Question

please help, i dont know what to do for this extra problem!

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

solution:

1 cup of coffee Lynn needs 4 spoonful of sugar.

the utility function is U = min (4C, S) or S = 4C

Budget equation is M = CPC + SPS

i) When PC = 0.30 and PS = 0.30

24 = 0.30C + 0.30S

24 = 0.30C + 0.30*4C

C = 24/(0.30 + 1.2) = 16 and S = 16*4 = 64

Hence, when PC = 0.30, C = 16 cups (A)

ii) When PC = 0.80 and PS = 0.30

24 = 0.80C + 0.30S

24 = 0.80C + 0.30*4C

C = 24/(0.80 + 1.2) = 12 and S = 12*4 = 48

Hence, when PC = 0.80, C = 12 cups (B)

iii) When PC = 1.20 and PS = 0.30

24 = 1.20C + 0.30S

24 = 1.20C + 0.30*4C

C = 24/(1.20 + 1.2) = 10 and S = 10*4 = 40

Hence, when PC = 1.20, C = 10 cups (C)

1B__ C2 Sugar BC3 BC2 0 10 20 30 50 60 70 80 40 Coffee