In 1991, good x cost $5 and good y cost $1. They now cost $9 and...
In 1991, good x cost $5 and good y cost $1. They now cost $9 and $5 respectively. In 1991 the consumption bundle of x and y was 4 x’s and 5 y’s. It is now 9 x’s and 7 y’s. Calculate the Laspeyres index of current prices relative to 1991 prices rounded to one decimal place. (Remember the Laspeyres index uses the old quantities for weights.)
| 0.5 |
| 2.4 |
| 2.5 |
| 2.2 |
| None of the above. |
Homework Answers
sum of PnQo/sum of PoQoConsider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a,...
Consider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a, b, c are constants. The prices of good x and y is denoted by pX and pY respectively. The income is denoted by m. Good z is provided by the government free of cost but the quantity of good z provided by the government depends on the consumption of good x and y chosen by the consumer. For example, if in equilibrium, the consumer...
) A consumer's utility function is given by: U(x,y) = 10xy Currently, the prices of goods x and y...
) A consumer's utility function is given by: U(x,y) = 10xy Currently, the prices of goods x and y are $3 and $5, respectively, and the consumer's income is $150 . a. Find the MRS for this consumer for any given bundle (x,y) . b. Find the optimal consumption bundle for this consumer. c. Suppose the price of good x doubles. How much income is required so that the Econ 201 Beomsoo Kim Spring 2018 consumer is able to purchase...
Bob's utility function is u(x,y)=xy where x is her consumption of good 1 and y is...
Bob's utility function is u(x,y)=xy where x is her consumption of good 1 and y is her consumption of good 2. Denote Bob's income by m, and denote the prices of good 1 and 2 by p1 and p2 respectively. let m=120, p1=20, p2=5, graph Bobs budget line.
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed...
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed when income falls if x and y are normal goods? Draw a budget constraint (before the income decrease) and a convex utility curve that corresponds to the optimal consumption bundle. Draw a new budget constraint (after income falls) and a new convex utility curve that corresponds to the optimal consumption bundle. Has the amount of x and y consumed increased or decreased due to...
Question 5 [8] 5.1. With reference to the indifference theory with good Y on the vertical axis and good X on the horizo...
Question 5 [8] 5.1. With reference to the indifference theory with good Y on the vertical axis and good X on the horizontal axis, graphically illustrate a change in consumer equilibrium due to a change in income. Remember to label the diagram correctly and to indicate the "income consumption curve clearly. 5.2. Referring to the graph above and consumer equilibrium, indicate what will happen to the budget line should there be an increase in the price of good X (on...
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , avail...
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , available in arbitrary non-negative quantities (so the the consumption set is R 4 +). A typical consumption bundle is therefore a vector (q, r, x, y), where q ≥ 0 is the quantity of good Q, r ≥ 0 is the quantity of good R, x ≥ 0 is the quantity of good X, and y ≥ 0 is the quantity of...
5. Country Y, a small country, does not have a copy paper industry but does have...
5. Country Y, a small country, does not have a copy paper
industry but does have vast forested areas that are not otherwise
being utilized. A study by the country’s development agency finds
that the production of copy paper could generate producer surplus
(and hence increase Country Y’s welfare). However, high initial
production costs currently prevent domestic firms from entering the
market. According to the study, the market today and the market in
the future look as depicted in the...
5. Melissa’s utility function for the bundle (x,y) is U(x,y)=xy. Price of good x is p1=1, price of good 2 is p2=2 and income m=10. If the price of good 1 goes up to p1=2, but the rest remain the same....
5. Melissa’s utility function for the bundle (x,y) is U(x,y)=xy. Price of good x is p1=1, price of good 2 is p2=2 and income m=10. If the price of good 1 goes up to p1=2, but the rest remain the same. Derive: Total effect? Substitution effect? Income effect?
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
A social planner is considering two items for the state budget: good 1 - education, X,...
A social planner is considering two items for the state budget: good 1 - education, X, and good 2 - health care, xz. Her preferences over the two items are given by the following function: U(x1,x2) = 3x2 + x2 The prices of education and healthcare are pz = $2 and P2 = $1; the state's budget I = $50. a) Solve for the marginal rate of substitution between the two goods (provide number). b) Find optimal consumption of X1...
Homework 3 Chapter 5: Demand 1. What happens to the amount of x and y consumed when income falls if x and y are normal goods? Draw a budget constraint (before the income decrease) and a convex utility curve that corresponds to the optimal consumption bundle. Draw a new budget constraint (after income falls) and a new convex utility curve that corresponds to the optimal consumption bundle. Has the amount of x and y consumed increased or decreased due to...
Question 5 [8] 5.1. With reference to the indifference theory with good Y on the vertical axis and good X on the horizontal axis, graphically illustrate a change in consumer equilibrium due to a change in income. Remember to label the diagram correctly and to indicate the "income consumption curve clearly. 5.2. Referring to the graph above and consumer equilibrium, indicate what will happen to the budget line should there be an increase in the price of good X (on...
5. Country Y, a small country, does not have a copy paper
industry but does have vast forested areas that are not otherwise
being utilized. A study by the country’s development agency finds
that the production of copy paper could generate producer surplus
(and hence increase Country Y’s welfare). However, high initial
production costs currently prevent domestic firms from entering the
market. According to the study, the market today and the market in
the future look as depicted in the...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
A social planner is considering two items for the state budget: good 1 - education, X, and good 2 - health care, xz. Her preferences over the two items are given by the following function: U(x1,x2) = 3x2 + x2 The prices of education and healthcare are pz = $2 and P2 = $1; the state's budget I = $50. a) Solve for the marginal rate of substitution between the two goods (provide number). b) Find optimal consumption of X1...
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