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 two goods substitutes or complements? Justify answers mathematically (ie., Use derivatives). (c) Suppose that px = $ 1 and m = $ 10. Write her demand function and inverse demand function for good y. Draw the function on a graph (include the intercept (s)). (d) Suppose that initially px = py = $ 1 and m $ 10. Then, the price of good x increases to px' = $ 2. Calculate the compensating variation and equivalent variation of the price change (round your answers to two decimal places).
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Anna's utility function is given by U (r.y) = (r + 3) (y + 2),
where...
3 Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y}...
3 Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y} The prices of the two goods are Px for good x and Py for good y. If her monthly income is $M, Derive her uncompensated demand function for good x Derive her uncompensated demand function for good y Derive the cross-price effects and show that the two goods are complementary goods.
Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y} The...
Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y} The prices of the two goods are Px for good x and Py for good y. If her monthly income is $M, Derive her uncompensated demand function for good x Derive her uncompensated demand function for good y Derive the cross-price effects and show that the two goods are complementary goods.
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...
A consumer buys two goods, good X and a composite good Y. The utility function is...
A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X,Y) = In3XY. The price of X is Py, the price of Y is Py and Income is I. 1) Derive the demand equation for good X. ( 5 marks) 2) Are the two goods X and Y complements or substitutes? Why? ( 5 marks) 3) Suppose that I=$10 and suppose that initially the Px = $1 and subsequently Px falls and...
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...
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...
Suppose your utility function is U (x, y) = 2 ln(2) + 4y c) Given PX...
Suppose your utility function is U (x, y) = 2 ln(2) + 4y c) Given PX - 1. Py = 2, and M =5. Find the elasticity of demand (own-price elasticity) for good x -- is good x ordinary or Giffen? Edit View Insert Format Tools Table 12pt Paragraph B I VART :
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (d) The initial income is $576, initial prices are...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (2) (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (2) c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (2) (d) The initial income is $576,...
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...
A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X,Y) = In3XY. The price of X is Py, the price of Y is Py and Income is I. 1) Derive the demand equation for good X. ( 5 marks) 2) Are the two goods X and Y complements or substitutes? Why? ( 5 marks) 3) Suppose that I=$10 and suppose that initially the Px = $1 and subsequently Px falls and...
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...
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...
Suppose your utility function is U (x, y) = 2 ln(2) + 4y c) Given PX - 1. Py = 2, and M =5. Find the elasticity of demand (own-price elasticity) for good x -- is good x ordinary or Giffen? Edit View Insert Format Tools Table 12pt Paragraph B I VART :
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
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