Question

In: Economics

John likes both carrots (good 1) and lettuce (good 2) His preferences are shown below by...

John likes both carrots (good 1) and lettuce (good 2)

His preferences are shown below by cobb douglas utility.

u(x1,x2)=x11/2+x21/2

a) Find marshallian demand functions for x1*(p1,p2, m) and x2*(p1,p2,m)

b) Find indirect utility function

Solutions

Expert Solution


Related Solutions

John really likes listening to music. His preferences for vintage records (?1) and music downloads (?2)...
John really likes listening to music. His preferences for vintage records (?1) and music downloads (?2) can be represented by the utility function ? = ?1?2. Initially, the price of a vintage record was $10, but it increased to $20 due to a new trend toward collecting vinyl. The price of a music download is $4 and John’s income is $240. How would you describe John’s preferences for vintage records and music downloads? The increase in the price of vintage...
John likes to run and plans to run a marathon on Sunday. He knows that his...
John likes to run and plans to run a marathon on Sunday. He knows that his friend Nigel will call him and invite him to go for a beer on Saturday night. John enjoys beer but knows if he takes a beer on Saturday he will not be able to perform so well in the marathon on Sunday. Suppose John would enjoy a utility of 5 on Saturday if he takes a beer, and 1 if he stays at home....
Frank likes to do rock climbing and it is important that his equipment be in good...
Frank likes to do rock climbing and it is important that his equipment be in good condition. Suppose the null hypothesis is H0: Frank’s rock climbing equipment is safe. -What is a type one error (false positive)? -What is a type two error (false negative)? -In this setting, which is worse?
Q9. Suppose that John spends $320 on good X and good Y; his utility function is...
Q9. Suppose that John spends $320 on good X and good Y; his utility function is given by U(X, Y) = 20 XY and that the price of X is $4 per unit while the price of Y is $8 per unit. (a) Solve for John’s optimal purchases of X and Y. (b) By how much would John’s utility change if his allowance were reduced by $1.50? (c) Redo part (a) if the price of Y is reduced, through a...
A person's preferences are represented by U=(XY)1/2 Find his Marshallian demand for x, his indirect utility...
A person's preferences are represented by U=(XY)1/2 Find his Marshallian demand for x, his indirect utility functions, his expenditure function and his Hicksian demand for good Y.
Use the table below for total utility for both Good A and Good B and calculate...
Use the table below for total utility for both Good A and Good B and calculate and plot both the marginal utility and the total utility on the same graph with the utility on the vertical axis and quantity on the horizontal axis. Assume the price of Good A is $2 and the price of Good B is $1 with an income of $12. Using the utility-maximizing rule that the marginal utility per dollar for each good must be equal,...
An agent considers good 1 and good 2 "perfect substitutes" and thus her preferences can be represented by the utility function u (x,y) = 4x + 2 y.
An agent considers good 1 and good 2 "perfect substitutes" and thus her preferences can be represented by the utility function u (x,y) = 4x + 2 y. The agent starts with $10. Use this information to answer the following questions. (a) What is the slope of this agents indifference curves (i.e. the mrs)? Hint: You do not need to use calculus if you solve for the equation of an indifference in slope-intercept form. (b) What is the maximum price at which...
1 - John, a consumer with preferences over oranges (O) and Sauerkraut (S) that give him...
1 - John, a consumer with preferences over oranges (O) and Sauerkraut (S) that give him a utility function U=ln(O) + S. a. Given that John has an allowance of I and faces prices of Po and Ps, use the Lagrangian Multiplier method to find his optimal consumption of O and S. b. Demonstrate whether Sauerkraut is a normal or inferior good for John. c. Find John’s indirect utility function. In a world where I=20, Po = 1 and Ps=2,...
John, a professor and his wife, Mary, a nurse, residence of Georgia both work in Alabama....
John, a professor and his wife, Mary, a nurse, residence of Georgia both work in Alabama. They return to Georgia on weekends where they have their permanent homes. Identify and discuss the sources of tax law applicable to John and Mary taking into account the fact that they are operating in more than one U.S. state (Georgia and Alabama). Can you please help to elaborate a statement regarding this case of taxes.
Danny likes to buy books (x1), and CDs (x2) with his monthly allowance. a)     (2) Suppose that...
Danny likes to buy books (x1), and CDs (x2) with his monthly allowance. a)     (2) Suppose that books cost $10 each and CDs cost $20 each, and Danny has $200 from his allowance to spend this month. Write down the equation of Danny’s budget line. b)     (4) Suppose Danny’s utility function is U (x1, x2) = 2x1+ x2. What can you say about Danny’s preferences for books and CDs. What is Danny’s optimal choice of books and CDs? Show the solution on...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT