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Task on Production Possibility Frontier and Labor Economics

## Dave and Diane's Production Possibility Frontier

1.Dave and Diane are married. Their individual production possibility frontiers (PPF) are as in the following picture:

i) How many dollars’ worth of Home Goods (H) should Dave give up in order to produce an extra dollar’s worth of Market Goods (M)? Explain.

ii) How many dollars’ worth of H should Diane give up in order to produce an extra dollar’s worth of M? Explain.

iii) Who has a comparative advantage in producing M between Diane and Dave? Explain.

iv) Draw the combined PPF.

v) Put the output combinations represented by the PPF on a per capita basis (i.e. draw a per capita combined PPF).

vi)Highlight the area in the graph representing the increased per capita output that is available if Diane and Dave decide to collaborate.

Dave and Diane have identical preferences. Assume that they have relatively stronger preferences for M. We also assume that relatively scarce goods are valued more than relatively abundant goods.

vii) Draw a set of indifference curves compatible with these assumptions and explain your reasoning.

viii) Let x denote dollar values of H and y denote dollar values of M. Which of the following

functional forms is compatible with the above assumptions on preferences?

a) U(x,y) = x0.5y0.5

b) U(x,y) = x2 y0.5

c) U(x,y) = x0.5y2

d) U(x,y) = x+2y

e) U(x,y) = x+y

f) U(x,y) = 2x+y

ix) Suppose David and Diane do not collaborate. Use the utility function you chose in point

viii) and the individual PPF to find analytically the amount of H and M that each of them consumes. Compute individual utilities as well. Sketch a graph and explain your reasoning

x) Suppose David and Diane decide to collaborate. Use the PPF you drew in point iv) and the utility function you chose in point viii) to find analytically the combination of H and M chosen by Dave and Diane. Sketch a graph and explain your reasoning.

xi) Compute the utility gain that David and Diane obtain from collaborating.

2.Diane sleeps 8 hours per night and is left with 16 hours to allocate between market and non-market activities. Diane has a non-labor income of \$12 per day. In the market, she knows she would earn \$w perhour of work.

i) Draw Diane’s budget constraint.

Diane Likes consuming market goods but she dislikes working (as it diminishes her leisure time). Her utility function is given by: where M denotes dollars’ worth of market goods and L denotes leisure time.

## Preferences for Market and Home Goods

ii) Derive the marginal rate of substitution between L and M and interpret it.

iii) Sketch the set of indifference curves representing Diane’s utility function. Interpret the shape of the curves (make sure you comment on the slope and convexity/concavity).

iv) What is the value of w at which Diane would be willing to split equally her time between leisure and

work (i.e. that value of w at which her optimal choice of L would be 11)? Show your reasoning.

v) Now assume that the market wage is the one you found in point iv). Explain graphically what would happen if Diane’s non-labor income increased.

vi) Explain graphically what would happen if the wage increased (clearly highlight substitution and income effect)

3.For each statement say if it is True or False and briefly explain why.

1. A substantial increase in women’s educational attainments may result in a decline of marriages.

2. David and Diane are married and David has an absolute advantage in both M and H. Then there is no benefit from specialization and exchange for David.

3. If Diane has a comparative advantage in H production, then David must necessarily have a comparative advantage in M production.

4. If Diane earns more than her husband in the labor market, then she will never earn more from specializing (to some extent) in housework.

5. Official statistics on female labor force participation suggest a U-shaped evolution between 1890 and 2011.

6. An increase in wages will always make individuals want to work more.

4.Fill the gaps in the following table (boxes highlighted in red

ii) Provide an example of an individual that would enter the category “Not in Labor Force.”

5.In less than 500 words describe and comment on the following graph. Suggested structure:

1. Describe the elements of the graph. What does the graph plot? What do the axis measure? How do we read the vertical axis (i.e. measures closer to zero correspond to what, in terms of female to male ratio)? What is the range of the measures employed? What does each line in the graph represent?

2. Describe the important features of the graph. No interpretation yet, just facts. What is the shape of the lines? How do different cohorts compare to one another? Report the relevant quantities in the graph.

3. Interpret and give possible explanations for the features of the graph that you reported in point 2.

4. Think of possible implications that the facts reported in this figure may have.