Question 1: Suppose a consumer endowed with N hours of labor. Differently from the consumer we studied in this module, this one does not value leisure. However, she does value the size of her family such that the consumer's utility function is U (C, F), where C denotes consumption, and F denotes the family size, Assume that the preferences over C and F are similar to the preferences over consumption and leisure discussed in class. a) In a graph with family size F in the X-axis and consumption C in the y-axis, show the indifference curves for these preferences The consumer receives a real wage w for each hour worked and a real dividend Tr, If the consumer chooses to have zero children, F = 0, she supplies N hours of labor. However, for each child, the consumer is required to forgo b hours of labor such that the labor income is w(N 13F), Note that, since hours worked cannot be negative, F cannot be larger than N [b b) Write the budget constraint of the consumer, Draw the budget constraint line in a graph with family size F in the X-axis and consumption C in the y-axis. Show the optimal choice of the consumer. (You can draw in the same graph of item a) c) Now, assume that the consumer is indifferent about the diversity in her consumption bundle, i.ei, the MRSF'C is constant. Repeat items (a) and (h) under this new assumption Question 2: In a graph with labor in the xaxis and output in the yaxis, draw the production function studied in class. Then, in the same graph, draw a second production function assuming the marginal product of labor is constant, ZOOM +