Question

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x 0.5y 0.5 and an initial income I of 100. Let initial price be px = 4 and py = 1. Now vary the price of x from 1 to 7 in steps of 1. So you have 7 prices for x. px = {1, 2, 3, 4, 5, 6, 7} For each of these px, py REMAINS the SAME at 1. In the excel sheet fill columns F (demand for x), G(demand for y), H(utility from x, y), K (marshallian demand x), L (hicksian demand x, xh), M (Income for hicksian demand), N (demand for y under hicksian case yh) and O (utility from xh, yh) For x

(a) compute and plot the Marshallian Demand

(b) compute and plot the Hicksian Demand assuming the base price of x, px = 4. or ensuring that utility is computed and kept constant when initial prices were px = 4, py = 1 and Income I = 100 Fill

Answer 1

substituting marshallian demand function for both goods in utility function

price of good x	marshallian demand function for good x	marshallian demand function for good y	utility	hicksian demand function for good x	hicksian demand function for good y
1	50	50	25	25	25
2	25	50	25	17.67	35.35
3	16.67	50	25	14.43	43.3
4	12.5	50	25	12.5	50
5	10	50	25	11.18	55.9
6	8.33	50	25	10.21	61.23
7	7.14	50	25	9.45	66.14