Question

Consider a couple (a husband and a wife) that jointly represents their collective preferences between combinations of household production time (X) and purchased goods and services (Y) according to the formula W = x2Y, where W represents the level of welfare. Suppose the maximum time available in a day is 18 hours and currently the wife devotes 6 hours to market work (H) at a wage of $15 per hour. a. What is the level of welfare associated with the wife's current situation? b. How much additional purchasing power would the wife contribute if her market work hours increased to 10? c. How much of an increase in purchased goods and services would be necessary to compensate for the additional 4 hours of lost household production? d. Should this couple choose to have the wife increase her market work by 4 hours? e. If this couple is raising a child, suppose that combinations of household production and purchased goods are now ranked according to the formula U = X3Y. Would the additional 4 hours of market work be a good move for the family in this situation?

Answer 1

A] Level of welfare : W = X²Y ; where X = household production time, Y = purchased goods & services

Total time = 18 hours, time devoted to work = 6 hours at 15 / hr. So, total income (Y) = 15 x 6 = 90, & household production time = 18 hrs - 6 hrs = 12hrs.

So, welfare = X²Y = (12)²(90) = 12960

B] Additional purchasing power, with market work hours increased to 10 :

New purchasing power : wage x hiked hours = 15 x 10 = 150. Additional purchasing power = new - old purchasing power = 150 - 90 = 60

C] Welfare function W = X²Y. Lost 4 hours of household production X would fall the welfare level 'W' to W / (4)² ie W / 16. So, to compensate for welfare level W loss, Y ie value of goods & services worth 16 should rise.

D] Previous W at (X,Y) ie (12,90) ; {as per part A} = 12960

• Work hours increase by 4 hours :- Y goods & services value rise to (6 + 4) hrs at 10 / hr = 10 x 15 = 150. And, This makes X household hours fall to 12 - 4 = 8.
• So, new W = X²Y = (8)² (150) = 9600.
• As welfare level in previous situation 12960 > Welfare level after working hours raised to ten, ie 9600. So, couple should not choose for wife to increase working hours by 4.