Cesar earns $60/week while attending UIC and consumes two goods: Beer (B) and Fo

Question

Cesar earns $60/week while attending UIC and consumes two goods: Beer (B) and Food (F). Beer costs $1/can and Food costs $3/lb. Cesar has the utility function U(B,F) = 2BF (with B in cans, F in lbs). This means his marginal utility from consuming beer is 2F and the marginal utility of consuming food is 2B.

Question 1: How many lbs of food (F) will Cesar purchase each week?

Question 2: What is his utility each week from consuming his utility maximizing bundle of B and F?

Question 3: The price of food drops to $1/lb. How much food does Cesar now consume each week?

Question 4: What is the size of the substitution effect in Question 3, going from $3/lb to $1/lb, in lbs of food?

Explanation / Answer

1)B+3F=60

Marginal utilities are 2F and 2B respectively.

For maximum utility, 2F=2B

F=B

4F=60

F=15 lb, B=15 cans

2)U=2BF=2*15*15=450

3)F+B=60

2F=2B

F=30lb

Substitution effect=dB/dPg=15/-2=-7.5 cans/$

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