04 Question (5 points) The Bureau of Labor Statistics collects extensive data on consumption expenditures. The table below shows income shares for selected spending categories by various groups. The data reported are percentages; note that the list is not exhaustive, so the numbers do not sum to 100 as you read down the columns. Table B. Shares of average annual expenditures on selected major components by composition of consumer unit, 2016 Item Married couple only Married couple with children Other married couple consumer units One parent, at least one child under 18 Single person and other consumer units 14.8 11.8 30.5 17.5 10.3 11.1 12.9 31.8 17.3 Food Housing Transportation Healthcare Personal insurance and pensions 14.5 30.5 18.6 7.8 11.6 38.0 17.0 12.4 36.7 15.9 7.3 8.9 12.5 Part 1 (2 points) See Hint Suppose a researcher wants to model demand for housing versus all other goods for typical consumers. She is planning to use the Cobb- Douglas utility function u(x, y) = x"y(l-a). If good x represents housing, what should be the value of a for households that consist of married couples only? Your answer should be a decimal, not a percentage. The researcher can then estimate changes in demand based on income or price changes. If prices do not change and income for only households of married couples increases by 10%, how much would she estimate that housing demand from these households would increase? Your answer should be a decimal, not a percentage. Part 2 (3 points) See Hint The researcher is now extending her work and has decided to model the behavior of households that consist of one parent and at least one child under 18. She has expanded her function now to include three goods: housing (x1), transportation (x2), and all other goods (x3). Write out a Cobb-Douglas utility function that accurately models consumption behavior for that group based on the data given in the table: u(x1, X2, X3) = x1^ 04 Question (5 points) The Bureau of Labor Statistics collects extensive data on consumption expenditures. The table below shows income shares for selected spending categories by various groups. The data reported are percentages; note that the list is not exhaustive, so the numbers do not sum to 100 as you read down the columns. Table B. Shares of average annual expenditures on selected major components by composition of consumer unit, 2016 Item Married couple only Married couple with children Other married couple consumer units One parent, at least one child under 18 Single person and other consumer units 14.8 11.8 30.5 17.5 10.3 11.1 12.9 31.8 17.3 Food Housing Transportation Healthcare Personal insurance and pensions 14.5 30.5 18.6 7.8 11.6 38.0 17.0 12.4 36.7 15.9 7.3 8.9 12.5 Part 1 (2 points) See Hint Suppose a researcher wants to model demand for housing versus all other goods for typical consumers. She is planning to use the Cobb- Douglas utility function u(x, y) = x"y(l-a). If good x represents housing, what should be the value of a for households that consist of married couples only? Your answer should be a decimal, not a percentage. The researcher can then estimate changes in demand based on income or price changes. If prices do not change and income for only households of married couples increases by 10%, how much would she estimate that housing demand from these households would increase? Your answer should be a decimal, not a percentage. Part 2 (3 points) See Hint The researcher is now extending her work and has decided to model the behavior of households that consist of one parent and at least one child under 18. She has expanded her function now to include three goods: housing (x1), transportation (x2), and all other goods (x3). Write out a Cobb-Douglas utility function that accurately models consumption behavior for that group based on the data given in the table: u(x1, X2, X3) = x1^