning the stock was
    5·1 answer
  • Suppose you owned a portfolio consisting of $250,000 of long-term U.S. government bonds. Would your portfolio be riskless? Expla
    6·1 answer
  • Working for the internal Revenue service is a career in public safety. True or false?
    15·2 answers
  • A car dealership union negotiates a contract that dramatically increases the salaries of all salesmen. If one of the salesmen is
    6·1 answer
  • Refer to the given consumption schedules. DI signifies disposable income and C represents consumption expenditures. All figures
    6·1 answer
  • Match each term with the correct definition.
    5·1 answer
  • Which type of money does the diagram best describe?
    6·1 answer
  • What is it determines a good trade agreement? (Economics)
    7·1 answer
  • In the market for labor, demand describes
    6·1 answer
  • Where do financial institutions get the funds that they lend to customers?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!