Sarah operates a dog walking service. Her production is Y(L) where L is the number of...

 

Transcribed Image Text:

Sarah operates a dog walking service. Her production is Y(L) where L is the number of labor- hours input in producing Y which is the number of dogs walked. We have measured her a²y production function as both increasing and concave in labor meaning > 0 and < 0. Sarah ƏL² charges a price p for each dog walked and she has an opportunity cost of c for each hour of labor. She must pay a one-time insurance fee, I, to start her business. She also has to pay a tax, t, for every dog walked. Əy ƏL 3.1 Suppose there is a decrease in the tax, t, and we are interested to see what will happen to Sarah's labor input. Derive a comparative static and necessary condition to sign the comparative static. [Hint: go through all the necessary steps of deriving a comparative static such as setting up the problem, deriving first and second order conditions, etc.] 3.2 If the insurance fee, I, increases, what will happen to the amount of labor that she uses? Derive the comparative static and the necessary conditions to sign the comparative static. What will happen to Sarah's profit? 3.3 Write a theory that explains how the tax affects Sarah's decision to provide labor input. Make sure all the elements of the theory are present. Sarah operates a dog walking service. Her production is Y(L) where L is the number of labor- hours input in producing Y which is the number of dogs walked. We have measured her a²y production function as both increasing and concave in labor meaning > 0 and < 0. Sarah ƏL² charges a price p for each dog walked and she has an opportunity cost of c for each hour of labor. She must pay a one-time insurance fee, I, to start her business. She also has to pay a tax, t, for every dog walked. Əy ƏL 3.1 Suppose there is a decrease in the tax, t, and we are interested to see what will happen to Sarah's labor input. Derive a comparative static and necessary condition to sign the comparative static. [Hint: go through all the necessary steps of deriving a comparative static such as setting up the problem, deriving first and second order conditions, etc.] 3.2 If the insurance fee, I, increases, what will happen to the amount of labor that she uses? Derive the comparative static and the necessary conditions to sign the comparative static. What will happen to Sarah's profit? 3.3 Write a theory that explains how the tax affects Sarah's decision to provide labor input. Make sure all the elements of the theory are present.

Answer rating: 100% (QA)

31 First we need to set up the problem Sarahs labor input is denoted by L her production is denoted ... View the full answer