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)

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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The British government has a consol bond outstanding paying 100 per year forever. Assume the current interest rate is 4% per year.
1) What is the value of the bond immediately after a payment is made?
2) What is the value of the bond immediately before a payment is made?

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Please help with the following problems.
10. Bond Returns
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a) If the bond in Quiz Question has a yield to maturity of 8% 1 year from now, what its price be?
b) What will be the rate of return on

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A $1000 face val

If the British government has a consol bond outstanding paying 100 pound per year forever. Assume the current intrest rate is 4% per year. What is the value of the bond immediately after a payment is made? What is the value of the bond immediately before a payment is made?

Consider the samples x1, ..., xN which satisfy the following model (see the attachment).
x_n - sqrt(0) + w_n; n = 1, ..., N
where [w_n] is i.i.d. with corresponding pdf f(w). We are interested in distinguishing between the two hypothesis Ho: theta = 0 and H1: theta > 0. Examine whether a locally optimum test exists that ca