Ture or False. Please Explain 1. Ambrose’s utility function is U(x,y) = x + 4y^(

Question

Ture or False. Please Explain

1. Ambrose’s utility function is U(x,y) = x + 4y^(1/2). The price of x is $1 and the price of y is $2. If his income rises from $100 to $150, his consumption of y increases by more than 10% but less than 50%.

2. Millie’s utility function is U(x, y) = min{x, y}. She maximizes her utility subject to a budget constraint. The price of x is the same as the price of y. If the price of x rises and the price of y and her income remain constant, then her consumption of y will certainly decrease.

3. George has $49 which he decides to spend on x and y. Commodity x costs $5 per unit and commodity y costs $11 per unit. He has the utility function U(x, y) = 3x2 + 6y2 and he can purchase fractional units of x and y. George will choose

a.

only y.

b.

some of each commodity but more x than y.

c.

only x.

d.

some of each commodity but more y than x.

e.

equal amounts of the two commodities.

4. Jane’s utility function is U(x, y) = x + 2y, where x is her consumption of good X and y is her consumption of good Y. Her income is $2. The price of Y is $2. The cost per unit of X depends on how many units she buys. The total cost of x units of X is the square root of x.

a.

The bundle (1/4,3/4) is Jane’s utility maximizing choice, given her budget.

b.

The bundle (1,1/2) is Jane’s utility maximizing choice, given her budget.

c.

Given her budget, Jane would maximize her utility by spending all of her income on good X.

d.

Given her budget, Jane would maximize her utility by spending all of her income on good Y.

e.

None of the above.

a.

only y.

b.

some of each commodity but more x than y.

c.

only x.

d.

some of each commodity but more y than x.

e.

equal amounts of the two commodities.

Explanation / Answer

1) false. because here preferences are quasi concave so consumption of y does not depend on income.

2) true, because both goods are complementory i.e they are used together. so, with rise in price of X, consumption of Y will certainly decrease.

3) here goods are perfect substitute of each other. and PX < PY. so, george will consume only good X.

so, correct option is C.

4) here goods are perfect substitute of each other.

MRS= 1/2

so, if MRS>PX /PY

then jane will consume only good X

so, if MRS<PX /PY

then jane will consume only good Y.

so, correct option is E.

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