GDP and Welfare In this assignment you will calculate a measure of welfare that is similar to - but somewhat simpler than Jones and Klenow {2016). The calculation will focus on consumption, inequality and life expectancy. In particular, you will explore the effect of different functional forms for the utility function on the welfare calcula- tion. The data for this assigrunent is in a separate Excel spreadsheet. You can carry out your calculations in that spreadsheet or use an alternative application like lGoogle Sheets, Apple's Numbers, or a programming language like Python, Fortran, Julia, or Matlab. lGenerically, the welfare function is given by: E 1-1502. 5} = E as [u {an} ._ (1) 11:1 where the expectation is over the realization of income. You can think of the expectation as the sum of probability-weighted income realizations: 4 E in tea] = :patca (2) i=1 Here, pi E [f]. 1) denotes the probability of outcome i at age a and cf, is the corre- sponding consumption level. In this example, there are four different realizations of income and hence consumption. Moreover, people live for up to five periods in this artificial economy and 3,, is the age-specific survival rate {at birth). This assumption is, of course, unrealistic but it keeps the calculations somewhat simple. Note, also, that at each age, individuals face the same income and consumption risk so the welfare calculation simplifies to: I-'Vc, s] = [E [a (c)] :1: an, [3) o.:l Question 2 [5 points] Next, you'll complete some basic calculations in the attached spreadsheet with cooked-up data for France and the United States. The designated cells are high- lighted in yellow. 1. Compute the consumption associated with each event in columns C and T, using the respective consumption-to-income ratios in A3 and R3. [2 points] 2. Compute the utility associated with each outcome in columns I-K and Z- AB, respectively. {a} In the first column, the utility function is given by -u[c]l = lnl[c). [1 point] {b} In the second column, the utility function is given by u(c) = c, which implies that people are rislc neutral. [1 point] {c} In the third column, the utility function is given by not) = \"11:1. This is a so-called constant relatioe risk aoersion (GEM) utility function and the parameter *7- determines the degree of risk aversion [higher values of c\G M O Q AA AB AC AD AE France Relative Welfare U.S.A. C/Y Consumption Income Mortality E[Income] u[c]=In[c] u[c]=c u[c]=CRRA W(In[c],s) W(c,s) W(CRRA,s) lambda C/Y Consumption Income Mortality E[Income] u[c]=In[c] u[c]=c u[c]=CRRA |W(In[c],s) W(c,s) W(CRRA,s 0.75 Probability Quantity Probability Quantity Survival Rate Age 0.75 for In[c] for c for CRRA 0.8 Probability Quantity Probability Quantity Survival Rate Age 0.75 0.2 0.2 4500 1 0.25 0.25 5400 0.3 0.3 8000 0.95 2019 2019 0.25 0.25 960 0.94 0.3 0.3 12000 0.9 0.25 0.25 14400 0.88 0.2 0.2 15500 0.85 0.25 0.25 18600 0.8 08 0.76