9. • An economy has 100 people divided among the following groups: 25 have full-time jobs, 20 have one part-time job, 5 have two part-time jobs, 10 would like to work and are looking for jobs, 10 would like to work but are so discouraged they have given up looking, 10 are running their own businesses, 10 are retired, and 10 are small children.

b. Calculate the number of unemployed and the unemployment rate.

c. Calculate total employment in two ways: as measured by the household survey and as

7.(This problem requires the use of calculus.) Consider a Cobb–Douglas productionfunction with three inputs.Kis capital (the number of machines),Lis labor (the number of workers), andHis human capital (the number of college degrees among the workers). The production function isY= K1/3L1/3H1/3 a.Derive an expression for the marginal product of labor. How does an increase in the .