Question

3. (10 total points) Suppose that Lynn enjoys sugar in her coffee. She has very particular preferences, and she must have exactly four spoonfuls of sugar for each cup of coffee. Let C be the number of cups of coffee, and S be the number of spoonfuls of sugar. Also, let Pc be the price of a cup of coffee. Suppose Lynn has $24 to spend on Coffee and Sugar. Also, the price of Sugar is $.30 per spoonful. Graph Lynn's Price consumption curve for prices, Pc = $.30, Pc = $.80, and Pc = $1.20. Please put the number of cups of coffee (C) on the horizontal axis, and the number of spoonfuls of Sugar (S) on the vertical axis. Be sure to graph each budget constraint associated with each price of Coffee, identify Lynn's optimal bundle on each budget constraint, and make sure your graph is labeled carefully and accurately.

Answer 1

Soi:- Given that four Spoonfuls of sugar for each cup of coffee Let c be the nom of cups of coffee s be the nom of spoonfuls of sugar Po be the price of a cup of coffee The utility function is U-min (40,5) or 5=40 Budget 2911 is ME CPC +SPS j) when Pc = 0.3 and Ps =03 24 = 0.30 +0-35 24 = 0-30 +0.3 (40) 24 = 0.30+ 1.20 24 = 6-50 c = 24/1-8 = 16 S = 40 = 4x16 = 64 Hence when Pc = 0.3, C = 16 cups sugar T BC3 | BC 2 0 10 70 80 20 30 40 50 60 coffee ii) when Pe=0.8 and Ps= 0.3 24 = 0.8C+0.35 24 - 0.8C+ 0.34C 24 = 20 c=12 5 - 4x0 = 4X12 = 48 Hence when Pc +0.8, Call cups ji) when Pc = 12 and Ps =0.3 24 - 1.207 0:35 24 - 1.20+ 0.3440 24 = 1.20+ 1-20 24 = 2.40 c=10 S-40 Hence, when Pc =12, C-10 CUPS