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The above result makes sense, because x commodity is a necessity and hence its demand function is independent of income M however that is not the case for commodity y.
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what about y*？
Consider the quasilinear utility function u(x, y) = 47x + y. Assuming...
d @ See page 78 06 Question (2 points) In addition to finding the optimal bundles...
d
@ See page 78 06 Question (2 points) In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). 1st attempt See Hint Consider the quasilinear utility function u(x, y) =...
Suppose that a consumer’s utility function is U(x,y)=xy＋10y. the marginal utilities for this utility function are...
Suppose that a consumer’s utility function is U(x,y)=xy＋10y. the marginal utilities for this utility function are MUx=y and MUy=x＋10. The price of x is Px and the price of y is Py, with both prices positive. The consumer has income I. (this problem shows that an optimal consumption choice need not be interior, and may be at a corner point.) Assume first that we are at an interior optimum. Show that the demand schedule for x can be written as...
This question explores some features of the quasilinear utility function. Avi’s utility function is ?(?, ?)...
This question explores some features of the quasilinear utility function. Avi’s utility function is ?(?, ?) = 4?1/2 + ?. Barry’s utility function is ?(?, ?) = ? + 3?1/3. Derive Avi’s demand functions for goods x and y. What must be true of Px for her to be at a corner solution? Which good would not be consumed under this condition? (10 points) Now assume an interior solution and graph Avi’s income consumption curve. (3 points) Derive Barry’s demand...
1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R....
1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R. Suppose the agent's wealth w is large enough that good 3 is demanded in non-zero quantities. Do not normalize the price of good 3 for this problem 1. Find the agent's Hicksian demand for each good. (Hint: first use the fact that goods 1 and 2 are optimally demanded in the same quantity. Then use the fact that bang for the buck for the...
3) A consumer's utility function is u(x,y)22 (a) Find the consumer's optimal choice for x, y...
3) A consumer's utility function is u(x,y)22 (a) Find the consumer's optimal choice for x, y as functions of income I and (b) Sketch the demand curves for x, y as functions of income I when prices prices pa,Py. (Be careful!) are p 16,Py 2. (Be careful!)
how to find indirect utility function here? Jeanette has the following utility function: U-ain(x) + b*In(y), where...
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where I and y are the two goods she consumes. The price of good r is p ,. The price of good y is Py. Her income is m. (a) Write her maximization problem and find her demand functions for the two goods. Is it always possible to have an interior solution? Justify your answer. (b) Are the two goods ordinary or giffen? Are the...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y}...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (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.p.m). Show all of your work and circle your final answers. (7...
d
@ See page 78 06 Question (2 points) In addition to finding the optimal bundles given prices and income, utility maximization can be used to find individual demand functions at any prices and income. Setting up the problem and solving it are the same, except that the prices of each good and the income will be left in variable form (economists call these parameters or exogenous variables). 1st attempt See Hint Consider the quasilinear utility function u(x, y) =...
1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R. Suppose the agent's wealth w is large enough that good 3 is demanded in non-zero quantities. Do not normalize the price of good 3 for this problem 1. Find the agent's Hicksian demand for each good. (Hint: first use the fact that goods 1 and 2 are optimally demanded in the same quantity. Then use the fact that bang for the buck for the...
3) A consumer's utility function is u(x,y)22 (a) Find the consumer's optimal choice for x, y as functions of income I and (b) Sketch the demand curves for x, y as functions of income I when prices prices pa,Py. (Be careful!) are p 16,Py 2. (Be careful!)
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (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.p.m). Show all of your work and circle your final answers. (7...
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