Mid-term考卷.doc

2010-2011年度中级经济学期中考试试卷
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Part Ⅰ(True or False) 1.5 points each
1. If the production function is f(x, y) = min{2x + y, x + 2y}, then there are constant returns to scale （规模收益不变）.
2. If the value of the marginal product of factor x （要素x的边际产量）increases as the quantity of x increases and the value of the marginal product of x （要素x的边际产量值） is equal to the wage rate, then the profit-maximizing amount of x is being used.
3. If the price elasticity of demand （需求价格弹性） for a good is -1, then doubling the price of that good will leave total expenditures on that good unchanged.
4. The average cost curve is decreasing with production quantity, if the production technology is decreasing returns to scale.
5. If preferences are quasilinear (拟线形), then the slope of the Engel curve for any good will decrease as income increases.
6. It is possible for a consumer to satisfy the weak axiom of revealed preference （弱显示性偏好公理） but violate the strong axiom of revealed preference.
7. If somebody is buying 10 units of x and the price of x falls by $4, then that person’s net consumer’s surplus （消费者剩余） must increase by at least $40.
8. If the equation for the demand curve is q = 50 - 4p, then the ratio of marginal revenue （边际收益） to price is constant as price changes.
9. If someone has the utility function U = 1,000 + 2 min {x, y}, then x and y are perfect complements （完美互补） for that person.
10. A person with the utility function U(x, y) = y + x2 has convex preferences （凸性偏好）.
Part Ⅱ(Single Choice) 2 points each
1. If a simultaneous （同时） and equal percentage （同比例） decrease in the use of all physical inputs leads to a larger percentage decrease in physical output, a firm’s production function is said to exhibit
a. decreasing returns to scale.
b. constant returns to scale.
c. increasing returns to scale.
d. diseconomies of scale.
2. The price elasticity of demand is the same thing as the negative of the
a. slope.
b. reciprocal of slope.
c. the first derivative of the demand function.
d. reciprocal of slope times the ratio of price to quantity.
e. all of the above.
3. If a profit-maximizing firm’s marginal product of labor equals 1 ton of output, while the marginal product of capital equals 7 tons of output and the use of capital is priced at $14 per unit, then
a. the price of labor must be $2.
b. the price of labor must be $7.
c. the price of labor must be $14 as well.
d. none of the above is true.
4. Mike consumes two commodities, x and y, and his utility function is min{x + 2y, y + 2x}. He chooses to buy 8 units of good x and 16 units of good y. The price of good y is $.50. What is his income?
a. $32 b. $40 c. $24 d. $16
e. Mike’s income cannot be found unless the price of x is given too.
5. Being a price taker （价格接受者） in a market means that the seller
a. charges each consumer the maximum that she will be3 able to pay for the product.
b. has no choice but to charge the equilibrium price that results from the market supply and demand curves.
c. takes her price from her average total cost curve.
d. sells her products at different prices to different customers.
6. When prices are ($4, $2), Tomoko chooses the bundle (9, 18), and when prices are ($1, $2), she chooses the bundle (8, 14).
a. The bundle (8, 14) is revealed preferred to the bundle (9, 18) and she does not violate WARP.
b. She violates SARP（强显示性偏好公理） but not WARP（弱显示性偏好公理）.
c. The bundle (9, 18) is revealed preferred to the bundle (8, 14) and she does not violate WARP.
d. She violates WARP. e. None of the above.
7. A competitive firm produces output using three fixed factors and one variable factor. The firm’s short-run production function is q = 524x - 4x2, where x is the amount of variable factor used. The price of the output is $3 per unit and the price of the variable factor is $12 per unit. In the short run, how many units of x should the firm use?
a. 130 b. 32 c. 25 d. 65 e. None of the above.
8. A competitive firm has the short-run cost function c(y) = 2y3 - 16y2 + 128y + 10. The firm will produce a positive amount in the short run if and only if the price is greater than
a. $192. b. $48. c. $99. d. $96. e. $95.
9. A firm has the short-run total cost function c(y) = 9y2 + 144. At what quantity of output is short-run average cost minimized（短期平均成本最小）?
a. 4 b. 16 c. 0.75 d. 3 e. None of the above
10. Madonna buys only two goods. Her utility function is Cobb-Douglas（科布道格拉斯）. Her demand functions have which of the following properties?
a. Her demand for one of the two goods does not depend on income.
b. Her demand for neither good depends on income.
c. Her demand for each of the goods depends on income and on the prices of both goods.
d. Her demand for each of the two goods depends only on her income and on the price of
that good itself.
e. One of the goods is an inferior good and the other is a normal good.
11. Katie Kwasi’s utility function is U(x1, x2) = 2(ln x1) + x2. Given her current income and the current relative prices, she consumes 10 units of x1 and 15 units of x2. If her income doubles, while prices stay constant, how many units of x1 will she consume after the change in income?
a. 20 b. 18 c. 10 d. 5
e. There is not enough information to determine how many.
12. Let A stand for the bundle (7, 9), B stand for the bundle (10, 5), and C stand for the bundle (6,6). When prices are (2, 4), Betty chooses C. When prices are (12, 3) she chooses A.
a. A is directly revealed preferred to B.
b. is indirectly revealed preferred to B.
c. C is directly revealed preferred to A.
d. B is directly revealed preferred to A.
e. None of the above.
13. The following can be said about the income and substitution effects （收入和替代效应） of a price increase on the demand for a good whose price rose:
a. The former is always positive and the latter is always negative.
b. Both can be either positive or negative.
c. While the latter is always negative, the former can be either positive or negative.
d. While the former is always negative, the latter can be either positive or negative.
e. The former can at times be negative, but it will never overwhelm the latter.
14. Bernice’s preferences can be represented by the utility function, U(x, y) = min{x, y}. She faces prices ($2, $1), and her income is $12. If prices change to ($3, $1), the compensating variation （补偿变化）
a. equals the equivalent variation.
b. is $2 greater than the equivalent variation.
c. is $2 smaller than the equivalent variation.
d. is $1 greater than the equivalent variation.
e. There is not enough information to determine which variation is larger.
15. If there are only two goods, an increase in the price of good 1 will increase the demand for
good 2
a. if and only if the price elasticity of demand for good 2 is greater than 1 in absolute value（绝对值）.
b. whenever both goods are normal goods.
c. only if the two goods are perfect substitutes.
d. never.
e. None of the above.
16. If you have an income of $40 to spend, commodity 1 costs $2 per unit, and commodity 2 costs $10 per unit, then the equation for your budget line can be written
a. x1 + 5x2 = 20. b. x1/2 + x2/10 = 40. c. (x1 + x2)/12 = 40.
d. 3x1 + 11x2 = 41. e. 12(x1 + x2) = 40.
17. Ernie’s utility function is U(x, y) = 32xy. He has 10 units of good x and 8 units of good y.
Waldo’s utility function for the same two goods is U(x, y) = 3x + 5y. Waldo has 9 units of x and 13 units of y.
a. Waldo prefers Ernie’s bundle to his own, but Ernie prefers his own bundle to Waldo’s.
b. Each prefers the other’s bundle to his own.
c. Neither prefers the other’s bundle to his own.
d. Ernie prefers Waldo’s bundle to his own bundle, but Waldo prefers his own bundle to
Ernie’s.
e. Since they have different preferences, there is not enough information to determine who
envies whom.
18. If the demand curve for a good is upward sloping（向上倾斜）, then which of the following statements must be true?
1. The good is inferior.
2. The substitution effect is in the opposite direction to the income effect.
3. The substitution effect overwhelms the income effect.
a. 1 only. b. 2 only c. 1 and 2 only. d. 2 and 3 only. e. 1, 2, and 3.
19. The marginal rate of substitution （边际替代率） between food and shelter for a given point on an indifference curve
a. is equal to the absolute value of the slope of the indifference curve at that point.
b. is equal to the rate at which the consumer is willing to exchange the two goods in the marketplace.
c. reflects the relative values the consumer attaches to the two good.
d. is described, in part, by each of the above statements.
20. When the prices were ($5, $1), Vanessa chose the bundle (x, y) = (6, 3). Now at the new prices, (px, py), she chooses the bundle (x, y) = (5, 7). For Vanessa’s behavior to be consistent with the weak axiom of revealed preference, it must be that
a. 4py < px.
b. px < 4py.
c. 5py < px.
d. py = 5px.
e. None of the above.

Part Ⅲ (Problems) 55 points Totally
1. (10 points.)The preferences of a consumer can be represented by: U= Min {2x1, 3x2}, the price of good 1 is $3, the price of good 2 is $2, and the total income is $60.
a. Explain using a graph how the optimum consumption bundle will change if the price of good 1 is $1.
b. Compute the substitution and income effects (of Slutsky effects) in the consumption of good 1.
2. (10 points.)Ray Starr has the utility function U(x, y) = y/(100 - x).
a. Does Ray prefer more to less of both goods?
b. Draw a diagram showing Ray’s indifference curves corresponding to the utility levels
U = 1/2, U = 1, and U = 2.
c. How can you describe the set of indifference curves for Ray?
d. If the price of x is $1 and the price of y is $1, find Ray’s demand for x as a function of
his income and draw a diagram showing his Engel curve for x.
3. (13 points.)Beth works for the federal government and her job is to analyze the market for oranges.
a) Suppose she found that the demand function is Q=50-5p, where Q is the quantity of oranges demanded and p is the ongoing price per pound. Graph the demand curve(remember to label the intercepts).
b) The federal government is considering imposing some restrictions on the production of oranges because of environmental concerns. The current price is 4$ per pound, but after the restrictions it would increase to 5$ per pound. What is the consumer surplus before and after the restrictions? What is the loss in consumer surplus due to the restrictions? If a consumer advocacy group would try to bribe Beth to convince federal authorities that the restrictions should not be imposed, how much would they be willing to spend?
c) Now suppose that Beth doesn’t know the demand function, but she observed that when the price of oranges grew from 4$ to 4.05$ per pound, the quantity of oranges demanded fell from 30 to 29 pounds. What is the elasticity of demand? Using this estimate, by how much would demand decrease if the government were to impose the quantity restrictions and raise the price from 4$ to 5$ per pound?
4. (12 points.)The demand curve for ski lessons is given by D(pD)=100-2pD and the supply curve is given by S(ps)=3ps.
a.What are the equilibrium price and quantity?
b.A tax of $10 per ski lesson is imposed on consumers. Write an equation that relates the price paid by demanders to the price received by suppliers. Write an equation that states that supply equals demand.
c.Solve these two equations for the two unknowns ps and pD. With the $10 tax, what is the the equilibrium price pD paid by consumers and the total number of lessons given?
d.A senator from a mountainous state suggests that although ski lesson consumers are rich and deserve to be taxed, ski instructors are poor and deserve a subsidy. He proposes a $6 subsidy (补贴) on production while maintaining the $10 tax on consumption of ski lessons. How do the effects for suppliers or for demanders of this policy compare to the effects of a tax of $4 per lesson?

2009-2010年度下学期期中考试试卷
学号： 姓名：

Part Ⅰ(True or false)
1. 2. 3. 4. 5. 6. 7.

8. 9. 10.

Part Ⅱ (Single choice)

1. 2. 3. 4. 5. 6. 7.

8. 9. 10. 11. 12. 14.

15. 16. 17. 18. 19. 20.
Part Ⅲ (Problems)