Assume that Smith consumes good X and his total utility function of good X is given by: ππ’π₯ = 30π2 β 0.5π3 I. Obtain ππ’π₯ and π΄π’π₯ functions.
II. At what level of good X, ππ’π₯ will be maximum?
III. Find the value of total utility where ππ’π₯ is maximum.
IV. From what level of good X, law of diminishing marginal utility will start to operate?
V. Find the value of good X where ππ’π₯ curve cuts the π΄π’π₯ curve at its maximum.
VI. At what level of good X, ππ’π₯ πππ’ππ π΄π’π₯ . What is their values at this unit of good X.
VII. How many units of good X, he should consume to get the maximum satisfaction? What is the maximum value of total satisfaction at this point?
VIII. Frome what unit of good X, ππ’π₯ become negavtive?
IX. Estimate the value of π΄π’π₯ π€βππ ππ’π₯ is maximum?
X. Draw the ππ’π₯ , ππ’π₯ and π΄π’π₯ curves on a graph and indicate the above all values on the graphs.
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