Question

Ember(E) and Rajan (R)are a couple with individual productivities in both the market and their home. Each has 10 hours per day to devote to work. E can earn $9 per hour in the market, and can produce goods worth $8 per hour at home. R can earn $12 per hour in the market, and can produce goods worth $6 per hour at home.
Market-produced goods cost $5 per unit.
1）Who has the higher opportunity cost of home production? Briefly explain how you determined this.
2）Suppose Ember and Rajan choose to divide their time so that Rajan works part time in the market and part time at home, while Ember works full time in the market. ls this division of time efficient? Briefly explain why or why not.
3）if the couple chose to consume more home produced goods than either Ember or Rajan could produce alone，and the couple wanted to maximize their joint utility, which partner would produce market goods? Briefly explain why. Note: you do not have enough information to provide a numerical answer.
4）What is the slope of the couple's joint production possibility frontier(ppf)? What changes at the kink in the joint ppf?
5）Suppose Ember and Rajan together initially chose a bundle of the two types of goods requiring Ember to work part time in both the market and their home. One effect of the COVID-19 lockdown was that Ember's return from market labour was reduced to $7 per hour, or $70 per day. Nothing else changed. Given their initial choice, how would you expect the allocation of the couple's labour to change as a result of this? Explain this, using income and substitution effects.

Answer 1

Solution For the above Problem

1) OPPORTUNITY COST is Return on Most Profitable Investment Choice - Return on Investment Chosen to Pursue

For Ember,

Opportunity cost of home productions is,

9*10 - 8*10 =$10

For Rajan, it is

12*10-6*10 = $60

So, Rajan has higher opportunity cost for home production as he will lose $60 for the same.

2) I think time division is not efficient because ember works full time in market whereas Rajan works part time at home and part time in market.

• So time division is efficient for Rajan but not for Ember because Ember work alone in market. So Ember feel some difficulty in market and he have to solve alone .
• In this problem the type of work is not mentioned, so time division may either be efficient or not efficient depending upon the work.
• But since the time division is on the belief of both so it may be efficient.

3) The couple would have to produce goods that they have comparative advantage in. But since they consume more homemade good than they can individually produce, both of them will have to produce homemade good and the person who doesn't have a comparative advantage in producing homemade good will have to produce market goods as well as per consumption requirements of the couple.

5) Initially Ember was working in both the market and the home while rajan was working in market only. And due to COVID-19 Ember's labor return from market was reduced to $7 per hour or $70 per day.

• Now due to reduced value of Ember's labor in the market two effects will come into play, one is income effect and second is substitution effect.
• The income effect will into play as the value of Ember's labor is reduced in market now she can earn less in market so her income is reduced or the income of the couple as a whole has gone down.
• So the income effect would suggest us that due to reduced income Ember's would work more hours in market and less hours in home to compensate for the reduced income of her.
• And the substitution effect will come in as well, since Ember's was working both in home and in the market, which means she must have felt that her opportunity cost of working only in home is higher(opportunity cost is the lost labor income form the market while working the same hours at home).
• But now since her income per hour is reduced that opportunity cost has itself decreased and Ember's has more reason to work only at home.
• So the substitution effect would suggest us that Ember's should work less hours in market and more hours at home.

Now what is going to be the net effect of these two forces, the income effect and the substitution effect. Well see we are given that rajan also works in market and the value of his labor hasn't change so the income effect becomes less significant for Ember given that Rajan can work hours in market at the same income per hour to offset the income effect. while the substitution effect remains the same. So we should expect that couple's labor allocation, Ember should work at home only and rajan should work more in market.

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