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If the utility function u(x1,x2) =min(x1,x2) represents a consumer's preferences, then another utility function,v(x1,x2) = min(x1,x2)+ 2 also represents her preferences
True.
U(x1,x2) and V(x1,x2) will represent the same preferences, since the operations of taking square root, adding a constant and taking the square of a function are all monotone transformations.
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A consumer considers apple pie and ice cream perfect complements. Then, his preferences are homothetic?
True.
By definition, all perfect substitutes, perfect complements and Cobb-Douglas functions are all homothetic preferences.
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If marginal products are declining this means that the underlying technology exhibits decreasing returns to scale.
False.
Diminishing marginal productivity and returns to scale are two entirely different concepts that do not correlate to one another.
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Carrie and Don both have Cobb-Douglas preferences over corn (good 1) and dairy (good 2). Carrie's utility function is X1^C X2^1-c and Don's x1^d x2^1-c.
If Carrie spends a higher proportion of her income on corn than Don does c>d?
True.
Both equations are proportionate to one another. Should Carrie spend more income on core, then the Cobb-Douglas preferences over corn will be higher.
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At any output level the short run average total cost curve and the short run average variable cost curve must slope in the same direction.
False.
Average total cost curve and short run average variable converge.
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For a Giffen good, the negative income effect dominates the positive substitution effect as the price of the good decreases
True.
In the Giffen goods situation, the income effect dominates, leading people to buy more of the goods, even as its price rises.
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If preferences were given by u(x1;x2) =x21x2; then both goods must be normal goods
True. This is a Cobbs-Douglas function and both equations
x1= 2/3 m/p1
and
x2 = 1/3 m/p2
Have income elasticities of one. Thus both are normal goods.
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A tangency condition is always both sufficient and necessary condition for utility maximization
False.
In general the tangency condition is only a necessary condition for optimality, but not sufficient.
Optimality should satisfy two conditions (1) the tangency condition and (2) the budget line.
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More than one utility function can represent a person's preferences and two consumers with the same utility function can have different preferences
True.
Any monotonic transformation of a utility function is also a function that can represent the same preference
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In the case of quasi-linear utility functions, the indifference curves are horizontal translate of each other
True.
In the case of a utility function that is linear in good 1
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If a utility function is homothetic then the Engel curve is a straight line from the origin.
True.
If preferences are homothetic, it means that when income is scaled up or down by t>0;the demanded bundle,(x1;x2) scales up or down by the same amount, i.e., the new bundle is(tx1;tx2)
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12. Income effect is zero if the utility function is quasi-linear
True.
Because in the case of a quasi-linear preferences, the entire change in demand is due to the substitution effect (because a shift in income causes no change in demand for good 1, for instance, when preferences are quasi-linear)
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Substitution effect is always positive if we have perfect complement good
False.
There is no substitution effect in the case of perfect complements
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Income effect = total effect, if we have perfect substitute good.
False.
The total effect is due to substitution effect in case of perfect substitution, i.e., there is no income effect
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If a consumer's preferences are not transitive, then they can not be represented by a utility function.
True.
Actually, for a preference relation to exist, the first three axioms of consumer preference should be satisfied. In particular, preferences should be complete, transitive, and reflexive.
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For a Giffen good, the negative income effect dominates the positive substitution effect as the price of the good decreases
True. Slutsky equation
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Mary always consumes one slice of cheese cake with a cup of coffee. If coffee costs more than before, Marie's consumption of cheese cake must fall
True.
There is no substitution effect in such a case. The total effect on the consumption of the good is due to income effect.
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Angela considers Coke and Pepsi as perfect substitutes. If the price of Coke goes up, Angela will be strictly worst off.
False. If the price of Coke goes up, Angela will spend her income on Pepsi.
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Indifference curves will never intersects
True.
- An indifference curve represents all points where different combinations
- of consumption yield the exact same level of utility (satisfaction). Different indifference curves are based on different levels of utility.
- A graph will show the equal levels of utility. A higher utility will simply mean an indifference curve that is farther away from the origin
- that a lower utility. It's simply a matter of what the graph is designed to show.
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Convexity of indifference curves ensures that the consumers will never specialize in one good
True. Averages are preferred to extremes
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A proportional increase in the prices and income will leave the consumer on the same budget constraint
True. See equation.
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Indifference curves exhibit diminishing marginal rate of substitution
False. Only convex indifference curves exhibit diminishing MRS.
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For homothetic preferences, the income o§er curve will always be a ray, i.e., a straight line through the origin
True. See Slutsky equation.
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The demand curve of a Giffen good is, like any other good, downward sloping
True. See Slutsky.
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If a consumer has perfect complements preferences, then neither of the two goods she consumes can be a luxury good
True. No luxury good has a perfect complement.
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A consumer always chooses the consumption bundle that maximizes her marginal utility given her budget constraint
False. max utility given the budget constraint
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The SE and IE reinforce each others, i.e., have the same sign, if the good is normal
True. See Slutsky equation.
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Two firms employ the same factors of production to produce the same product. Their technologies both exhibit constant returns to scale. Thus, if the factors that Firm 1 uses are exactly twice the amount of those Firm 2 uses, Firm 1 must produce twice the output that Firm 2 produces
False.
Although both firms have technologies that exhibit CRS, we do not know whether they are using the same technology. The statement would be true if they are
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If the marginal cost curve lies above the average cost curve, then the average cost curve must be sloping upward
True. See graph.
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The short-run cost function is always greater than the long-run cost function
False. The short-run cost function and the long-run cost function can coincide
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Increasing returns to scale is incompatible with the law of diminishing marginal product.
True. Returns to scale is a long-run phenomenon, while diminishing marginal product is a short-run one.Therefore, both of them can not hold for a firm at the same time
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If the average product of an input is falling, then the average product must exceed the marginal product at that input level
True. Graph
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If the production function exhibits increasing returns to scale, average cost must be decreasing
True. Graph
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Knowing a Firm's production function is sufficient information for determining the firm's efficient combination of inputs?
- False. The cost function should be known too. The firm's problem is min C = w1x1 + w2x2
- subject to f(x1,x2) = y
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If marginal cost is rising, then average cost must also be rising
False. MC attains its minimum before the AC.
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When Marginal cost curve attains its minimum, the marginal product is at its maximum
True.Graph
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A profit maximizing firm will always minimize cost
True.
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When MC is increasing, AVC must be increasing too
False. See the graph
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