Question

Consider the problem of a rational consumer with an experienced utility function given by 10x√+m. let q denote the market price of good x. question. what is the expression for the consumer surplus if the consumer receives a total cash rebate of qx√ when he buys x units of the good?

Answer 1

Consumer surplus with a rebate is calculated by subtracting the total cost including the rebate from the consumer's total valuation of the units bought. The surplus for a utility function of 10x√ with a qx√ rebate per unit is the experienced utility minus market cost plus the rebate.

Step-by-step explanation:

Consumer surplus represents the difference between what consumers are willing to pay for a good or service and what they actually pay. Given a utility function of 10x√ and a rebate of qx√ when purchasing x units, the consumer surplus can be expressed as:

Consumer Surplus = (Willingness to Pay) - (Market Price Paid) + (Rebate)

Assuming the demand function reflects the willingness to pay, the consumer surplus with the rebate included can be calculated by subtracting the total cost including the rebate from the consumer's total valuation of the x units bought based on the utility function. If the market price is q and the rebate is qx√ per unit, for x units, the consumer surplus will be:

Consumer Surplus = 10x√ - (qx - qx√)

This is under the assumption that q represents the consumer's willingness to pay without the rebate, the value gained from the experienced utility function is 10x√, and the total cash rebate is qx√.

Answer 2

Consumer Surplus = Total utility - expenditure of consumer;

In our case the market price is q and consumer gets a rebate ( discount ) of q sqrt (x). According this the expenditure is q - q sqrt (x).

The total utility is given with 10x√+m.

So, the expression for the consumer surplus is: 10x√+m -q - q sqrt (x).