Chapter 10, Problem 4P

To determine

Concept introduction:

Budget Line: It is defined as the combination of all goods that a consumer can buy exhausting his all income. Formula for the budget line is:

Here,

• is the quantity of good X.
  
• is the quantity of good Y.
  
• is the total income.
  
• is the price of good X.
  
• is the price of good Y.
  

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

Or

Here,
• is the marginal utility.
  
• is the total utility.
  
• X is the quantity of any good.
• N is the number of goods.

Marginal Utility per dollar: It is the ratio of marginal utility to that of the price of a good. The formula to calculate the marginal utility per dollar is:

Here,

• is the marginal utility per dollar.
  
• is the price of good X.
  

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


Here,
• is the marginal utility of good X.
  
• is the marginal utility of good Y.
  
• is the price of good X.
  
• is the price of good Y.