[試題] 102-1 胡明哲 工程經濟 期末考
課程名稱︰工程經濟(Engineering Economy)
課程性質︰選修
課程教師︰胡明哲
開課學院：生農
開課系所︰生工
考試日期（年月日）︰103/1/8
考試時限（分鐘）：3hrs
是否需發放獎勵金：Y
（如未明確表示，則不予發放）
試題 :共四大題每題25分 總分100分
1. (a) suppose that there are only 8-onunce and 16-ounce beers available to
Sarsh. An 8-ounce beer costs $0.75 and 16-ounce beer cost $1.Assume
X1 is the number of 8-ounce beer and X2 is the number of 16-ounce beer.
Also, Sarah has $30 to spend on beer. What is Sarah's budget constraint
?(5points)
(b) Sarah thinks that two 8-ounce cans of beer are exact as good as one
16-ounce can of beer.What is Sarah's utility function,U(x1,x2)?
(Hint: two 8 ounce beers is "perfect substitute " of one 16-ounce beer)
(5points)
(c) Draw a graph to show Sarah's budget constraint,most preferred
affordable choice, and an indifference curve that goes through the most
preferred affordable choice.(5 points)
(d) What is "most preferred affordable choice " for Sarah? Show every step
of your calculation.(5 points)
(e) what is Sarah's demand curve?Draw Sarah's demand curve.(5points)
2. Clara's utility function is U(x,y)=(x+2)(y+1),where x is her consumption
of good 1 and y is her consumption of good 2.Suppose the price of eace
good is 1 and Clara has an income of 11.
(a) Write a general expression for Clara's marginal utility with respect
to good 1 and good 2 ,MU1 and MU2(10 points)
(b) Write a general expression for Clara's marginal rate of substitution
(MRS) (5points)
(c) find Clara's most preferred affordable choice.(First,show two
equation.)(10points)
3. Consider a case of Cournot quantity competition model with two firms.Let
the inverse demand function be given by P = 105 - Q where P is market
price and Q is totoal market quantity. Production cost is 5 for firm 1 and
production cost is 10 for firm 2.
(a) Formulate the profit function for firm 1 and firm 2.(10 points )
(b) Derive optimal conditions for firm 1 and firm 2.(10 points)
(c) What is equilibrium solution for the Cournot model?
(Hint: Solve the system of equations derived from(b))(5points)
4. (a)What is the mathematical definition of Nash Equilbrirm? Use your own
word to explain Nsh Equilbrium.(10 points)
The payoff table is listed in following. Notice that players 1 and 2
both prefer high number in payoff table.
(b) Is (Middle,Left)=(+2,-2) a Nash Equilibrium? Why?(5 points )
(c) Which solution is the pure Nash Equilibrium in this game ?
(10points)
player 2
LEFT CENTRE RIGHT
TOP (-4,+4) (0,0) (-1,+1)
player 1 MIDDLE (+2,-2) (+1,-1) (+2,-2)
BOTTOM (+1,-1) (0,0) (+4,-4)
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