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Anarel [89]
3 years ago
6

Tim spends his income on donuts (D) and coffee (C). Coffee is $2 per cup and donuts are $1 each. Assume that Tim has $10 to spen

d, and his utility function is given by ????(D,C)=D0.5C0.5 . For this utility function, ????????D=0.5D−0.5C0.5 and ????????C=0.5D0.5C−0.5 . a. Calculate the optimal number of donuts and coffee for Tim to purchase. Assume that he can purchase partial donuts or cups of coffee. Round answers to two places after the decimal where necessary.
Business
1 answer:
stealth61 [152]3 years ago
7 0

Answer:

Optimal number of donuts = 5 Donuts

Optimal cups of coffee = 2.5 cups.

Explanation:

Optimal numbers of donuts and coffee can be calculated as follow

First, we need to determine the budget constraint as below

M = ( P(D) x D ) + ( P(C) x C )

Placig values in the formula

10 = D + 2C

Now make utility function as:

U(D,C) = D0.5 C0.5

Marginal Utility donuts

MU(D) = 0.5D-0.5C0.5

Marginal Utility Coffee

MU(C) = 0.5D0.5C-0.5

The formula for marginal rate of substitution

(MRSD,C)= MU(D) / MU(C)  = 0.5D - 0.5C0.5 / 0.5D0.5C - 0.5  = C/D

Now calculate the optimal consumption level  

MRSD,C = P(D) / P(C)

C/D = 1/2

D = 2C (Equation 1 )

Placing the value of D resulted from equation 1, in the budget constraint we as below

10 = D + 2C

10 = 2C + 2C

10 = 4C

C = 10/4 = 2.5

NOw place the value of C in equation 1

D = 2C = 2(2.5) = 5

Optimal number of donuts = 5 Donuts

Optimal cups of coffee = 2.5 cups.

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vazorg [7]

For the statement  "The payoff matrix represents hypothetical profits that could be earned by two milk..." and the Milky Mose table  Both will cheat Option C. This is further explained below.

<h3>What is a payoff matrix?</h3>

Generally, payoff matrix is simply defined as when one player's tactics and those of the other are represented in a table called a payoff matrix, they are listed in rows.

In conclusion, In order to get an edge, both parties will engage in dishonesty. As a result, both parties will be tempted to cheat in order to gain an unfair advantage.

The payoff matrix below represents hypothetical profits that could be earned by two milk sellers who have formed a cartel. Each seller must decide if they want to cheat or not to cheat on the production quotas in the cartel agreement. Use the payoff matrix to answer the questions below. Does either member have an incentive to cheat? Heifer's Gold will cheat, but Milky Moo will not. No, neither has an incentive to cheat, Yes, both will cheat. Milky Moo's will cheat, but Heifer's Gold will not

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8 0
2 years ago
If a company's cost of capital increases unexpectedly, which of the following actions will help it maintain or increase its stoc
Kitty [74]

Answer:

III) Increase its gross margin

Explanation:

If the company increases its gross margin, it will have a direct impact on the company's net profit. The higher a company's net profit, the higher its value = higher stock price.

The only option that increases the value of the company is to increase its net profit, since:

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  • a decrease in the asset turnover ratio will result in a lower stock price
  • the issuing of stock dividends will only increase the price of stock in the short run, later the price will adjust down since the company's book value will lower
4 0
3 years ago
The artisans at Jewelry Junction in Phoenix are preparing to make gold jewelry during a 2-month period for the Christmas season.
SVEN [57.7K]

Answer:

The max revenue is "$32,300". The further explanation is described below.

Explanation:

(a)

The composition as well as response of models within 6 rows seems to be as described in the following:  

Maximum 1650B + 850N + 790P (B bracelets, N necklaces and P pins produce overall revenue)  

Yes of course,

The total gold ounces will be:

⇒  6.3B+3.9N+3.1P < = 125

The total labor hours will be:

⇒  17B+10N+7P < = 320

Integers B, N, P will become  

The response for LINDO is:

B=10.0.

N=0  

P=20  

Final Value of Maximization will be:

= 32,300

(b)

  • 10 bracelets, hardly any necklaces as well as 20 pins should always be made by the shop.  
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  • It would use 310 hours of labor although 10 hours would then stay unused.  

The maximum salary will become:

= $32,300.

8 0
3 years ago
Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the marginal revenue for a product is MR = 1
n200080 [17]

Answer:

Profit 6,130

Explanation:

MC = 30X + 4

when X=5

Cost to produce 5 units:

We will need to calcualte the MC for 1, 2 , 3, 4 and 5 units and then add them together

MC = 30(5) + 4 = 150 + 4 = 154

MC = 30(4) + 4 = 150 + 4 = 124

MC = 30(3) + 4 = 150 + 4 =  94

MC = 30(2) + 4 = 150 + 4 =  64

MC = 30(1) + 4 = 150 + 4 =   34

Total                                   470

Giving this, now anther way, more easy would be to use the Gauss method to a summatory:

S=\frac{n\times(n+1)}{2}

S to 5 from 1 of (30x+4) =

30 \times \frac{5\times6}{2} +4 \times 5

S = 470

Now we can continue:

Total Marginal cost 470 + Fixed Cost: 900 = 1370

MR = 1500 revenue for adding 1 unit

1500 x 5 = 7500 total revenue

total revenue - total cost = profit

7500 - 1370 = 6,130

3 0
3 years ago
Data for 2021 were as follows: PBO, January 1, $243,000 and December 31, $278,000; pension plan assets (fair value) January 1, $
tester [92]

Answer:

$45,000

Explanation:

Computation for the projected benefit obligation

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December 31 Plan assets 233,000

Funded status($45,000)

Therefore the projected benefit obligation was underfunded at the end of 2021 by: $45,000

7 0
3 years ago
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