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Tutorial 5: Consumer choice (cont.)

 

The Budget Constraint

In the first part of  Tutorial 5 we learned that a consumer seeks a bundle of goods, a market basket, the consumption of which generates the maximum  happiness (utility). Graphically, such a basket is found on the indifference curve as far from the origin as possible. Of course these goods are not free, and one's money income is not limitless. So one's goal of maximizing utility is subject to the constraint imposed by one's budget. In this tutorial we will develop a model of the consumer's budget constraint.

Suppose a consumer has a fixed periodic money income, represented by I, and must pay a price, Pf, for each unit of food, and a price, Pc, for each unit of clothing. The consumer's budget can be represented by the identity shown in equation (1),

Equation 1 - The consumer's budget constraint.,

where Pf*F indicates the amount of money income I spent on food, and Pc*C is the amount of money income spent on clothing. Equation (1) simply indicates that the sum of spending on food and clothing must equal the amount of money income available.

To add this constraint to our model, we need to rewrite it in a form that can be plotted in (F, C) space. We can do that by simply rewriting equation (1) so that C is the dependent variable.
 

Manipulation of consumer's budget constraint to derive an equation.

...subtracting Pc*C from both sides.

...multiplying both sides by -1.
 

...dividing both sides by Pc.
 
 

...rearranging terms.

Now we have an equation that can be plotted in (F, C) space, where C is the dependent variable, F is the independent variable, and I, Pf, and Pc are parameters with known values:

Equation 2 - the consumer's budget constraint with C as a function of F.

Let's read equation (2). First of all, C(F) tells us that the amount of clothing one can buy depends on the amount of food one has purchased. The y-intercept term, I/Pc, indicates the amount of clothing that may be purchased, given income and the price of clothing, if one buys no food (i.e., if F = 0). The slope term, Pf/Pc, indicates the amount of clothing that must be given up in order to free up enough money to buy one more unit of food.

Let I = $80 per period, Pc = $2 per unit, and Pf = $5 per unit. Given these parameter values, equation (2) would be written

Equation 2 with numerical data supplied for I, Pc, and Pf.,

which is an equation of a straight line (e.g., y = a +b*x), where a = I/Pc, and b = -Pf/Pc. A graph of this equation is shown as B1 in Figure 6 below. The vertical intercept is 40 units/t. It is the amount of clothing that may be purchased given an income of $80 and a price of clothing equal to $2 per unit (e.g., 40 = $80/$2). How is the horizontal intercept, 16, calculated? [Hint: The horizontal intercept, 16, is the amount of food that may be purchased with an income of $80 and a price of food of $5 per unit.]

 

Figure 6

Figure 6 - the budget constraint.

 

The slope is equal to 5/2 = 2.5 units. It tells us that one must give up 2.5 units of clothing in order to free up enough cash to buy one unit of food. How's that? Well, a unit of clothing is priced at $2. So, "selling off" 2.5 units of clothing would bring you $5:

2.5 * $2 = $5,

which is the price of a unit of food. Thus, selling 2.5 units of clothing gives you enough money to buy 1 unit of food.

 

Changes in Parameter Values Top of page.

Now let's explore what happens to the budget line when income or the prices of the goods changes.

Increases (decreases) in income result in an outward (inward) shift in the budget line parallel to the original. This is because more (less) income expands (contracts) the set of affordable baskets of food and clothing. On the graph, as income rises (falls), both the vertical intercept, I/Pc, and horizontal intercept, I/Pf, rise (fall). Why? Because each intercept term shows the maximum amount of a good one can by given one's income and the price of the good. Thus as income rises (falls), the maximum amount of a good one can afford to buy rises (falls), assuming the prices of the goods remain constant.

A decrease (increase) in the price of food lowers (raises) the slope of the budget line (Pf/Pc) by raising (lowering) the horizontal intercept (I/Pf), leaving the vertical intercept (I/Pc) unaltered. Similarly, decreases (increases) in the price of clothing raise (lower) the slope of the budget line by raising (lowering) the vertical intercept, leaving the horizontal intercept unaltered. In both cases, a decrease (increase) in price expands (contracts) the set of affordable baskets of food and clothing.

 

Now it's time to "do the thing".

Click on the following link to download the Consumer Choice Workbook. Work through Tutorial 5 Questions 4 and 5a - 5f to improve your understanding of the budget constraint model.

Return here when you have finished.

Need help downloading the Excel file?

 

Special Issues: In-kind Gifts and Product Rationing Top of page.

There are several other factors that alter the consumer's budget constraint, two of them are in-kind gifts and product rationing. As the name implies, in-kind gifts are units of a good, food for example, that are given to the consumer free of charge. They serve to expand the amount of goods that may be purchased by providing the consumer a certain number of units without the sacrifice of any income. 

Contrariwise, when a good is rationed, the consumer is barred from buying beyond the ration limit regardless the amount of income the consumer has. This serves to contract the amount of goods that may be purchased by limiting the quantities of one good available.

To see how gifts and rationing affect the budget constraint, work through the rest of Tutorial 5 Question 5 now.

 

Now it's time to "do the thing".

Click on the following link to download the Consumer Choice Workbook. Work through Tutorial 5 Questions 5g - 5h to continue improving your understanding of the budget constraint model.

Return here when you have finished.

Need help downloading the Excel file?

 

Now we are ready to put both of the parts of this consumer choice model together. We will use the completed model to analyse how consumer's choose to maximize the satisfaction they receive from the consumption of a bundle of goods, subject to the constraint imposed on their choice by their income and the prices of the goods they buy.