Respuesta :
The joy or pleasure that consumers derive from purchasing a commodity or service is known as utility in economics. A set of products and services are measured using the utility function.
As per the question the utility function of individual A=
UA(X1A + X2A)= logX1A+ logX2A
And the utility function of individual B=
UB(X1B + X2B) = logX1B + logX2B
here the utility coefficient beta responsible for risk taking capability.
U'A= 1/. X1A + B*1/. X1B
U''A=Beta ............ So when U''A= Beta , the utility function will risk taking Convex function
when b<0, the utility function will risk avarse Concave function
when b=0 the utility function will be risk neutral linear function
The benefit or enjoyment that consumers experience is abstract and challenging to quantify, but utility function is quantified in units called utils—the Spanish word for useful. As a result, economists gauge utility by looking at customer decisions in terms of disclosed preferences. The utility function ordering of consumption baskets from least liked to most favored is then created by economists.
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The complete question is
Imagine an economy with the following set of assumption:
1) There is only one good in the economy that is consumed for two periods:X, and X2
2) Two (groups of) individuals: Individual A and Individual B
3) Utility function of Individual A: UX(X1X,X2A) = logX1A + B^logX2A
4) Utility function of Individual B: UR(X18, X2R) = logX1g + bBlogX2g
5) Individuals have period 1 endowment (e1,e) = (40,20)
6) Individuals do not have any endowments in period 2. Instead, in period 1, they own shares of the company that will produce the consumption good in period 2. One share of the stock is a claim to 1 unit of consumption good to be produced in period 2. The company will produce 40 units of good in period 2 and the current ownership of the firm is as follows:
(A,B) = (15,25)
7) Individuals can trade shares in period 1. The relative price of the share is Te.
