The price of DVDs (D) is \(20, and the price of CDs (C) is \)10. Philip has a budget of $100 to spend on the two goods. Suppose that he has already bought one DVD and one CD. In addition, there are 3 more DVDs and 5 more CDs that he would really like to buy.

a. Given the above prices and income, draw his budget line on a graph with CDs on the horizontal axis.

b. Considering what he has already purchased and what he still wants to purchase, identify the three different bundles of CDs and DVDs that he could choose. For this part of the question, assume that he cannot purchase fractional units.

The budget equation is given by:

$P_{C}C+P_{D}D\le M$

where M: Phillip's Income

P_C: Price of CD

P_D: Price of DVD

C: Number of CD

D: Number of DVD

When the price of CD and DVD are $10 and $20, respectively, Philip income after purchasing one CD and DVD each will be:

10 x 1 +20 x 1 = 30

Thus, the budget equation for the remaining income (70=100-30) will be:

$10C+20D\le 70$

But Philip is willing to purchase 3 more CDs and 5 more DVDs, which does not satisfy the budget constraint.

The below diagram shows Philip’s willingness to purchase the total number of CDs and DVDs. At the given prices, Philip’s income should be $140, as computed below.

10 x 6 + 20 x 4 = 140

Since the remaining income after purchasing each unit CD and DVD is $70, Philip must have an extra $40 to buy 3 more DVDs and 5 more CDs.

Infinite possible bundles give the same satisfaction level on an indifference curve, but the actual possible number of bundles can be obtained according to budget constraints.

Thus, the budget equation for the remaining income will be:

$10C+20D\le 70$

The consumption bundle available is (5,3). Suppose Philips uses all his income to purchase CDs and DVDs; his budget equation will be 10C + 20D = 70.

The three combinations of bundles that satisfy the above budget equation will be (5,1), (1,3), and (3,2). It is shown by the following computation:

for (5,1): LHS = 10 x 5 +20 x 1 = 70

for (1,3): LHS = 10 x 1 +20 x 3 = 70

for (3,2): LHS = 10 x 3 +20 x 2 = 70

Where the RHS of the budget equation is 70. Thus, LHS=RHS.

Thus, the total number of CDs and DVDs which Philip can choose when his income is $100, given that he has already purchased 1 CD and 1 DVD each, will be (6,2), (2,4) and (4,3). A similar computation done in the previous step can be carried out to prove it.