Question 1

If the price of x falls,the budget constraint&#10;A)shifts outward in a parallel fashion.&#10;B)shifts inward in a parallel fashion.&#10;C)rotates outward about the x?intercept.&#10;D)rotates outward about the y?intercept.

Accepted Answer

D

Question 2

Suppose an individual's MRS (of steak for beer)is 2:1.That is,at the current consumption choices he or she is willing to give up 2 beers to get an extra steak.Suppose also that the price of a steak is $1 and a beer is 254.Then in order to increase utility the individual should

A)buy more steak and less beer.
B)buy more beer and less steak.
C)continue with current consumption plans.

B

Accepted Answer

B

Question 3

The slope of the budget constraint line is A)the ratio of the prices (p_x/p_y). B)the negative of the ratio of the prices (p_x/p_y). C)the ratio of income divided by price of y (I/p_y). D)none of these is correct.

Accepted Answer

The slope of the budget constraint line is the negative of the ratio of the prices, as the slope shows how much of y must be given up to obtain one additional unit of x. Therefore, the correct formula is -p_x/p_y.

Question 4

If an individual's utility function for coffee (x)and cream (y)is given by U(x,y)= min (x,5y),the demand function for coffee is given by A)X = I/2p_x . B)X = I/(p_x + p_y). C)X = I/(p_x + 0.2p_y). D)X = I/(p_x + p_y)².

Accepted Answer

The utility function U(x,y) = min(x, 5y) indicates a perfect complement relationship where the consumer wants 1 unit of coffee for every 5 units of cream. The demand for coffee is determined by the budget constraint I = p_xx + p_yy, and the condition x = 5y. Solving these gives x = I/(p_x + 0.2p_y).

Question 5

An individual has a utility function for tennis rackets (x)and tennis balls (y)of the form U(x,y)= min (3x,y).His or her expenditure function is given by&#10;A)   .&#10;B)   .&#10;C)   .&#10;D)   .

Accepted Answer

The utility function U(x,y) = min(3x, y) implies the consumer wants to maintain a ratio of 3 tennis rackets to 1 tennis ball. The expenditure function reflects the cost of achieving a certain utility level, considering this ratio. Therefore, the expenditure function is E = (1/3 px + py)U, which accounts for the cost of maintaining the ratio of 3x to y.

Question 6

Suppose utility is given by U(x,y)= ln x + ln y and p_x = 1,I = 10.If y must be purchased in whole units,what is the maximum price this person would pay for that good? A)1. B)5. C)10. D)20.

Accepted Answer

We can solve for the optimal bundle of goods using the Lagrangian method:

L = ln x + ln y + λ (p1x + p2y - I)

Taking partial derivatives and setting them equal to zero:

dL/dx = 1/x + λp1 = 0
dL/dy = 1/y + λp2 = 0
dL/dλ = p1x + p2y - I = 0

Solving for x and y:

x = 1/(λp1)
y = 1/(λp2)

Substituting into the budget constraint:

p1/x + p2/y = I
p1/(1/(λp1)) + p2/(1/(λp2)) = I
λp1p2(p2 + p1) = I

Solving for λ:

λ = I/(p1p2(p1 + p2))

Substituting back into the optimal bundle:

x = p2(p1 + p2)/I
y = p1(p1 + p2)/I

Since y must be purchased in whole units, the maximum value of p2 that satisfies the budget constraint is such that:

p2 = k,
where k is an integer and k <= I/p1.

Substituting back into the optimal bundle for x and y:

x = k(p1 + k)/I
y = p1(p1 + k)/I

To find the maximum value of p2, we want to maximize y, so we look at the expression for y:

y = p1(p1 + k)/I

Taking the derivative with respect to k and setting it equal to zero:

(dy/dk) = p1/I = 0
k = 0

But k can't be 0 since we are told that y must be purchased in whole units. So we plug in k = 1:

y = p1(p1 + 1)/I

Now we plug in our values for p1 and I:

y = 1/10(10 + 1) = 1/11

So the maximum price this person would pay for y is:

p2*y = 5*1/11 = 5/11

Therefore, the answer is B) 5.

Question 7

If utility is given by and p_x = 2,p_y = 3,I = 50,this person will choose A)(10,10). B)(15,6.67). C)(25,0). D)(0,50/3).

Accepted Answer

The consumer maximizes utility subject to the budget constraint $2x + 3y = 50$. The utility function $U(x, y) = x^2 + y^2$ suggests that the consumer will spend all income on the good that provides the highest utility per unit cost. Here, $x$ provides more utility per unit cost than $y$, so the consumer will choose $x = 25$ and $y = 0$.

Question 8

&#34;If an individual is to maximize the utility received from consumption,he or she should spend all available income....&#34; This statement assumes&#10;A)that saving is impossible.&#10;B)that the individual is not satiated in all goods.&#10;C)that no goods are &#34;inferior.&#34;&#10;D)that saving is impossible and that the individual is not satiated in all goods.

Accepted Answer

The statement assumes that the individual is not satiated in all goods, as it states that the individual should spend all available income to maximize utility. This implies that the individual still derives satisfaction from consuming more goods.

Question 9

Suppose that at current consumption levels an individual's marginal utility of consuming an extra hot dog is 10 whereas the marginal utility of consuming an extra soft drink is 2.Then the MRS (of soft drinks for hot dogs)-- that is,the number of hot dogs the individual is willing to give up to get one more soft drink-is

A)5.
B)2.
C)1/2.
D)1/5.

Accepted Answer

The MRS (of soft drinks for hot dogs) is determined by the ratio of their marginal utilities, which is 2/10 or 1/5. This means that the individual is willing to give up 1/5 of a hot dog to get one more soft drink. Therefore, the answer is D, 1/5.

Question 10

If an individual's indifference curve map does not obey the assumption of a diminishing MRS,then&#10;A)the individual will not maximize utility.&#10;B)the individual will buy none of good X.&#10;C)tangencies of indifference curves to the budget constraint may not be points of utility maximization.&#10;D)the budget constraint cannot be tangent to an appropriate indifference curve.

Accepted Answer

The assumption of diminishing marginal rate of substitution (MRS) is necessary for the tangency of indifference curves to the budget constraint to represent a point of utility maximization. If the MRS does not decrease as more of one good is substituted for another, then the individual may have non-standard preferences that cannot be represented by a typical indifference curve map. Therefore, the tangencies of indifference curves to the budget constraint may not necessarily be optimal points for the individual.

Question 11

An increase in an individual's income without changing relative prices will&#10;A)rotate the budget constraint about the X?axis.&#10;B)shift the indifference curves outward.&#10;C)shift the budget constraint outward in a parallel way.&#10;D)rotate the budget constraint about the Y axis.

Accepted Answer

The answer of An increase in an individual's income without...

Question 12

Suppose that an individual has a constant MRS of shoes for sneakers of : (that is,he or she is always willing to give up 3 pairs of sneakers to get 4 pairs of shoes).Then,if sneakers and shoes are equally costly,he or she will

A)buy only sneakers.
B)buy only shoes.
C)spend his or her income equally on sneakers and shoes.
D)wear sneakers only 3/4 of the time.

Accepted Answer

The answer of Suppose that an individual has a constant...

Question 13

If an individual's utility function is given by and I = 100, p_x = 1,p_y = 4,his or her preferred consumption bundle will be: A)(20,20). B)(50,12.5). C)(40,15). D)(30,15).

Accepted Answer

The answer of If an individual's utility function is given...

Deck 2: Utility Maximization and Choice