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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 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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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) = ...

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