Question

A college student has 2 options for meals: eating at the dining hall for $6 per meal, or eating a Cup O' Soup for $1.50 per meal. His weekly food budget is $60.
a. Draw the budget constrain showing the trade-off between dining hall meals and Cups O' Soup. Assuming that he spend equal amounts on both goods, draw an indifferencecurve showing the optimum choice. Label the optimum as point A.
b. Suppose the price of a Cup O' Soup now rises to $2. Using the diagram from part (a), show the consequences of this change in price. Assume that our student nowspend only 30 percent of his income on dining hall meals. Label the new optimum as point B.
c. What happened to the quantity of Cups O' Soup consumed as a result of this price change? What does this result say about the income and substitutions effects?Explain.
d. Use points A and B to draw a demand curve for Cup O' Soup. What is this type of good called?

Answer 1

(a) Here know that the Budget or Price line indicates the purchasing combination of two goods is when the prices of those two goods and the consumer's income are constant. In our solution, the budget constraint for a college student can be drawn by calculating the horizontal and vertical intercepts' values. The value of vertical intercept is calculated as shown below:

Here,

The food budget \(=\$ 60\) Price of the meal at the dining hall \(=\$ 6\)

Then,

$$ \begin{aligned} \text { Value of vertical intercept } &=\frac{\text { Food Budget }}{\text { Price of the meal at the dining hall }} \\ &=\frac{\$ 60}{\$ 6} \\ &=10 \end{aligned} $$

Here,

The food budget \(=\$ 60\)

Price of the cups \(\mathrm{O}^{\prime}\) soup \(=\$ 1.50\)

Value of horizontal intercept \(=\frac{\text { Food Budget }}{\text { Price of Cups O'soup }}\)

Then,

$$ \begin{array}{l} =\frac{\$ 60}{\$ 1.50} \\ =40 \end{array} $$

By using the above values, we can draw a student budget constraint as shown below:

In the above diagram, the \(\mathrm{BL}\) is the student's budget line. If the student assumed to spending equal amounts on both goods like meals at the dining hall and cup O' soup, then his budget line is tangent to his indifference curve (IC), is at point \(A\). This point \(A\) indicates the optimum consumption of 5 meals at the dining hall and 20 cups of \(O\) ' soups.

(b) In our solution, if the price of Cups O' soup increases to \(\$ 2,\) then the value of the horizontal intercepts changes as follow:

Here,

The food budget \(=\$ 60\)

Price of cups \(\mathrm{O}^{\prime}\) soup \(=\$ 2\)

$$ \begin{aligned} \text { Value of horizontal intercept } &=\frac{\text { Food Budget }}{\text { Price of Cups O'soup }} \\ &=\frac{\$ 60}{\$ 2} \\ &=30 \end{aligned} $$

As a result the, the budget constraint BL shifts inwards to the left to \(\mathrm{BL}_{1}\) as shown in the following diagram.

In the above diagram, the new optimum point shown at \(\mathrm{B}\) is on the new indifference curve. This is due to the increased price level of cups of O' soup from \(\$ 1.50\) to \(\$ 2 .\) At this level, the student's optimum combination is 3 meals at the dining hall and 21 cups of O' soups.

Now, if the student is assuming to spend only \(30 \%\) of his food budget \((\$ 60)\) on dining hall meals, then the amount will spent on meals at dining hall is,

$$ \begin{array}{l} \text { Spent Amount on meals at dining hall }=\text { Total Budget } \times \frac{\left(\begin{array}{l} \text { spending percentage on } \\ \text { meals at dining hall } \end{array}\right)}{100} \\ =\$ 60 \times \frac{30}{100} \\ =\$ 60 \times 0.3 \\ =\$ 18 \end{array} $$

So, the student will consume on dining hall meals is,

Here,

Total amount \(=\$ 18\)

Price of meals at dining hall \(=\$ 6\)

Then,

$$ \begin{aligned} \text { The consumption on dining hall meals } &=\frac{\text { Total spent amount }}{\text { Price of meal at dinind hall }} \\ &=\frac{\$ 18}{\$ 6} \\ &=3 \end{aligned} $$

This new combination of goods having 3 dining hall meals is showed as point \(B\) on indifference curve \(\mathrm{IC}_{1}\), is shown as below:

(c) We drew the consumption of 3 meals at the dining hall on indifference curve \(I C_{1}\), the bundle \(B\)

will constitute an increased quantity of Cups O' soups. Thus, the quantity consumed cups O' soups increases due to a price increase. The substitution effect of the price rise makes the consumer buy fewer soups, and the income effect makes the student buy more soups. From in student's point of view, the cups O' soups are the inferior good. Thus he will purchase more cups. Hence, the income effect is negative and stronger than the substitution effect.

(d) We already discussed and indicate that the good Cups O' soup is a Giffen good. Since there is a direct relation between the quantity demanded of the good and its price. Here, increasing-price leads to an increase in the demand for the good. Thus the demand curve for Giffen good is an upward slope. Using the points \(A\) and \(B\), we can draw the demand curve for Cups O' soup as shown in the below diagram.

In the above diagram, we used the values like \(P\) and \(P_{1}\) instead of normal value. The upper portion of the diagram shows the optimal consumption bundle \(A\), and \(B\) on \(B L\) and \(B L_{1},\) and the lower portion of the diagram shows the quantity of cups O' soup purchased at the price levels that correspond to the budget lines. At point \(A, O Q\) is the cups \(O\) ' soups demanded and at \(O P_{1}\) price is at point \(B\); the demanded quantity of cups O' soups is \(\mathrm{OQ}_{1}\). Hence the demand curve, which has an upward slope, is \(D\) is by joining both points \(A\) and \(B\).