3. Jeff considers one banana to be equivalent to three apples. a. Let a denote apples and b denote bananas. Write down a utility function U(a, b) that represents Jeff’s preferences over apples and bananas. b. Jeff has an income of Y and the prices of apples and bananas are pa and pb, respectively. Derive Jeff’s ordinary Marshallian demand functions for apples and bananas. Do these demand functions satisfy the law of demand? c. Derive Jeff’s Hicksian demand functions for apples and bananas

Afreelance​ singer-songwriter is planning the restoration of a recently purchased civil​ war-era farmhouse. while he professes an enjoyment​ of, and talent in the construction​ trades, the theory of comparative advantage implies that a. the value of what he imports​ (in this​ case, professional contractor​ services) must equal the value of what he exports​ (songs). b. he should concentrate on the restoration work since his​ out-of-pocket costs will be much lower than if he hires professionals. c. ​self-sufficiency is​ advantageous, hence he should split his time between music and construction. d. the income lost while away from music will likely exceed the savings realized by doing the work​ himself, thus, he should hire professionals to do the restoration work. e. he ought to do as much of the work himself as possible since imports​ (in this​ case, professional contractor​ services) should always be restricted to those things that cannot be done internall

All of the industries and businesses in the country of marksenia are privately owned and sell products at different prices that are not controlled by the government or any other organizational body. consumers in marksenia are free to buy as much of the products as they like from the businesses they want. the country of marksenia has a

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.