Consider the problem of a rational consumer with an experienced utility function given by 10ln(x)+m and a wealth level W=100. Suppose that the market price for good x is p=$2 per unit.
You are asked to analyze the impact on the consumer's demand of the following three policies, under the assumption that the market price does not change
A. The consumer receives a 'buying incentive' from the governmnet equal to $1 per unit of x bought.
B. If the consumer buys x units of the good, he receives a total cash rebate of pln(x) dollars.
C. If the consumer buys x units of the good, then he receives another x units for free.
What is the amount purchased by the consumer at the policy that generates the largest demand ?