we discussed different versions of a model of firms emitting pollution. This problem walks through a...

 

Transcribed Image Text:

we discussed different versions of a model of firms emitting pollution. This problem walks through a simple variation of that model and has you think about its interpretation. Consider the following description of firm production: Q=(1-s)L Z=(1-s)(1/a)L Here Q represents the quantity of the firm's output, Z is pollution emissions in tons, s is the share of productive factors dedicated to abating pollution (rather than producing output), L is the amount of productive factor inputs (i.e., labor), and a is a parameter. a. A firm with constant-returns-to-scale, Cobb-Douglas production technology, has Q=A³B", where A and B are inputs to production and ß and μ are parameters, with B+u=1. Rewrite output as a function of pollution and labor and show that it is Cobb- Douglas. What are the exponents on each input? b. In 1-3 sentences, explain what it means to have output as a function of pollution. C. One property of Cobb-Douglas technology is that each productive input has "constant factor shares." For example, if a firm has the production technology Q-A³B", this would imply that the firm's total expenditure on input A is BC, where C is the firm's total spending. What does this property imply is total spending on pollution taxes? d. Does the parameter a tell us directly about spending on pollution abatement technologies? Why or why not? we discussed different versions of a model of firms emitting pollution. This problem walks through a simple variation of that model and has you think about its interpretation. Consider the following description of firm production: Q=(1-s)L Z=(1-s)(1/a)L Here Q represents the quantity of the firm's output, Z is pollution emissions in tons, s is the share of productive factors dedicated to abating pollution (rather than producing output), L is the amount of productive factor inputs (i.e., labor), and a is a parameter. a. A firm with constant-returns-to-scale, Cobb-Douglas production technology, has Q=A³B", where A and B are inputs to production and ß and μ are parameters, with B+u=1. Rewrite output as a function of pollution and labor and show that it is Cobb- Douglas. What are the exponents on each input? b. In 1-3 sentences, explain what it means to have output as a function of pollution. C. One property of Cobb-Douglas technology is that each productive input has "constant factor shares." For example, if a firm has the production technology Q-A³B", this would imply that the firm's total expenditure on input A is BC, where C is the firm's total spending. What does this property imply is total spending on pollution taxes? d. Does the parameter a tell us directly about spending on pollution abatement technologies? Why or why not?

Answer rating: 100% (QA)

a us 1 Hence the answer is us 1 Explanation a ... View the full answer