Daily exercise on deducing preferences

Suppose the following data has been collected from three households, A, B and C, in two consecutive years, 2015 and 2016. Please use it to answer the questions below.

HH	Year	`M`	`P_x`	`P_y`	`Q_x`	`Q_y`
A	2015	4500	12	12	250	125
A	2016	5100	18	15	200	100
B	2015	2880	12	12	120	120
B	2016	3600	18	15	90	132
C	2015	1200	12	12	50	50
C	2016	1800	18	15	50	60

Please answer the following questions.

One of the households has Cobb-Douglas preferences. Please determine which one and calculate the value of parameter `g` in the Cobb-Douglas utility function and demand equations below.

`U=(Q_x)^g (Q_y)^{1-g}`,

`Q_x={gM}/P_x`,

`Q_y={(1-g)M}/P_y`

Now suppose that in 2017 the household's circumstances have changed as follows: `M=1920`, `P_x=16` and `P_y=20`. Please calculate the household's new equilibrium and draw and appropriate diagram to illustrate it.

Please scan and upload your answer.

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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 10/26/2023