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Optimum combination of resources and consol bonds

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Question 1
A firm combines two resources, X and Y, to produce an output level Q in a purely competitive market. The cost of a unit of X is $15 and the cost of a unit of Y is $8. The marginal product of X is 30 units and the marginal product of Y is currently 24 units at output level Q. What would you recommend that the firm do given this resource combination?
MP(X)/MP(Y) should be equal to ratio P(X)/P(Y)

Question 2
To fund its wars against Napoleon, the British government sold consol bonds. They were referred to as "perpetuities" because they would pay Ã?£3 every year in perpetuity (forever).
1. If a citizen could purchase a consol for Ã?£25, what would its annual interest rate be? (16.7 points)
2. What if the price were Ã?£50? Ã?£100? Bonds are known as "fixed income" securities because the future payments that they will make to investors are fixed by the bond agreement in advance. (16.7 points)
3. Do the interest rates of bonds and other investments that offer fixed future payments vary positively or inversely with their current prices? (16.7 points)

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Solution Preview

Question 1
A firm combines two resources, X and Y, to produce an output level Q in a purely competitive market. The cost of a unit of X is $15 and the cost of a unit of Y is $8. The marginal product of X is 30 units and the marginal product of Y is currently 24 units at output level Q. What would you recommend that the firm do given this resource combination?
MP(X)/MP(Y) should be equal to ratio P(X)/P(Y)

Solution: At optimum utilization of resources
MP(X) / MP(Y) = ...

Solution Summary

This post solves two problems. The first problem is on how to determine the optimum combination of resources. The second one shows how the calculate the price of a perpetual bond.

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Process Identification and Analysis

From the student:

Wow, was this a hard assignment for the team.We came up with Nintendo as the organzation and the Production Procees (inventory to keep up with customer demand - why is it out of stock so much and why can't Nintendo produce the amounts needed - is it poor planning, etc.)? I have section A (A description of the process targeted for improvement). About four hundred or so words if you can help me out with this. Thanks again with all your help in my studies. I have really learned alot from you as a mentor.

The problem:

Your Learning Team represents a group of employees or managers in the organization and has been selected to run a pilot process improvement team. Select an organization that is agreed upon by your LT and prepare a 1,400 - 2,100 word paper in which you choose a process for improvement in your selected organization. Include the following ...
a. A description of the process targeted for improvement
b. A description of why analyzing a process can be useful in improving quality
c. Quality tools that you would recommend using to collect and present data from this type of process
d. An analysis of the process variability based upon your understanding of the process and any data collected
Conclude your presentation by providing recommendations for process improvement strategies for your selected process. Be sure to include a discussion of how your quality improvement strategy is linked to the strategic goals of the organization.

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