Modern Principles: Microeconomics
Modern Principles: Microeconomics
4th Edition
ISBN: 9781319108786
Author: COWEN
Publisher: MAC HIGHER
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Chapter 23, Problem 1FT

Subpart (a):

To determine

Rule of 70.

Subpart (a):

Expert Solution
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Explanation of Solution

By the rule of 70, if one invests $3000 in a bank account and earns 2% real annual return on average, then it would take 35 years (702) until it is worth $6,000. This $6,000 would take another 35 years (702) to double up to $12,000 by the rule of 70. Therefore, $3,000 would take 70 years (35+35)  until it was worth $12,000.

Economics Concept Introduction

Concept introduction:

Rule of 70: By the rule of 70, if the rate of return which is the annual percentage increase in value including dividends is x% of an investment, then the doubling time is 70x   years.

Subpart (b):

To determine

Rule of 70.

Subpart (b):

Expert Solution
Check Mark

Explanation of Solution

By the rule of 70, if one invests $3000 in mutual and earns 7% real annual return on average, then it would take 10 years (707) until it is worth $6,000. This $6000 would take another 10 years (707) to double up to $12,000 by the rule of 70. Therefore, $3000 would take 20 years (10+10)  until it was worth $12,000.

Economics Concept Introduction

Concept introduction:

Rule of 70: By the rule of 70, if the rate of return which is the annual percentage increase in value including dividends is x% of an investment, then the doubling time is 70x   years.

Subpart (c):

To determine

Rule of 70.

Subpart (c):

Expert Solution
Check Mark

Explanation of Solution

By the rule of 70, if one invests $3000 together in bank and mutual fund and earns 5% real annual return on average, then it would take 14 years (705) until it is worth $6,000. This $6000 would take another 14 years (705) to double up to $12,000 by the rule of 70 Therefore, $3000 would take 28 years (14+14)  until it was worth $12,000.

Economics Concept Introduction

Concept introduction:

Rule of 70: By the rule of 70, if the rate of return which is the annual percentage increase in value including dividends is x% of an investment, then the doubling time is 70x   years.

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Please answer questions D-H, I have already answered A , B,C but it may help you to still solve them yourself. Thank you!
2. A firm’s production function is given by:Q = 10KLThe unit capital and labour costs are 2 and 1 pounds respectively. The firm is contracted to produce2000 units.(a) Write out the optimisation problem of the firm. (b) Express this problem using a Lagrangian function. (c) Find values of K and L which fulfil the contract with minimal cost to the firm. (d) Calculate the total cost to the firm.
3. Consider the following estimated regression equation, estimated using a sample of firms, where RDis total firm spending on research and development in USD ($), Revenue is total firm revenuein USD ($), and W ages is the firms’ total spending on wages in USD ($) (standard errors inparentheses):RDd = 1000(600)+ 0.5(0.1)Revenue + 1.5(0.5)W ages,(a) Interpret the coefficients on each of the explanatory variables. (b) Which of the three coefficients are statistically significant at the 5% level of significance? Howdo you know? A researcher runs a two-sided statistical test of the null hypothesis that both the coefficients onthe explanatory variables above are jointly equal to 0.25 (mathematically, that β1 = β2 = 0.25),and reports a p-value of 0.045.(c) What does this p-value mean for the outcome of the test? (d) What would an appropriate two-sided alternative hypothesis look like?
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