课程名称︰个体经济理论一
课程性质︰必修
课程教师︰王道一
开课学院：社科院
开课系所︰经济所
考试日期（年月日）︰103.10.17
考试时限（分钟）：1420-1620 (120m)
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
Part A (35%): The CES Utility Function
Consider the utility function
U(x1,x2)=(α1x1^(1-1/θ)+α2x2^(1-1/θ))^(1/(1-1/θ)) α1,α2,θ>0,θ≠1.
1.(5%)Is the preference represented by this utility function homothetic or
not? Why?
2.(15%)For a consumer with this utility function facing price vector p and
income I, solve for demend xj(p,I). (Note that you can either solve the
consumer problem or derive the indirect utility function and appeal to Roy's
identity. Either case, you have to state all assumptions required and verify
that they indeed hold.)
3.(5%)Show that when θ=1, the demend xj(p,I) of this utility function
coincides with that of Cobb-Douglas preference U(x1,x2)=x1^α1*x2^α2,
α1,α2>0
4.(5%)What is ε(x2c/x1c,p1/p2) for this utility function?
5.(5%)Depict the income expantion path for a consumer with this utility
function.
Part B (25%): The 2x2 Exchange Economy
Consider two consumers, A and B, having utility functions
uA(xb,xg)=2xb+xg
{
uB(xb,xg)√(xbxg)
1.(10%)Draw the edgeworth box for this two-person economy and carefully depict
these Pareto efficient allocations. (Note: You will have to justify your
answers, say, by appealing to the Kuhn-Tucker conditions.)
2.(10%)Suppose endowments are (ωbA,ωgA)=(689,689) and (ωgB,ωgB)=(300,300).
What is the Walrasian equilibrium for these two consumers?
3.(5%)Are all Pareto efficient allocations implementable as Walrasian
equilibrium? Why or why not?
(Hint: You should use what you have learned in the previous part.)
Part C (40%): Edgeworth Box Bargaining of 689 and the Zhan-Zhong Trio.
Consider an exchange economy with 692 consumers. Three "big" consumers each
have endowment (100,100) and utility function u(xb,xg)=ln(xb)/2+ln(xg)/2,
while the remaining consumers have endowment (1,1) and utility function
u(xb,xg)=xb+10xg.
1.(15%)What is the Walrasian equilibrium for these 692 consumers? Is the
equilibrium outcome Pareto efficient? Why or why not?
2.(15%)Consider the exchange economy replacing the three big consumers with
one "huge" consumer with endowment (300,300) and utility function
u(xb,xg)=100xb. What is the Walrasian equilibrium for these 690 consumers?
Is the equilibrium outcome Pareto efficient? Why or why not?
3.(5%)Are small consumers better-off facing one huge consumer than three big
consumers? Why or why not?
4.(5%)What assumptions do you need to take this model to real world bargaining
situation? Are they likely to hold? Explain.
(Hint: You should use what you have learned in the previous part.)