Assume that Smith consumes good X and his total utility function of good X is given by: 𝑇𝑢𝑥 = 30𝑋2 – 0.5𝑋3 I. Obtain 𝑀𝑢𝑥 and 𝐴𝑢𝑥 functions.
II. At what level of good X, 𝑀𝑢𝑥 will be maximum?
III. Find the value of total utility where 𝑀𝑢𝑥 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 𝑀𝑢𝑥 curve cuts the 𝐴𝑢𝑥 curve at its maximum.
VI. At what level of good X, 𝑀𝑢𝑥 𝑒𝑞𝑢𝑎𝑙 𝐴𝑢𝑥 . 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, 𝑀𝑢𝑥 become negavtive?
IX. Estimate the value of 𝐴𝑢𝑥 𝑤ℎ𝑒𝑛 𝑀𝑢𝑥 is maximum?
X. Draw the 𝑇𝑢𝑥 , 𝑀𝑢𝑥 and 𝐴𝑢𝑥 curves on a graph and indicate the above all values on the graphs.
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