Chapter 4 Appendix: The Calculus of Utility Maximization and Expenditure Minimization 1. Mark's utility function over...
Chapter 4 Appendix: The Calculus of Utility Maximization and Expenditure Minimization
1. Mark's utility function over football tickets (F) and
baseball tickets (B) can be expressed as U(F,B) = F + 5B. a. What
is his marginal utility of football tickets?
b. What is his marginal utility of baseball tickets?
c. What is his marginal rate of substitution MRSFB?
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Chapter 4 Appendix: The Calculus of Utility Maximization and
Expenditure Minimization
1. Mark's utility function over...
1. SHORT ANSWER QUESTIONS 1. Explain why utility maximization requires that a consumer's budget is allocated...
1. SHORT ANSWER QUESTIONS 1. Explain why utility maximization requires that a consumer's budget is allocated so that the marginal utility per dollar of expenditure is the same for each good. 2. Theresa likes to talk on the telephone. We can represent her preferences with the utility function U(B,J)12B 24J, where B and J are minutes of conversation per month with Bill and Jackie respectivcly. What is the formula for her indiffcrencc curve to get U units of utility (that...
1 Expenditure Minimization (10 points) Sally the Sleek's preferences can be described by the utility function...
1 Expenditure Minimization (10 points) Sally the Sleek's preferences can be described by the utility function U(z, y)/1024. Prices are Pz 2 and py 4. (a) If Sally initially consumed 10 units of a and 5 units of y, how much could she save if she consumed 8 more (small units of z and kept utility constant?1 Therefore, can it be optimal to consume the bundle (10,5)? (4) in order to attain that utility? (4) round to two decimal places...
1. Suppose a consumer has the utility function over goods x and y u(x, y) =...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
QUESTION 4 Reshad's preferences over goods 1 and 2 are given by the following utility function:...
QUESTION 4 Reshad's preferences over goods 1 and 2 are given by the following utility function: U(q1, q2)q2Select all that applies: O a His preferences satisfy "more is better O b. His preferences fail the transitivity assumption C. His indifference curves are downward sloping His preferences are convex D e. He dislikes good 1 Marginal rate of substitution for his preferences is given by MRS12
1. Solve the maximization problem: mary = 29.252.0,75 s.t.100 – 2.11 - 4.02 = 0 (1)...
1. Solve the maximization problem: mary = 29.252.0,75 s.t.100 – 2.11 - 4.02 = 0 (1) 2. Suppose that Jeff cares only about basketball (B) and football (F). His utility function is U = B04F0.6The price of a basketball ticket is $5, and the price of a football ticket is $10. Jeff has a budget of $100. What is the solution to Bruce's maximization problem? 3. Find level set and tangent line at (1,1) of the function: y = x...
1. Solve the maximization problem: maxy = 20,25,975 s.t.100 - 201 - 4x2 = 0 (1)...
1. Solve the maximization problem: maxy = 20,25,975 s.t.100 - 201 - 4x2 = 0 (1) 2. Suppose that Jeff cares only about basketball (B) and football (F). His utility function is U =B04F06 The price of a basketball ticket is $5, and the price of a football ticket is $10. Jeff has a budget of $100. What is the solution to Bruce's maximization problem? 3. Find level set and tangent line at (1,1) of the function: y = x...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U = XL2, SO MUx = L2 and MUL = 2xL.The individual may work up to 24 hours per day at wage rate, w = $10 per hour, and he has non-labor income of $50 per day. The price of x, px, is $5. (a) Find the utility-maximizing x and L. (b) Show that at the utility- maximizing quantities of x and L, the consumer's...
4. consider the following utility functions a) for each of these utility function what is the equation of an indifferenc...
4. consider the following utility functions
a) for each of these utility function what is the equation of an
indifference curve ?
c) for each utility function show weather the function exhibits
the diminishing rate of substitution property
d) do the above utility function represent the same preference
ordering? why or why not?
c) Suppose the price of beer doubles, but the price of pizza and Tom's income stay the same. How much beer is Tom consuming as a percentage...
3. Nora enjoys fish (F) and chips(C). Her utility function is U(C, F) = 2CF. Her...
3. Nora enjoys fish (F) and chips(C). Her utility function is U(C, F) = 2CF. Her income is B per month. The price of fish is Pf and the price of chips is P. Place fish on the horizontal axis and chips on the vertical axis in the diagrams involving indifference curves and budget lines. (a) What is the equation for Nora’s budget line? (b) The marginal utility of fish is MUf = 2C and the Marginal utility of chips...
1. SHORT ANSWER QUESTIONS 1. Explain why utility maximization requires that a consumer's budget is allocated so that the marginal utility per dollar of expenditure is the same for each good. 2. Theresa likes to talk on the telephone. We can represent her preferences with the utility function U(B,J)12B 24J, where B and J are minutes of conversation per month with Bill and Jackie respectivcly. What is the formula for her indiffcrencc curve to get U units of utility (that...
1 Expenditure Minimization (10 points) Sally the Sleek's preferences can be described by the utility function U(z, y)/1024. Prices are Pz 2 and py 4. (a) If Sally initially consumed 10 units of a and 5 units of y, how much could she save if she consumed 8 more (small units of z and kept utility constant?1 Therefore, can it be optimal to consume the bundle (10,5)? (4) in order to attain that utility? (4) round to two decimal places...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
QUESTION 4 Reshad's preferences over goods 1 and 2 are given by the following utility function: U(q1, q2)q2Select all that applies: O a His preferences satisfy "more is better O b. His preferences fail the transitivity assumption C. His indifference curves are downward sloping His preferences are convex D e. He dislikes good 1 Marginal rate of substitution for his preferences is given by MRS12
1. Solve the maximization problem: mary = 29.252.0,75 s.t.100 – 2.11 - 4.02 = 0 (1) 2. Suppose that Jeff cares only about basketball (B) and football (F). His utility function is U = B04F0.6The price of a basketball ticket is $5, and the price of a football ticket is $10. Jeff has a budget of $100. What is the solution to Bruce's maximization problem? 3. Find level set and tangent line at (1,1) of the function: y = x...
1. Solve the maximization problem: maxy = 20,25,975 s.t.100 - 201 - 4x2 = 0 (1) 2. Suppose that Jeff cares only about basketball (B) and football (F). His utility function is U =B04F06 The price of a basketball ticket is $5, and the price of a football ticket is $10. Jeff has a budget of $100. What is the solution to Bruce's maximization problem? 3. Find level set and tangent line at (1,1) of the function: y = x...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U = XL2, SO MUx = L2 and MUL = 2xL.The individual may work up to 24 hours per day at wage rate, w = $10 per hour, and he has non-labor income of $50 per day. The price of x, px, is $5. (a) Find the utility-maximizing x and L. (b) Show that at the utility- maximizing quantities of x and L, the consumer's...
4. consider the following utility functions
a) for each of these utility function what is the equation of an
indifference curve ?
c) for each utility function show weather the function exhibits
the diminishing rate of substitution property
d) do the above utility function represent the same preference
ordering? why or why not?
c) Suppose the price of beer doubles, but the price of pizza and Tom's income stay the same. How much beer is Tom consuming as a percentage...
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