Question

In the labor-leisure model, the representative consumer receives satisfaction from consumption of goods (C) and from the consumption of Leisure (L). Let C be the composite good with price $1 and L determines the number of hours of leisure this person consumes. Therefore U = f(C,L) for this consumer. This consumer’s consumption is constrained by time and income. Let her non-labor income, V, be $1200 per week, let the hourly wage rate be $8 and h be the number of hours this consumer allocates to the labor market. Let 500 hours be the total time available to this consumer per week.

a. Identify the equation of the budget constraint faced by this consumer given the above information and represent this constraint graphically.

b. Now assume that the hourly wage rate reduces to $5. Identify the new budget constraint’s equation and show the change graphically. Given this change in the wage rate, what effects will impact the consumer choice?

Answer 1

Given U = f(C,L)

a) V = $1200

h = no. of hours that a person is willing to work

T = 500

Person's budget constraint:

C = wh + V

that is the dollar value of expenditure on goods is equal to the sum of the labor earnings and non-labor earnings. Now a person can either work or take leisure, therefore T = h + L where L is the total amount of leisure. Therefore the above equation will be:

C = w(T - L) + V

C = (wT + V) - wL

So the slope of is negative (-w).

C = (8*500 + 1200) - 8L

C = 5200 - 8L

b. C = (wT + V) - wL

C = (5*500 + 1200) -5L

C = 3700 - 5L

Consumer will demand less.