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pshichka [43]
3 years ago
7

There are two routes for driving from A to B. One is freeway, and the other consists of local roads. The benefit of using the fr

eeway is constant and equal to 3.6, irrespective of the number of people using it. Local roads get congested when too many people use this alternative, but if not enough peoople use it, the few isolated drivers run the risk of becoming victims of crimes. Suppose that when a fraction of x of the population is using the local roads, the benefit of this mode to each driver is given by:
1 + 8x – 9x²

Required:
a. Draw a graph showing the benefits of the two driving routes as functions of x, regarding x as a continuous variable between 0 and 1.
b. Identify all possible equilibrium traffic patterns from your graph in part (a). Which equilibria are stable? Which ones are unstable? Explain.
c. What value of x maximizes the total benefit to the whole population?
Business
1 answer:
STALIN [3.7K]3 years ago
5 0

Answer:

a) attached below

b) stable equilibria = x = 0.1 , x = 0.8

   unstable equilibria = other value except 0.1 , 0.8

c) 0.5 , 0.6

Explanation:

Benefit of using the local roads = 1 + 8x - 9x^2

Benefit of using the free way = 3.6

a) Attached below is the required graph

<u>b) Determine The possible equilibrium traffic patterns from the graph </u>

stable equilibria : x = 0.1 ,  x = 0.8 ( this id because at these given value the benefits of using either routes is equal )

unstable equilibria :  every other value of X except 0.1 and 0.8

<u>c) Determine the value of x that maximizes the total benefit to the population</u>

The value of X that maximizes the total benefit to the population = 0.5 and 0.6

attached below is the detailed solution

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Ravine Corporation purchased 30 percent ownership of Valley Industries for $92,700 on January 1, 20X6, when Valley had capital s
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Answer:

The Various answers are clearly explained in the Explanations. Thank you.

Explanation:

First, we calcuate the Net Income of Ravine Corporation Based on the FairValue Method

Year    OPerating Income    UnrealizedGain   Dividend inc.   Net Income

20x6   $140,000                  11,000                    6,000                        $157,000

20x7    80,000                     11,000                   12,000                     $103,000

20x8   220,000                     11,000                  12,000                   $243,000  

20x9   160,000                      11,000                  6,000                        $177,000

Kindly note, thta the dividend income for each year is based on 30% of the Dividend of Valley for that year for instance, Dividend income for 20x6 = 0.3 x $20,000 = $6,000

Next we calculate the Net Income of Ravine Corpoartion Under the Equity Method

Year    OPerating Income  Share ofo Income in Valley  Net Income  

20x6   $140,000                   9,000                                    149 ,000                        

20x7    80,000                    15,000                                    95,000                    

20x8   220,000                    3,000                                    223,000                      

20x9   160,000                  12,000                                     172,0000      

NOte as well that the Share of Income in Valley is 30% of the yearly net income of Valley Industries.                

Question B) Part 1

Ravine Corporation Journal Entries

S/N                                       Description                        Debit        Credit

1                                         Cash                                   12,000

                                        Dividend Revenue                                 12,000

Being the record of dividend received from valley industries

2.                                        Fair Value Adjustment       11,000

                             Unrealized holding gain or loss                       11,000    

Being the rcord of fair value change in value of the investments

Question B) Part 2

S/N                                       Description                        Debit        Credit

1                                         Cash                                   12,000

                                        Investment in Valley                               12,000

Being the record of dividend received from valley industries

2.                                        Investment in Valley      3,000

                             Investment Income                                        3,000  

BBeing the share of income of Ravine in Valley

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