Consider the problem of a rational consumer with an experienced utility function given by 10√x+m. Let q denote the market price of good x.

What is the expression for the consumer surplus if the consumer receives a total cash rebate of q√x when he buys x units of the good?

To find the expression for the consumer surplus in this scenario, we need to start by calculating the consumer's willingness to pay (WTP) for x units of the good.

The consumer's experienced utility function is given by 10√x + m, and let's assume the consumer's income is y. So, the maximum amount the consumer is willing to pay for x units of the good is equal to the experienced utility minus the consumer's income:

WTP = (10√x + m) - y

The consumer's surplus is the difference between the maximum amount the consumer is willing to pay (WTP) and the actual amount paid, which is q√x after receiving the cash rebate. Therefore, the expression for the consumer surplus is:

Consumer Surplus = WTP - q√x

Substituting the WTP expression, we get:

Consumer Surplus = (10√x + m) - y - q√x

So, the expression for the consumer surplus, when the consumer receives a total cash rebate of q√x when buying x units of the good, is (10√x + m) - y - q√x.

To find the expression for the consumer surplus, we need to first understand what consumer surplus is. Consumer surplus is the difference between the total amount a consumer is willing to pay for a certain quantity of a good and the actual amount the consumer has to pay.

Given the utility function 10√x + m, we can assume that the consumer's willingness to pay for a quantity of good x is equivalent to the utility function. Therefore, the maximum amount the consumer is willing to pay for x units of the good is given by 10√x + m.

Now, let's calculate the actual amount the consumer has to pay. Since the consumer receives a cash rebate of q√x for purchasing x units of the good, the effective price the consumer has to pay is reduced by the value of the cash rebate. Therefore, the actual amount the consumer has to pay is q - q√x.

To find the consumer surplus, we subtract the actual amount the consumer has to pay from the maximum amount the consumer is willing to pay:

Consumer Surplus = (10√x + m) - (q - q√x)

Simplifying further, we can distribute the negative sign:

Consumer Surplus = 10√x + m - q + q√x

Thus, the expression for the consumer surplus is 10√x + q√x + m - q.