Please show enough work to demonstrate how you arrived at the calculation. Florian has preferences over cash (c), pens (p) and mugs (m) as...

Please show enough work to demonstrate how you arrived at the calculation.

Florian has preferences over cash (c), pens (p) and mugs (m) as represented by the following utility function: u(c,p,m,rc,rp,rm) = c + 2p + 3m + v(c − rc) + 2v(p − rp) + 3v(m − rm), where v(x) = x if x ≥ 0 and v(x) = 3x if x ≤ 0. Assume that Florian's reference point is his current endowment of c, p and m.

a) How much would Florian pay for a pen? 

b) How much would he pay for a mug? Now assume that that Florian has at least 1 mug and 1 pen. 

c) For how much money would Florian be willing to sell a pen? How about a mug? 

d) Calculate Florian's choosing price for a pen (mug). In other words, what amount of money would make Florian indifferent between that amount of money and a pen (mug)? Why is Florian's choosing price different from his buying price? 

e) Would Florian trade a mug for a pen? What about one of his pens for a mug? Explain why this behavior is either consistent or inconsistent with standard economic theory.