1. (10 points) Given Z = 2111(3x) ny Find the partial derivative aszbc and 62/63; 2. (15 points) A consumer has his or her utility/benefit function Z=u(x1,x2) = xlxz to measure 62 32 the happiness of consumption of good x1 and good x2 . Find the partial derivates gand ax , 1 2 and indicate their economic meanings. 3. (20 points) A Tacoma financial services allocates funds to: stocks, bonds, mutual funds, and cash. For each instrument, rate of return and risk are as shown: Stock Bond Mutual Fund Cash Total risk is limited to value based on client tvpe. Currently we have a client with max risk tolerance of 0.5. The company has the following guidelines: - No more than 70% of investment in stocks - Investment in mutual funds must be at least as much as in bonds - Amount of cash at least 8%, but no more than 25% In figuring out the optimal investment allocation for this client, please answer the following three questions: a. What are the decision variables? b. What is the objective function? c. List all the constraints. 4. (30 points) For the population of people in the workforce in 1976, WAGEl data was used to analyze how a person's wage is associated with observed education. The table 1 list summarize statistics of the variables in the dataset. Table 2 reports the regression results from four different models, where column (1) is simple linear model with dependent variable wage, while column (2) (4) use log wage as dependent variable. Answer the following questions using information from Table 1 and Table 2 below. Table 1: Summarize Statistics Statistic N Mean 5:. Dev. Min Max wage 526 5.896 3.693 6.536 24.986 educ 526 12.563 2.769 6 18 exper 526 17.617 13.5?2 1 51 tenure 526 5.165 2.224 6 44 nonwhite 526 6.163 6.364 6 1 female 526 6.479 6.566 6 1 married 526 6.668 6.489 6 1 numdep 526 1.644 1.262 6 6 Table 2: Regression Results Dependent variable: wage lwage ________________-212.--________Z_i>___________3_3___________ii>______ educ 6.54*** 6.68*** 6.16*** 6.69*** (6.65) (6.61) (6.61) (6.61) exper 6.61*** 6.64*** (6.662) (6.61) expersqu 6.661*** (6.6661) Constant 6.96 6.58*** 6.22** 6.13 _ _______________ (.9291). ________ 931.19}. ________ 9.113_________'3__'ll____ Observa:ions 526 526 526 526 R2 6 :6 6.19 6.25 6 36 Adjus:ed R2 6.16 6.18 6.25 6.36 F Statistic 163.36*** 119.58*** 86.86*** 74.6?*** Note: *pIt1) (Intercept) 1. 389660 0. 187515 7.411 2. 43e-12 * * * Zinc 0. 839183 0. 019572 42. 876 ltl) (Intercept) 1.389660 0.187515 7.411 2.43e12 *** linc 0.839183 0.019572 42.876