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Q4: Emily and Emma are identical twins. They were adopted by two very different families when they were still infants. Thirty years later, Emma has a college degree in engineering and is making $110K annually. Emily dropped out of high school and is currently working part-time at a local grocery store, making an income of about $10K per year. Let's measure a person's happiness by a metric called \"n.\" The more units of (1 one attains, the happier one is. Now, given that Emily and Emma are identical twins, they have the identical "happiness function which relates the level of happiness as a function of income. As shown in the table next page, at the income level of $10K, Emily's happiness is 100 n, and at the income level of $110K, Emma's happiness is 210 n. Emma Emily Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Income Level Total Utility Marginal Utility Income Level | Total Utility Marginal Utility $10K 100 0 $10K 100 0 $20K 120 $20K 120 Q $30K 138 0 $30K 138 0 $40K 154 0 $40K 154 0 $50K 168 0 $50K 168 0 $60K 180 0 $60K 180 0 $70K 190 Q $70K 190 Q $80K 198 0 SBOK 198 0 $90K 204 0 $9OK 204 0 $10OK 208 0 $100K 208 0 $110K 210 0 $110K 210 0 (1) (i) Compute the marginal happiness (in units of Q) as Emily and Emma move from one income level to the next income level. Fill in the blanks in Columns 3 and 6. (ii) Given the values in Columns 3 and 6, is mariginal happiness: (A) an increasing function of income, or (B) a decreasing function of income? Answer: (iii) What is the theory depicting the observed phenonomon in (ii)? Answer: The Law of D of I (iv) Given their current incomes of (Emily, Emma) = ($110K, $10K), what is the total level of happiness that Emily and Emma attain? Answer:{2) Income Redistribution 1: Suppose the government is to take $10K awayr from Em ma and give it to Emily. Use data in the table to answer the questions below. (i) Given Column 6, what would be the change in Emily's level of happiness when her income is increased from $10K to $20K? {If the change is negative, include a minus sign.) Answer: ('1 (ii) Given Column 3, what would be the change in Emma's level of happiness when her income is decreased from $110K to 5100K? {If the change is negative, include a minus sign.) Answer: :1 (iii) What would be the net change in the societh total level of happiness by changing income levels from Emily, Emma) = [510' $110K] to [Eml , Emma) = {520' $100K)? {If the net change is negative, include a minus sign.) Answer: :1 {3) Income Redistribution 2: Suppose the government is to take another$10lt away from Emma and give it to Emily. (i) Given Column 6, what would be the change in Emily's level of happiness when her income is increased from $20K to $30K? [If the change is negative, include a minus sign.) Answer: :1 (ii) Given Column 3, what would be the change in Emma's level of happiness when her income is decreased from $100K to $90K? {If the change is negative, include a min us sign.) Answer: :1 {iii} What would be the net change in the societYstotal level of happiness by changing income levels from (Emily, Emma) = ISZDK, SINK) to (Emily, Emma) = ($30K, $90K)? (If the net change is negative, include a minus sign.) Answer: a {4) Income Redistribution 3: What would be the net change in the society's total level of happiness by changing income levels from (Emily, Emma) = {SM $90K) to (Emily, Em ma} = {$40K $80K)? {If the net change is negative, include a minus sign.) Answer: :1 {5) Income Redistribution 4: What would be the net change in the society's total level of happiness by changing income levels from Emily, Emma) = [$41]; $80K) to (Emily, Em ma) = [$50K, $70K)? [If the net change is negative, include a minus sign.) Answer: a (6) Income Redistribution 5: What would be the net change in the society' 5 total level of happiness by changing income levels from lEmilv, Emma) = [$50K $70K} to lEmiIv, Emma) = [$60K, 6|] K)? (If the net change is negative, include a minus sign.) Answer: :1 {7) Income Redistribution 6: Suppose we go one step further by take another $10K away from Em ma and give it to Emilv. {i} [3 ptsi Given Column 6, what would be the change in Emily's level of happiness when her income is increased from $60K to $10K? (If the change is negative, include a minus sign.} Answer: :1 {iii {3 pts} Given Column 3, what would be the change in Emma's level of happiness when her income is decreased from $60K to $50!? [If the change is negative, include a minus sign.} Answer: :1 {ill} {3 pts} What would be the net change in the society's total level of happiness by changing Income levels from (Emily, Emma] I [$60K $60K) to (Emily, Emma} I ($10K, $50Kl? (If the net change is negative, include a minus sign .} Answer: n {8} To maximize the total happiness of this two-person society, what should be the optimal Income distribution? Answer: lEmlIv, Emmal I {5 _K . 5K) {9} The Case for Equality: {True or False?) The above results support the argument that redistributions that promote income equality will increase the wellbelng of society. because the utility gain from the poor will outweigh the utility loss to the rich. Answer: (10} The Case Against Equalityu A counter argument is that income redistribution can redue an lndivldual's Incentive to work and, hence, reduce society's total income. {i} Suppose the income redistribution scheme in [8} would reduce Emma's incentive to work and, thus, lower her gross annual income from $110K to $80K. Suppose Emily's incentive to work remains constant, earning $10K before taxes and transfers. What would then be the total inoome of the two individuals? Answer: s It iii] {Yes or lilo?! Given the total income available in [lo-i}, would the optimal income redistribution scheme in {3] still be feasible? Answer: [iii] The above highlighs the tradeoffs between E and E AWE andE