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Rationing and Marginal Benefit to Consumers

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Please help with this problem. I'm not looking for a final answer, but I am definitely looking for the mathematical approach used. Thank you!

MB1=150-Q1 is the marginal willingness to pay, or marginal benefit, function for Consumer 1 who consumes Q1 of the commodity Q per month. For example, when Q1=1, MB=149, meaning that the consumer would be willing to pay at most 149 for 1 unit of consumption of good Q. MB for Q1 can be thought of as the marginal rate of substitution (MRS) for Q, in terms of the most the consumer would be willing to trade off in everything else (measured in $) for the consumption of Q. Under some strong assumptions, it can be thought of as the consumer's ordinary demand curve for good Q.

Similarly, MB2=75-.5Q2 is the corresponding marginal benefit function of good Q for Consumer 2.

a. Suppose these consumers live in Cuba and get a ration of 50 units of Q each month. What is the marginal willingness to pay at this level of consumption for each consumer? What is the total benefit each consumer receives from this policy-determined quantity ration?

b. Suppose these consumers enter the black market and illegally trade with one another. How much will they trade with each other, what will be their final level of consumption, and their MRS's in equilibrium? What will be the relationship between Q1 and Q2 be in ANY trading equilibrium involving these two consumers? What is the total benefit each consumer receives in the trading equilibrium? How does the total consumption benefit (sum of each consumer benefit) compare in this trading equilibrium with the total consumption benefit in the policy-determined quantity ration in the previous answer?

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Solution Preview

You can calculate the the willingness to pay by inserting the rationed amount into the demand functions you are given. The marginal rate of substitution (MRS) is also the willingness to pay. Thus for consumer 1, you would have:
MRS= 150-50 = 100
and in the same way you would get 50 for consumer 2.

The total benefit is found by integrating the demand function from zero to the quantity obtained. Thus for the first consumer we ...

Solution Summary

Marginal benefit used to determine impact of rations on an eceonomy

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Hi
I need solution for these few questions. It is a review that will help me prepare for the final.
Thanks

Question 1:

A. A firm has $1.2 million in current assets and $1.0 million in current liabilities. If it uses $.5 million of cash to pay off some of its accounts payable, what will happen (amount increase or decrease) to the current ratio?

What happens to net working capital?

B. A firm uses cash on hand to pay for additional inventories. What will happen to the current ratio?

What will happen to the quick ratio?

Question 2:

A. Receivables. Chik's Chickens has average accounts receivable of $6,333. Sales for the year were $9,800. What is its average collection period?

B. Inventory. Salad Daze maintains an inventory of produce worth $400. Its total bill for produce over the course of the year was $73,000. How old on average is the lettuce it serves its customers?

Question 3:

Compensating Balances. A bank loan has a quoted annual rate of 6 percent. However, the borrower must maintain a balance of 25 percent of the amount of the loan, and the balance does not earn any interest.

A. What is the effective rate of interest if the loan is for 1 year and is paid off in one payment at the end of the year?

B. What is the effective rate of interest if the loan is for 1 month?

Question 4:

Sanyo produces audio and video consumer goods and exports a large fraction of its output to the United States under its own name and the Fisher brand name. It prices its products in yen, meaning that it seeks to maintain a fixed price in terms of yen. Suppose the yen moves from ¥103.155/$ to ¥97/$. What risk does Sanyo face?

How can it reduce its exposure?

Question 5:

Bank of America acquired Countrywide Mortgage. Considering the expected or unexpected risks associated with the mortgage crisis and the bail out money, how do you think this acquisition impacted the organizations' shareholders? How do you feel this
acquisition impacted the consumers?

Question 6:

You are the capital budgeting analyst for XYZ company and has been asked to evaluate a proposal. The manager of the automotive division believes that replacing the robotics used on the heavy truck gear line will produce total benefits of $550,000 (in today's dollars) over the next 5 years. The existing robotics would produce benefits of $421,000 (also in today's dollars) over the same period. An initial cash investment of $220,000 would be required to install the new equipment. The manager estimates that the existing robotics can be sold for $73,000. Show how you will apply marginal analysis techniques to answer the following questions.

a. How much is the marginal benefit of the proposed new robotics?

b. How much is the marginal cost of the proposed new robotics?

c. How much is the net benefit of the proposed new robotics?

d. Should they replace the old robotics with the new one?

Question 7:

Calculate the future value of the single cash flow deposited today that will be available at the end of the deposit period if the interest is compounded annually at the rate specified below:

Single Cash Flow: $21,700

Interest Rate: 12% Period: 15 Years

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