2Z03: Practice Questions for Midterm 2
中级微观经济学代考 Consider Dave, who has a utility function u(w) = 0.5w + 1. Suppose that Dave is facing the same two gamblesas Which of the following is true?
1)Kurthas a utility function v(w) = w 2 over wealth and faces the choice between two alternative His current wealth is 0. 中级微观经济学代考
Gamble 1 is based on the throw of a fair coin: if the outcome is heads he receives $20, otherwise he receives $5.
Gamble 2 is based on the throw of a fair six-sided die. If the outcome is 1 or 6 he receives $18. If the outcome is 2 or 5 he receives $16. If the outcome is 3 or 4 he receives $3.5. Which of the following is true?
a.Kurtis willing to pay more money to play Gamble 1 than Gamble 2.
b.Kurtis indifferent between taking Gamble 1 or Gamble 2.
c.Theexpected value of Gamble 1 is higher than the expected value of Gamble 2.
d.Kurtwould rather receive $13 with certainty than participate in Gamble 2.
e.None of theabove
2)Consider Dave, who has a utility function u(w) = 0.5w + 1. Suppose that Dave is facing the same two gamblesas Which of the following is true?
a.Daveis willing to pay more money to participate in Gamble 1 than Gamble 2
b.Daveis indifferent between taking Gamble 1 and Gamble 2
c.Dave’s expected utility from Gamble 1 is higher than his expected utility of Gamble2
d.Davewould prefer to receive $13 with certainty than to play Gamble 2
e.Morethan one of the above 中级微观经济学代考
3)Which of the following utility functions would express risk-neutral preferences of an expected utility maximizer, where w represents income received withcertainty?
a.u(w) = 2 +2w2
b.u(w) = 4 +2w
c.u(w)=w1/2
d.Morethan one of the above
e.None of theabove
4)Max has utility from wealth given by u(w) = w1/2. He owns a lottery ticket for a prize of $70, Max is aware that the probability of winning the prize is one in a thousand, otherwise the ticket is worthless. Among the following amounts, which is the minimum amount of money that Max would accept in exchange for his ticket, assuming his current wealth is 0?
a.8cents
b.80cents
c.8dollars
d.12dollars
e.Maxwould not accept any of the above amounts
5)Bob is an expected utility maximizer, with u(w) = w3/2 his utility from having w dollars with certainty. 中级微观经济学代考
He is considering buying the lottery ticket from Among the following amounts, which is the maximum amount of money that Bob is willing to pay for Max’s ticket, assuming his current wealth is 1000?
a.$192
b.$585
c.$219
d.$700
e.Bobwouldnot buy Max’s ticket at any of the above prices
6)Mary has utility from wealth given by u(w) = 2w. What is the maximum amount of money she would be willing to pay for Max’sticket?
a.$7
b.$70
c.70cents
d.$700
e.Themaximumamount she would be willing to pay is not listed above.
7)Threeagents have the following utility functions for wealth:
Agent 1:u1(w) = √w
Agent 2:u2(w) = w4
Agent 3:u3(w) = ln w
Each of them has initial wealth $30 and faces a gamble where they could win or lose $15 with equal probability.
Which of the following numbers is closest to Agent 3’s expected utility from the gamble? a. 0.04
a.0.7
b.2
c.3.4
d.5.8
8)Considerthe three agents from the earlier Rank them according to their risk aversion with Agent i ≻ Agent j meaning Agent i is more risk-averse than Agent j. 中级微观经济学代考
a.Agent 1 ≻ Agent 2 ≻ Agent 3
b.Agent 1 ≻ Agent 3 ≻ Agent 2
c.Agent 2 ≻ Agent 1 ≻Agent 3
d.Agent 3 ≻ Agent 1 ≻Agent 2
e.Agent 3 ≻ Agent 2 ≻Agent 1
9)Consider the three agents from the earlier question. Which ones would prefer to take the gamble to keeping their initialwealth?
a.Agent 1
b.Agent 2
c.Agent 3
d.Two out of the three
e.All three
10)ConsiderAgent 1 from the earlier Which of the following is closest to his certainty equivalent of the gamble?
a.33
b.30
c.28
d.8
e.5
11)A firm uses 8-bit chips (input 1) and 16-bit chips (input 2) to produce calculators. A calculator can be produced using two 8-bit chips or one 16-bit chip. Which of the following production functions describesthe firm’s technology for producing calculators?
a.f(x1,x2) = (x1)(2x2)
b.f(x1, x2) = Axa1 xb2
c.f(x1, x2) = min{ax1, bx2}
d.f(x1, x2) = ax1 + bx2
e.f (x1, x2) = x1x2
12)At Monde Green Lawn Service lawn mowers and labor are used to produce cut grass. A lawn mower cannot cut grass without a labourer and a labourer cannot cut grass without a lawn mower. Which of the above graphs best represents the isoquants for this firm’s technology?
a.Graph(a)
b.Graph(b)
c.Graph(c)
d.Graph(d)
e.None of theabove
13)A firm has the production function y = 2x1/2x1/3. Assume w1 = $10 and w2 = $15. How much of 1 2 input 1 is the profit maximizing firm using when total costs equal $2, 500? 中级微观经济学代考
a. x1 = 150
b.x1=175
c.x1=200
d.x1=225
e.None of theabove
14)Asassistant vice president in charge of production for a computer firm, you are asked to calculate the cost of producing 200 computers. The production function is y = min x1, 2x2 where x1 and x2 are the amounts of two factors The price of x1 is $34 and the price of x2 is $16. What is your answer?
a.$3,600
b.$3,800
c.$4,200
d.$7,200
e.$8,400
15)A competitive firm uses two inputs, x1and x2. The production function is f (x1, x2) = √x1√x2. 中级微观经济学代考
The price of x1 is $16 and the price of x2 is $ To maximize profits, the company spends $512 on input x1. How much of input x2 must it be using?
a.128units
b.256units
c.512units
d.640units
e.Cannot be determined without furtherinformation
16)A firm produces output with the technology y = K1/2L3/4 where K is number of hours of capital (machines) input and L is the number of hours of labour input. The firm can freely choose both K and L. If the price of capital is $6 per machine-hour and the price of labor is $18 per person-hour, the cheapest way to produce any level of output requires using capital and labor in the ratio
17)Afirm has a production function y = 3x1 + x2. If the factor prices are $12 for factor 1 and $3 for factor 2, what is the minimum cost of producing 60 units of output?
a.$1,170
b.$1,080
c.$360
d.$180
e.$90
18)Theproduction function is y(L, K) = 2L1/2K1/2, where L is the number of units of labour and K is the number of units of capital If the cost of labour is $36 per unit and the cost of capital is $4 per unit, then the lowest total cost of producing 48 units of output will be
a.$144
b.$432
c.$288
d.$388
e.$576
19)Bob produces birthday cakes with the production function y = min x1, 1x2 , where x1 and x2 are the two inputs of production, which cost $6 and $4 respectively. What is the minimum level of costs to produce 45 birthday cakes?
a.$468
b.$194
c.$288
d.388
e.$810
20)If output is produced according to y = 12K + 8L the price of K is $20, and the price of L is $12, then thecost minimizing combination of K and L capable of producing 96 units of output is 中级微观经济学代考
a.L = 12 and K =0
b.L = 24 and K = 0
c.L = 24 and K =32
d.L = 24 and K =18
e.L = 0 and K =18
21)A factory needs three workers and one machine for each unit of the good it produces. If the workers are paid $15 an hour, and the machine costs $23 an hour to rent, what is the best approximation to thelowest per-hour costs that the firm can incur if it chooses to produce 3 units?
a.$200
b.$250
c.$300
d.$350
e.$400
22)A firm produces output with the technology y = K 8 L 4 where K is capital and L is labour. If the price ofcapital is $3 and the price of labour is $6, the cheapest way to produce any level of output requires using capital and labour in the ratio
23)Theproduction function is f (K, L) = L 2 K 2 , where K is capital and L is If the cost of labour is $5 per unit and the cost of capital is $4 per unit, which levels of output is the firm unable to produce when it spends $40 on inputs?
a.4
b.4.5
c.5
d.two of theabove
e.all of a,b andc
24)A firm’s production function is given by f (x1, x2) = 3x1+ 3x2 where x1 and x2 are the units of input 1 and 2, respectively. Suppose the price of input 1 is $8 and the price of input 2 is $11. What is the maximum quantity the firm can produce if it spends no more than $88 on inputs? 中级微观经济学代考
a.11units
b.24units
c.33units
d.88units
e.None of theabove
25)Supposea firm’s production technology has constant returns to Which of the following statements is always true without making further assumptions?
a.It can double its profits by doubling inputs.
b.Theprofit maximisation problem has no solution.
c.Theprofit maximisation problem has a unique solution.
d.Morethan one of the above
e.None of theabove
1 Problem 1
Consider Kurt from the multiple-choice questions. Prove that all of the answers that you did not choose as true are indeed false.
2 Problem 2
a)Consider Mary from the multiple-choice questions. What is the maximum price she would be willing to pay for Max’sticket?
b)Suppose instead that Bob from the multiple-choice questions is the owner of the ticket. Find his expectedutility from paying each of the four different prices for the ticket listed in the multiple-choice question. What can you conclude about the maximum price Bob is willing to pay for the ticket?
c)SupposeBob had the Would he sell it to Mary?
3 Problem 3 中级微观经济学代考
Emily is an expected utility maximizer with u(w) = w. Her current wealth is $1000. She has the option to bet $100 of her wealth on the roll of a fair die. If the roll is 1 or 2 she loses her bet, if the roll is 5 or 6 she wins $200 (her bet plus $100) and if the roll is 4 or 3 she gets her bet back.
a)Calculate Emily’s expected utility from playing the gamble. Explain why she is indifferent between playingthe gamble or keeping her money with certainty.
b)Redo part a) under the assumption that her utility is instead u(w) = w1/2. Is she still indifferent between playing the gamble versus keeping her money with certainty? Why or why not?
c)Redopart a) under the assumption that her utility is instead u(w) = w2. Is she still indifferent between playing the gamble versus keeping her money with certainty? Why or why not?
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