The unit price of market goods is $1. Each person has 8 hours to work each day. Another couple, Sylvan and Alex, have the same productivities: Sylvan is identical to Rajan, while Alex and Esther are

The unit price of market goods is $1. Each person has 8 hours to work each day. 

Another couple, Sylvan and Alex, have the same productivities: Sylvan is identical to Rajan, while Alex and Esther are identical. Esther and Rajan both engage in market work. Sylvan works full time at home, so only Alex works in the market.

 a) Given this information, which couple has the higher opportunity cost of home produced goods? Explain how you determined this. You can add a diagram if that helps, but you are not required to include one. 

b) Can you determine which couple has the higher utility? Explain why or why not. Suppose now that value of market production for both Alex and Esther increased to $12/per hour. 

c) Explain the change in the household joint production possibility frontier generated by this change. 

d) Explain what would happen to each couple’s choice of both household and market produced goods, using an analysis by means of income and substitution effects. 

e) What changes in time allocation for each couple that would be necessary to produce and consume this new bundle? Briefly explain your reasoning.