Question

please answer both（b）and（d）

thank you

3. Nick enjoys having soda (a) with his cheese pizza (c): his preferences are represented by the utility function u(a,c) = min(a, 2e) (a) Suppose Nick has 10 slices of cheese pizza (e), how many sodas must he consume in order to have a utility of 40? (2 points) U=40. (=10. - 4020 & 40=22 (b) Setup Nick's utility maximization problem. Solve for his optimal levels of pizza and soda as functions of prices a" (Pa, Pc,m) and c* (Pa, Pc,m) where pa is the price of soda, pe is the price of cheese pizza, and m is the money Nick has to spend on soda and pizza. Be sure to show all your work. (6 points)

Answer 1

Solution: 3) @ Given uc gc) = min (920) ich has to slices of cheese pizza (c) consume in order for utility of you No of todas must he > olac) <min (9,20) u=40 c=10 then yoza, 40=20 .. with to pizza ,u=40, cant be achieved) O optimim level of pizza, and foda for nick: → Peis the price of cheese pizza and mis the money, pa is the price of Soda. at a =2c, from bepaa tPcc =m Puta = 20, 2c Pat Epc =m

at = 2m 2PatPc (C) Price elasticity: fora is ez lehe . e= (-2m (apat pc *2)) #Pa 9r) Capatic) (det = -2m (2Pa + pc*2)) dla = -umpa * (2P at Pc) am (2PatPc)? -opa apatPc cross elasticity:

'c *-2m (alat Pc). am Calat Pc) alatpe) 2 12 Epatpe) = pe (2Pa + Pc) Grosselasticity: e-te a zope Реда* = Pc *-2m Calat Pc) #1 200 CP Pa+PC) = Pc - Cepat Pc) ChatPc)2 - Pc opatre) in corrie elasticity: = m o om = M * 2 (2 punt pc) Zlatke

(d) mso, paso, Pcs Then whether nick sees sodas as an ordinary (6) inelastic good! -) a = soda, as pa increases at falls, so soda is ordinary good of perpendicular c', so in elastic good . Capacap a TPC) as Pc increases, a* falls, Csince cross price - elasticity is negative) So complement. • as income elasticity so, of mincreases, a* increases, so normal good.