Question

The price of DVDs (D) is $20 and the Price of CDs (C) is $10. Phillip has a budget of $100 to spend on goods.

A). Given the above prices and income, Write and equation for Philips budget line and draw his budget line on a graph with CDs on the horizontal axis. Also calculate the slope of his budget line.

B). List all the market bundles(baskets) of DVDs and CDs that he could choose. For this part of the question, assume that he cannot purchase fractional units.

C). If philips utility function is U(D,C)=C D^2, which bundle is most preffered?

D). If phillips utility function is U(D,C)= C^2 D, which bundle is most preffered?

Answer 1

Philips budget equation can be given as follows

Phillips can always spend less than equal to budget

100<=20D+10C

Slope of budget line is price ratio of D and C

CD is on horizontal axis and DVD is on vertical axis

Slope is Price of CD/Price of DVD=-10/20=-1/2

Negative sign means as Price of CD increases Consumption of CD decreases similarity for DVD

Assuming all the income is exhausted on CD and DVD then we can buy 5 DVDs and 0 CD =(0,5) ; (2,4); (4,3); (6,2); (8,1); (10,0)

If the Philips utility is U(C,D)=CD^2

We know at equilibrium slope of budget line and slope of indifference curve is same

Slope of indifference curve =MRS=MUx/MUy

MUx=dU/dC=D^2 and MUd=dU/dD=2CD

MRS=D/2C

Slope of line =modulus of slope of budget line =|0.5|

D/2C=0.5

D=C

Now using this equality into budget equation we get

100=20D+10C=30D

D=3.33 and C=3.33

Most preferred bundle if no fraction of goods are allowed then (D,C)=(3,4) because this bundle is close to (3.33,3.33)

If U(C,D)=C^2D

MRS=2CD/C^2=2D/C=1/2

4D=C

Using this equality into budget equation we have

100=20D+10C=60D

D=1.67 and C=6.67

therefore most preferred bundle will be (2,6)