How does the share of income spent on each good change

Reference no: EM13178626

Suppose that a consumer has a Cobb-Douglas utility function:

U(a,b) = a^? * b^(1-?)

where a and b are consumption of environmental goods and consumer goods, respectively (assume that 0 < ? < 1). Suppose further that the prices of the two goods are pa and pb, and that total income is M.

(i) Form the lagrangian and derive the first-order conditions.

(ii) Solve for the optimal demands for a and b as a function of ?, pa, pb, and M. Explain intuitively the effect of these four parameters on the consumer's optimal choices.

(iii) Plot the optimal demands for a and b as of pb. Explain why the functions are shaped as they are. How does the share of income spent on each good change with pb? If consumers' preferences defined by a Cobb-Douglas utility function, what does your result suggest about their expenditure patterns?

Reference no: EM13178626

Questions Cloud

Determine how the abatement levels should be reallocated : It is well documented that carbon monoxide (CO) emissions from combustible engines increase in colder climates. This implies that damages are expected to be less severe in summer months than in winter. Nonetheless, air quality control authorities..

Find a scientific calculator online : Where did the 2.65 come from? Almost all calculators will calculate the value of a number raised to a power. If you don't know how to do it on your calculator, get out the instruction book. Or find a scientific calculator online -- there are plent..

In what ways do you use estimating in your everyday life : The interest formula shows how interest, rate, and time are related. It gives you a way of finding one of these values if the other three values are known. Even though you try to be careful in your calculations, there will always be that occasion ..

Find the linear correlation coefficient for the systolic : Use the Excel Analysis ToolPak to find the linear correlation coefficient for the systolic and diastolic measurements.

How does the share of income spent on each good change : How does the share of income spent on each good change with pb? If consumers' preferences defined by a Cobb-Douglas utility function, what does your result suggest about their expenditure patterns?

Draw a histogram to represent the distribution : Obtain (generate) a random sample of 180 numbers between 1 and 60. You may use a calculator, excel, or a table of random numbers to achieve this. Use your sample to answer the following questions.

Analysis into action plan-steps to developing a labor force : Identify and explain the essential factors that a human resource manager must consider prior to their company expanding into a new country located in the United Arab Emirates.

Should she quit her current job to become an entrepreneur : For the internet opportunity she anticipates costs for land labor and capitol of$ 3,250,000 per year as compared to revenues of $3,275,000 per year. Should she quit her current job to become an entrepreneur? If she does not quit her current job wh..

What effect does changing the level of con?dence : What effect does changing the level of con?dence have on the sample size? Explain.

User Account

All Pages