Brad needs to pick up beer for his super cool party tonight. He can pick between

Question

Brad needs to pick up beer for his super cool party tonight. He can pick between PBR brand beer (P) or Renier brand beer(R). Brad has $100 to spend, PBR costs $2/can, and Renier costs $3/can. For Brad, PBR and Renier are the same thing (ie, he has no preference of one over the other), and as such his utility is denoted by: U(P, R) = P + R a) What is Brad's best feasible bundle? b) Graphically depict the best feasible bundle (make sure to label your axes, include a B.C., and an indifference curve(s)). c) Holding constant your income and the price of PBR, what will be the new optimal bundle if Renier is now half off (per bottle)? d) Explain how the optimal consumption bundle will change if the price of PBR is the same as the price of Renier?

Explanation / Answer

Answer(a)

The equilibrium feasible bundle of goods exists at the point where

MUx/Px=MUy/Py=MUm……………………………….(1)

Here X=P Brand and Y=R Brand(the print is not clearly visible so referring the second brand as R Brand) and M= Money, Mu is the Marginal Utility, Px and Py is the price of X and Y respectively

Now, From the given Utility function

MUx= R and MUy=P( using the rules of partial differentiation)

Now putting the values as known in eqn (1) above

R/2=P/3=100

Or R/P=2/3…………..(2)

From 2

R=2P/3

Now we know that this has to be put equal to $100 to exhaust the amount

2P +3R=100 and R=2P/3…………………(3)

So

P=25 and R= 16.67 or 16(whole)

Thus, the optimum combination is 25 units of P and 16 units of R

Part(c)

If the Price of R halfs keeping everything constant

Py=1.5 Putting this in equation 1

We get R=4P/3………………..(4)

Putting 4 in equation 2P+1.5R=100 we get

P=37.5 (or 37) and R=50

Optimum combination is thus 37 units of P and 50 units of R

Part (d)

If the Price of P is also $3 then eqn 2 yield

R=P…………(5)

Now

3R+3P=100

Or 6P=100

Or P=16.67 and since R=P from (5) R=16.67

Thus, the optimum combination is 16 and 16 for both brands.

Part b

(1)The X-axis here is the R brand and Y axis is the PBR Brand.

(2) Put different combinations of P and R such that 2P and+3R=100, this gives us the IC curve(Convex to the origin; values can be added to give it an apt shape)

(3) The budget line tells us that if rand spends all amount on P he can buy 50 units of P and 0 units of Y(0,50) and if he spends all amount on R he buys 0 units of P and 33.33 units of R(33.33,0). Joining these two points we get the budget line.

The point of tangency of IC and Budget line gives us the equilibrium. IN this case this occurs at the point E where 25 units of P and 16 units of R are purchased.

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