1. The government is considering two ways of constructing a public facility. The
ID: 1113555 • Letter: 1
Question
1. The government is considering two ways of constructing a public facility. The two ways are almost identical except the use of labor and an input. The first way uses 30 units of the input and 60 units of labor. The second way uses 40 units of the input and 40 units of labor. The input is traded in a monopoly market. The market demand and production cost of the input are p-400-q and c(q)=9,000+120q, respectively. The market wage is $170. (a) What is the shadow price of each unit of the input if z units are used for a public project. (b) What is the shadow wage of labor if the society has full employment? (c) What is the shadow wage of labor if the unemployment rate of the society is 20%? (d) Which way of construction is better if the society has full employment? (e) Which way of construction is better if the unemployment rate of the society is 20%?Explanation / Answer
a)400-q=9000+12q
-13q=9000-400
-13q=8600
q=-8969
b)The shadow wage of labor is equal to Market wage i.e $170, if the labour markets is clear
c)If the unemplyment rate of the society is 20% then shadow wage of labor be 20% below the market wage i.e (20/100)x 170=34. So the shadow wage of labor is 170-34=136.
d)The second way of construction is better if the society has full employment.
e)The first way of construction is better if the society has unemployment rate of 20%
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