a Denis is buying beer and pizza Pizza P costs 1slice and Be

a. Denis is buying beer and pizza. Pizza (P) costs $1/slice and Beer (B) costs $5/can. Denis\'s marginal rate of substitution of beer for pizza is MRS_BP = B/P. If Denis has $130 to spend, how many slices of pizza will he buy?

b. Denis is buying beer and pizza. Pizza (P) costs $1/slice and Beer (B) costs $5/can. Denis\'s marginal rate of substitution of beer for pizza is MRS_BP = P. If Denis has $100 to spend, how many cans of beer will he buy?

Solution

A)

Price of Pizza (Pp) = $1

Price of Beer (Pb) = $5

MRS_BP = B/P

Budget constraint = Pp*P + Pb*B = 130

At equilibrium,

MRS_BP = Pb/Pp

B/P = 5/1

B = 5P

Putting the values of Pp and Pb in the budget constraint we get

P + 5B = 130

Put B = 5P, we get

P + 5*5P = 130

26P = 130

P* = 5

From B = 5P we have, B* = 25

B)

MRS_BP = P

Budget constraint = Pp*P + Pb*B = 100

At equilibrium,

MRS_BP = Pb/Pp

P* = 5/1 = 5

Put the value of P, Pp and Pb in the budget constraint we get,

1*5 + 5*B = 100

5*B = 95

B* = 19 units