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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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2 years ago
Karen and Anika, the owners of a new personal assistant firm called Assist You 2, are interested in offering their services in a
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The first thing Karen and Anika should do is to understand the position of competitors by using the positioning process.

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4 0
2 years ago
Suppose that the last four months of sales were 8, 10, 15, and 9 units, respectively. Suppose further that the last four forecas
Wewaii [24]

Answer:

3

Explanation:

Data provided in the question:

Sales for the last four months :

8, 10, 15, and 9 units

Last four forecast of sales:

9, 11, 8 and 12 units

Now,

The mean absolute deviation (MAD) value of these forecast will be calculated as:

MAD = [ ∑|Sales - Forecast sales| ] ÷ [ Total number of forecast ]

or

MAD =  [ |8 - 9| + |10 - 11| + |15 - 8| + |9 - 12| ] ÷ 4

or

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4 0
2 years ago
Suppose the government wants to reduce the total pollution emitted by three local firms. Currently, each firm is creating 4 unit
murzikaleks [220]

Answer:

yep

Explanation:

Suppose the government wants to reduce the total pollution emitted by three local firms. Currently, each firm is creating 4 units of pollution in the area, for a total of 12 pollution units. If the government wants to reduce total pollution in the area to 6 units, it can choose between the following two methods:

Available Methods to Reduce Pollution

1. The government sets pollution standards using regulation.

2. The government allocates tradable pollution permits.

Each firm faces different costs, so reducing pollution is more difficult for some firms than others. The following table shows the cost each firm faces to eliminate each unit of pollution. For each firm, assume that the cost of reducing pollution to zero (that is, eliminating all 4 units of pollution) is prohibitively expensive.

Firm X 80 130 210

Firm Y 75 90 130

Firm Z 550 700 1,075

Now, imagine that two government employees proposed alternative plans for reducing pollution by 6 units.

Method 1: Regulation

The first government employee suggests to limit pollution through regulation. To meet the pollution goal, the government requires each firm to reduce its pollution by 2 units.

Complete the following table with the total cost to each firm of reducing its pollution by 2 units.

Firm Total Cost of Eliminating Two Units of Pollution (Dollars)

Firm X

Firm Y

Firm Z

Meanwhile, the other employee proposes using a different strategy to achieve the government's goal of reducing pollution in the area from 12 units to 6 units. This employee suggests that the government issue two pollution permits to each firm. For each permit a firm has in its possession, it can emit 1 unit of pollution. Firms are free to trade pollution permits with one another (that is, buy and sell them) as long as both firms can agree on a price. For example, if firm X agrees to sell a permit to firm Y at an agreed-upon price, then firm Y would end up with three permits and would need to reduce its pollution by only 1 unit while firm X would end up with only one permit and would have to reduce its pollution by 3 units. Assume the negotiation and exchange of permits are costless. Because firm Y has high pollution-reduction costs, it thinks it might be better off buying a permit from firm Z and a permit from firm X so that it doesn't have to reduce its own pollution emissions. What prices is firm Z willing to sell one of its permits to firm Y, but firm X is not?

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valina [46]

Answer: cost

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Hence we can conclude that the correct answer is cost.  

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