Question

3. Think about you benefit from food. Let c be the market value of the amount of food you have in a given day and u(c) the utility from consuming c.

(a) Plot u(c) (utility on the y axis, consumption on the x axis). Explain why it is the shape it is.

(b) If you have enough money to consume C in a week, how much would you spend each day? Is this consistent with your plot?

(c) You are offered the choice between (A) $150 dollars worth of food for the week (B) 50% chance that you get $600 worth of food for the week and 50% you get $0 worth of food for the week.

If this is the only source of food (e.g. if you are unlucky and get $0 worth of food for the week you literally get no food for the week), then which option do you prefer?

Answer 1

Before approaching sub-parts we must know about the law to diminishing marginal utility, which states that " as a consumer has more and more of a commodity the marginal utility of the commodity falls".

a) The graph is attached as an image.

As you can see from the graph, the Total Utility (T.U.) curve starts from the origin, increase at a decreasing rate, reaches a maximum(saturation point) and starts falling.

Marginal Curve (M.C.) is the utility that a person gets when he consumes an additional unit of the good, is the slope of T.U. curve, when T.U. is at maximum called saturation point M.U. is zero (since the slope of T.U. at that point is zero).

When T.U. is rising M.U. curve falls; when T.U. is falling M.U. is negative. The falling M.U. shows the law of Diminishing Marginal Utility.

The shape is due to the law of diminishing marginal utility.

B) We will spend each day (1/7)th of the total money because if we try to consume entire money in short span of time we will suffer from the negative utility due to the law of diminishing marginal utility.

Yes, it will be consistent with our plot.

C) This choice depends on whether we are risk-averse or risk-lover.

If we are risk-averse, then we will take no risk and go for option A.

If we are risk-lover, then we have to calculate the expected value of our deal.

Which is  $Expected Value = 50/100*(600)+ 50/100*(0) = $300$

Hence, we will go for option B.