karls preferences over hamburger (h) and beer (b) are described by the utility f

Question

karls preferences over hamburger (h) and beer (b) are described by the utility function U(h,b)=min(2h,3b). his monthly income is M dollars and he only buys these two goods out of his income. denote the price of hamburgers by Ph and beer by Pb.

A. derive Karls demand curve for beer as a function of exogenous variables (ie income, prices) hint draw his indifferece curves and budget constraint and think about what must be true at his optimal bundle.

B. Which affects karls consumption of beer more: a one dollar increase in Ph or one dollar increase in Pb

Explanation / Answer

Given: Ph, Pb, I
U=min(2H;3B)

2H=3B
2H=3B
H=3B/2=1.5B
B=2H/3
I=HPh+BPb = 1.5BPh+BPb = B(1.5Ph+Pb)
B = I / (1.5Ph+Pb)

Price of hamburgers will affect consumption of beer more (because of higher factor in (1.5Ph+Pb) part of Marshallian demand equation).

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