Question

Question 2-2 (20 percent) Elizabeth only cares for raspberries r and apples a. In fact, her utility function is given by U(r,a)-r"за" з . Assume Elizabeth has a budget of M-60 , and let the price of apples be pa (a) Write down the consumer's problem that Elizabeth solves in case the price of raspberries is p, -1. Explain in words what it says (b) Derive Elizabeth's optimum bundle in case the price of raspberries is p, -1 (c) Derive and draw Elizabeth's individual demand function for raspberries. (d) Consider Geoffrey with the following demand function for raspberries: qG 10-2p,. Derive the aggregated demand function in an economy of Elizabeth and Geoffrey.

Answer 1

a) utility maximization problem imply that we have to maximize utility with respect to the budget constraint

at eqm

budget constraint is tangent to Indifference Curve

o a) u= 8/32 213 , M=60 Pa = 8, Max Ucria) St Satr= M 2 satr = 60 Now L= 8/3 a 213 + a[60- 8a-oJ Foco ah 7 a 213.8-213 -1 o. & alta = 28113 a 113 – 80 =0. thus from foc: Calo) 23 = 2 (61a)"} 8 . 8= 4a. 8a=ar. So from B.C.. put 4a=28 so Havello a = 60/12 = 5, Sa+4 a=60 8=20. Ans c. Now demand funch for Raspberries Let Porce of 8 = Po so from eam condition, MRS = Polla MRS = Bulor a aulaa gr. So at Eqm, a = Po 4a=A&P from B.C. → M=2888+ &= 1 ko M=60 Ang

Demand function of r

1 Price of r Ñ 10 Raspberries r 20

d) Met ad cow is horizontal summation of Individual demand curves, so. 96= 10-28 qe po po So. Q = VG + QE = 10-2p+ 2010. Q = 10+ 20 - 221 Ago dd funch →