Economics
Economics
5th Edition
ISBN: 9781319066604
Author: Paul Krugman, Robin Wells
Publisher: Worth Publishers
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Chapter 10, Problem 7P
To determine

Concept introduction:

Budget line: it is defined as the combination of all goods that a consumer can purchase, exhausting all his income. The formula for the budget line is:

    Economics, Chapter 10, Problem 7P , additional homework tip  1

Here,

  • Economics, Chapter 10, Problem 7P , additional homework tip  2is the quantity of good X.
  • Economics, Chapter 10, Problem 7P , additional homework tip  3is the quantity of good Y.
  • Economics, Chapter 10, Problem 7P , additional homework tip  4is the total income.
  • Economics, Chapter 10, Problem 7P , additional homework tip  5is the price of good X.
  • Economics, Chapter 10, Problem 7P , additional homework tip  6is the price of good Y.

Marginal Utility: It is defined as the change in the total utility due to a change in an additional unit of a good. It may be diminishing, increasing, or constant.

    Economics, Chapter 10, Problem 7P , additional homework tip  7or
    Economics, Chapter 10, Problem 7P , additional homework tip  8

Here,

  • Economics, Chapter 10, Problem 7P , additional homework tip  9is the marginal utility.
  • Economics, Chapter 10, Problem 7P , additional homework tip  10is the total utility.
  • X is the quantity of any good.

Maximizing utility Principle: Maximizing utility in the case of two goods states that the equilibrium level of consumption of the two goods for a consumer is achieved when the Marginal Utility per dollar of two goods are equal, provided that the marginal utility of money is constant. This means that the following conditions must be fulfilled:

    Economics, Chapter 10, Problem 7P , additional homework tip  11

Here,
  • Economics, Chapter 10, Problem 7P , additional homework tip  12is the marginal utility of good X
  • Economics, Chapter 10, Problem 7P , additional homework tip  13is the marginal utility of good Y
  • Economics, Chapter 10, Problem 7P , additional homework tip  14is the price of good X
  • Economics, Chapter 10, Problem 7P , additional homework tip  15is the price of good Y

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1. Lisa has $48 per week set aside for coffees (x) and lunches (z). The price of coffee is $4 and lunches are $6. What is Lisa's budget line equation (with z on the left-hand side)? Graph the budget line, and show how it changes when the price of lunches rise to $8 (including intercepts). What is the new budget line equation? 2. Suppose utility for a consumer of movies (x) and golf (z) is U = 20x0.420.5. The consumer has set aside $1000 to consumer movies and golf for a year. a. If the price of movies is $20 and the price of golf is $40, what is the utility-maximizing consumption of movies and golf? b. Show the optimal consumption bundle on a graph, showing a budget line (with intercepts), a tangent indifference curve, and the optimal choice. 3. Sam has set aside $480 for entertainment this month, which is golf (x) and/or bowling (z). A round of golf is $40 and a night of bowling is $30. His utility function is U = 3x + 2z. a. What is his MRS? b. Solve for the optimal choice of golf…
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