Financial theory

Ok guys, I'm studying from Danthine and Donaldson - Intermediate Financial Theory. The book itself doesn't have a lot of worked examples, and I'm lacking the basics for understanding some concepts related to utility functions. This is the text of the exercise I'm stuck with:

Consider a two goods/two agents pure exchange economy where agents' utility functions ade of the form: $U(c_1^j,c_2^j) = (c_1^j)^{\alpha}(c_2^j)^{1-\alpha}, j=1, 2$ with $\alpha=0.5$. Initial endowments are $e_1^1 = 6$, $e_2^1 = 4$, $e_1^2 = 14$, $e_2^2 = 16$ (superscripts represent agents).

a) describe the Pareto set (the set of Pareto optima)

b) assume that there exists a competitive market for each good. What is the equilibrium allocation? What are the equilibrium prices? Comment. What are the utility levels and MRS after trading? What do you conclude?

Now, can anybody suggest me a reference, lecture notes, and maybe worked examples that can help me understand better this kind of exercises? Thanks to everybody who wants to help!

• Look at any Microeconomics textbook. – noob2 Aug 13 '15 at 12:40
• I know, but even if I've solved the 1st request I don't seem to solve the second... And I was looking for a similar worked example – james42 Aug 13 '15 at 23:08