solution_hmk2 - 1 Exercise 10 page 107 Initially there are...

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1 Exercise 10, page 107 Initially, there are 2000 workers, of which 1900 are employed. Each works 40 hours per week. The production function is Y = 10 L; where L is measured in hours of labor. (a) Total hours worked per week =1900 workers ° 40 hours per worker =76,000 hours per week. Total output per week =76,000 total hours per week ° 10 units of output per hour =760,000 units of output. The unemployment rate is 100 unemployed/2000 labor supply =0.05, or 5%. (b) Employment falls 4% from 1900 to: (1°0.04) ° 1900 =1824. The labor force falls 0.2% from 2000 to: (1°0.002) ° 2000 = 1996. With a labor force of 1996 and employment of 1824, unemployment is 1996 °1824 =172. The unemployment rate is 172/1996 =0.086, or 8.6%. Hours worked per employed worker falls 2.5% from 40 to: (1 °0.025) ° 40 =39. Total hours per week = 39 hours per worker ° 1824 workers =71,136. So total hours per week falls by (76,000 °71,136)/76,000 =0.064 =6.4%. Total output per week falls 1.4% for every 1% drop in hours, so output falls by 6.4% ° 1.4 =8.96%. Since output was 760,000, it now falls to 760,000 ° (1 °0.0896) =691,904. 2 Exercise 6, page 107 Let E denotes total employment, U total unemployment, E + U the labor force, O the people out of the labor force, and E + U + O the working age population. (a) The unemployment rate is: u = U E + U and the employment ratio er = E E + U + O : The answer is yes. We can have u and er go up at the same time. For example, initially, E + U = 100 ; U = 10 ; and O = 50 . Thus: u = 0 : 10 ; er = 0 : 60 : Now, reduce O to 40 and E to 89, while U becomes 11 . You get: u = 0 : 11 ; er = 0 : 64 : (b) The participation rate is pr = E + U E + U + O : It can fall when er rises. Suppose that in the example above O remains at 50, while E + U falls to 95, U falls to 4 and E goes to 91. Then, pr goes from 100 = 150 = 0 : 67 to pr = 95 = 145 = 0 : 65 : The employment rate er goes from 0.60 to 91 = 145 = 0 : 63 : 1
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3 Exercise 7, page 107 Let W denote the hourly wage (in $) and l the number of hours worked by an individual in a year, so that Wl is his/her annual income. The social security tax T for a self-employed individual has the following structure: T = ° 0 : 124 ( Wl ) if Wl ± $94 ; 200 ; 11 ; 681 if Wl > $94 ; 200 : Thus, a worker±s wage W is taxed at the rate 12.4% up to an income of $94 ; 200 and zero for any additional dollar of income beyond $94 ; 200 : The new proposals are: T A = ° 0
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