Question

Why does C=M? Seeking tutorial for this solution.

(5) Steven has non-labor income each week of $500. He can work up to 100 hours per week for an hourly wage of $10 per hour. His utility for recreation (R) and consumption (C) is given by U(R,C) = 2R2C. What is Steven's reservation wage if the price of consumption is unity? (a) $30 (b) $40 (c) $50 (d) $60 (e) None of the above The reservation wage is equal to the MRS when the individual has L=0. Therefore, we need to find the MRS at L=0, R=100, C=M=500. MRS = 2,2020 = 20 = 1000 = 10. 2R2 100

Answer 1

Reservation wage is the highest wage at which Steven is indifferent between working and not working. Steven will work only if wage rate offered in the market is greater than the reservation wage. He will not work if the wage rate offered in the market is less than the reservation wage. Reservation wage is solved by finding the marginal rate of substitution at the point when he is not working that is the endowment point. If he is not working he will spend all his non-labor income on consumption.

If non-labor income increases reservation wage of the person also increases because he does not feel the need to work as his consumption is covered by his receipts of non-labor income.

Non-labor income each week is $500

Hours available to work per week is 100

Market hourly wage is $10

Utiltiy function, U(CAR) = 2R-C

Price of consumption is $1

MUC Marginal Rate of substitution, MRS = MUR MUC is marginal utility from consumption MUR is marginal utility from leisure au MUC = ac = 4RC MUR= 20 = 2R

MRS = a 4RC 20 R2 = R

Now since consumer is not working, his consumption is financed by the non-labor income. Therefore, his consumption is equal to non-labor income and he is enjoying leisure for all 100 hours available for work.

4RC MRS = 2R2 2C R 2 * 500 100 -= 10

Steven's reservation wage is $10

Correct answer is (e) None of the above