Eco 2144c (microeconomic theory i) midterm exam 2

 

 

ECO 2144C (Microeconomic Theory I) Midterm Exam 2

MULTIPLE CHOICE.   (50 points – 2 points per question)
Circle the letter of the choice that best completes the statement or answers the question.   If you
need to change your answer, very clearly cross out your previous answer, and circle and put an arrow identifying the correct answer.   If the distinction between your old and new answers is not clear, no points will be awarded.

1.  Jeong’s uncompensated demand for pizza is given by Q = 30 – 2p.   Jeong’s marginal willingness to pay function is

A)    -2.
B)    30-2p. C)    30-2Q. D)    15-.5Q.

2.  Sandy’s current consumer surplus for candy is $20.   Candy is a normal good for her.   When her income increases and the price of candy remains unchanged, her consumer surplus will

A)    decrease. B)    increase.
C)    remain the same.
D)    Not enough information.

3.  Compensating variation for an increase in the price of a good is

A)    the change in utility resulting from the increase in price.
B)    the change in consumer surplus resulting from a price increase.
C)    the maximum amount of money a consumer would pay to avoid the price increase.
D)    the minimum amount of money a consumer would accept to voluntarily accept the price increase.

4.  Compensation variation and equivalent variation will be closer to each other when

A)    the budget share is greater. B)    the income effect is greater.
C)    the income elasticity is smaller. D)    the income elasticity is greater.

5.  A quota will reduce consumer welfare when

A)    the quota is greater than the amount purchased without the quota. B)    the quota is on a good with high income elasticity.
C)    the quota is less than the amount purchased without the quota. D)    Quotas always reduce consumer welfare.

6.  If a person supplies more hours of labour in response to a wage increase, then

A)    the income effect equals the substitution effect.
B)    the substitution effect is greater than the income effect. C)    the person is not maximizing utility.
D)    the income effect is greater than the substitution effect.

7.  A backward-bending labour supply curve could possibly imply which of the following cases?

A)    Leisure is a normal good. B)    Leisure is an inferior good.
C)    Leisure is a normal good at low wages and inferior at high wages. D)    None of the above.

8.  If workers are in the backward-bending section of their labour supply curves, then an increase in the income tax rate will

A)    decrease tax revenue and increase the number of hours worked. B)    decrease tax revenue and decrease the number of hours worked. C)    increase tax revenue and decrease the number of hours worked. D)    increase tax revenue and increase the number of hours worked.

9.  Homer’s Donut Shoppe has the production function, q = 10L + 20L2 – 5L3.   The marginal product of labour is

A)    MP = 10 + 20L – 5L2
B)    MP = 10L
C)    MP = 10 + 20L
D)    MP = 10 + 40L – 15L2

10. Average productivity will fall as long as

A)    it is less than marginal productivity. B)    marginal productivity is falling.
C)    the number of workers is increasing. D)    it exceeds marginal productivity.

11. Suppose an analyst attempts to estimate a consumer’s willingness to pay for a policy that lowers the price of childcare.   The willingness to pay should be measured as

 

A)    BCA to BCB. B)    BCafter to BCA.
C)    BCafter to BCbefore. D)    BCafter to BCB.

12. If marginal productivity is increasing, then total product is

A)    increasing at a constant rate.
B)    decreasing at an increasing rate. C)    increasing at a decreasing rate. D)    increasing at an increasing rate.

13. To say that isoquants are convex is to say that

A)    capital and labour are perfect substitutes. B)    there are constant returns to scale.
C)    the marginal rate of technical substitution falls as labour increases.
D)    labour, but not capital, is subject to the law of diminishing marginal returns.

14. One way to explain the convexity of isoquants is to say that

A)    as labour increases and capital decreases, MP    and MP    both rise. B)    as labour increases and capital decreases, MP    and MP    both fall.
C)    as labour increases and capital decreases, MP    falls while MP    rises. D)    as labour increases and capital decreases, MP    rises while MP    falls.

15. Isoquants that are downward-sloping straight lines imply that the inputs

A)    must be used together in a certain proportion. B)    are imperfect substitutes.
C)    are perfect substitutes. D)    cannot be used together.

16. Returns to scale refers to the change in output when

A)    specialization improves.
B)    labour increases holding all other inputs fixed. C)    capital equipment is doubled.
D)    all inputs increase proportionately.

17. Suppose the production of VCRs can be represented by the production function,   =   .   . .
Which of the following statements is (are) TRUE?

A)    Capital and labour can be substituted for one another.
B)    The production function has decreasing returns to scale.
C)    The marginal productivity of labour falls as labour increases in the short run. D)    All of the above.

18. Suppose the production function for a certain device is q = L + K.   If neutral technical change has occurred, which of the following could be the new production function?

A)    q = 5L + K B)    q = L + 5K C)    q = 5(L + K)
D)    All of the above are possible.

19. The cost of waiting two months for health care to address a debilitating problem in Canada is most accurately described as

A)    an opportunity cost. B)    no real cost.
C)    an explicit cost.
D)    an accounting cost.

20. Suppose the short-run production function is q = 10L.   If the wage rate is $10 per unit of labour, then AVC equals

A)    q.
B)    10/q. C)    1.
D)    q/10.

21. In the short run, the point at which diminishing marginal returns to labour begin is the point at which the marginal cost curve

A)    peaks.
B)    is upward sloping.
C)    is downward sloping. D)    bottoms out.

22. A specific tax of $1 per unit of output will affect a firm’s

A)    average total cost, average variable cost, average fixed cost, and marginal cost. B)    average total cost, average variable cost, and marginal cost.
C)    average total cost, average variable cost, and average fixed cost. D)    marginal cost only.

K

 

 

3                                      C

2                             B                             q = 6000

1                    A                             q = 3,000

q = 1,000
0                                                                                      L
1       2       3

23. The figure above shows the long-run expansion path.   The long-run average cost curve will be

A)    downward sloping. B)    vertical.
C)    upward sloping. D)    horizontal.

24. The slope of the isocost line tells the firm how much

A)    more expensive a unit of capital is relative to a unit of labour.
B)    capital must be reduced to keep total cost constant when hiring one more unit of labour. C)    the isocost curve will shift outward if the firm wishes to produce more.
D)    capital must be increased to keep total cost constant when hiring one more unit of labour.

25. If the marginal rate of technical substitution for a cost minimizing firm is 10, and the wage rate for labour is $5, what is the rental rate for capital in dollars?

A)    10
B)    1
C)    0.5
D)    2

TRUE/FALSE.   (5 points)
For the following, answer “True” or “False” and briefly explain why.   Label and explain clearly
any diagrams.

26. (2 points) The length of the short-run is the same for all firms.

False.   Firms differ in their ability to change the amount of capital they employ.   Therefore, the short-run period is likely different for firms in different industries and can even vary within industries.

 

27. (3 points) The “Law of Diminishing Marginal Returns” could also be termed the “Law of
Increasing Marginal Costs”.
 

True.   Since     =   

  
 

in the short run, the fact that    
 

eventually declines means that
    must eventually increase.

SHORT ANSWER.   (45 points)
Write your answer in the space provided.   Show all your work.   Label and explain clearly any
diagrams.

28. (7 points) Suppose a person’s utility for leisure (N) and consumption (Y) is expressed U = YN
and this person has no non-labour income.   How many hours per day will the person work?

  =      where w is the wage rate and H is hours worked.

  = 24 − 

Thus, through substitution,    =     =        24 −   .

Choose the optimal H by maximizing    =        24 −    subject to H and setting the derivative equal to zero.

   =    24 −    +      −1 =  24 − 2      =    24 − 2    = 0

Thus,    = 12  hours of work per day.

 

 

 

 

29. (8 points) Consider the short-run production function,   = 5  $ −  %/3.   At what level of L
does diminishing marginal returns begin?   At what level of L does diminishing returns begin?

     = 10   −  $

Diminishing marginal returns means that the        is falling.   This begins when the        is at its maximum.   This occurs when the amount of labour employed is such that the slope of the
      is zero.

(     = 0 = 10 − 2
(

Thus,   = 5 is the point at which diminishing marginal returns begin.

Diminishing returns means that increases in labour cause output to fall.   This begins when the amount of labour employed is such that the        is zero.

     = 10   −  $  = 0 when   = 10.

Thus,   = 10 is the point at which diminishing returns begin.

30. (15 points total) Ed’s utility function for bacon (B) and coffee (C) is U(B,C) = BC.   Last week, the price of bacon was $5 per package and the price of coffee was $2.50 per cup.   This week, the price of coffee rose to $3.00 per cup, but the price of bacon remained the same.   Ed’s income is $120.

a.      (5 points) Derive Ed’s uncompensated demand function for coffee.

  ) = * and    + = 
 

Thus,
 
 ,-
 ,.
 
=  +  =   –
)     .
 
⇒  + * =  )  

  =    * +      = 2        ⇒        ,       =  0
$  –

 

 

b.     (1 point) How much coffee did Ed consume last week?
 
  =  0
$  –
 
=  1$
$ $.2
 

= 24 cups of coffee

 

c.      (5 points) Calculate his change in consumers surplus resulting from the change in the price of coffee.
 
%
∆  4 = − 5      ) ,      6  ) = −
 
%  6  )
5
 
3
= −6089 ) :
 

= −60 ln3 − ln2.5  = −10.94

$.2
 
2  $.2    )
 
2.5

 

 

d.     (2 points) Derive Ed’s uncompensated demand function for bacon.

0                                        0
From part a,   + * =  )   = $  ⇒ *  + ,    = $

 

e.      (1 point) How much bacon did Ed consume last week?
 
* =  0
$  .
 
=  1$  = 12 packages
$ 2 

 

f.      (1 point) What was Ed’s utility from consuming bacon and coffee last week?

  = *  = 24 × 12 = 288

31. (15 points total) Erica is starting a new restaurant in Ottawa.   While she plans to do the cooking herself, she will need to employ workers and machinery to produce food.   She estimates her production function as    = 15    .$2 .   Erica is able to accumulate $10,000 to finance the business.   Workers cost $10 per hour and the rental price of capital is $50 per unit.

a.   (8 points) If Erica wishes to produce the most output with the finances available, how much labour and capital should she employ?

A                                       A
    =   and      B = B
 

So,
 

  

  C
 
=  B  = 
          D
 
= 1
2
 
⇒ 50  = 40 

  =    + E  ⇒ 10,000 = 10  + 50  = 50

Thus,   = 200  and    = 160.

 

b.  (1 point) How much food does Erica produce using this bundle of labour and capital?

  = 15     .$2  = 15  200    .$2 160  = 9,025 units

 

c.   (6 points) Does this bundle of capital and labour also minimize the costs?   Explain using a graph.

Yes.   See slide 17 of my notes for Chapter 7.

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