Problem 3 (Labor Supply - Optimal time allocation - When income from other sources increases) Each week, Holga has 120 hours that she can spend on paid activities (H work time ) and on unpaid activities (L leisure/home production). Her hourly pay is w=$20. The price level is pC=1. Holga uses her cash income to buy consumption goods (C consumption). 1. In a graph where you measure leisure/home production along the horizontal axis and consumption along the vertical axis, draw Holga's budget constraint. Clearly label the L-axis intercept and the C-axis intercept. 2. Write the expression for Holga's budget constraint. Holga's utility from leisure/home production and consumption is U(C,L)=C1/3L2/3. 3. Holga's utility function belongs to the class of functions called Cobb-Douglas. Write one salient feature of these utility functions that you remember. 4. Write the expression of Holga's marginal rate of substitution as a function of L and C. (Keep in mind that leisure time is measured along the horizontal axis). 5. By solving Holga's tangency condition and budget constraint or by invoking the properties of Cobb-Douglas utility functions find Holga's optimal number of hours of leisure time, her optimal number of hours worked, and her optimal consumption. 6. Add an indifference curve to you graph and illustrate Holga's optimal choice. In your graph, do not forget to also mark Holga's number of hours worked. uppose Holga decides to become an Airbnb host and starts letting one of the rooms in her home. On average, she earns $300 per week rent 7. Explain why hosting for Airbnb does not changes Holga's opportunity cost of leisure time. Then, in your graph, illustrate how hosting for Airbnb affects Holga's budget constraint. 8. Now that she hosts for Airbnb will Holga work longer hours, shorter hours, or the same number of hours? ast consider Dana. Dana is a single parent and her utility for consumption and leisure time/home production is UD=4C+L. Just like Holga, Dana can work at a rate of w=$20 an hour. 9. Suppose that just like Holga, Dana decides to become a Airbnb host. Will she work shorter hours, the same number of hours or longer hours than before? Problem 3 (Labor Supply - Optimal time allocation - When income from other sources increases) Each week, Holga has 120 hours that she can spend on paid activities (H work time ) and on unpaid activities (L leisure/home production). Her hourly pay is w=$20. The price level is pC=1. Holga uses her cash income to buy consumption goods (C consumption). 1. In a graph where you measure leisure/home production along the horizontal axis and consumption along the vertical axis, draw Holga's budget constraint. Clearly label the L-axis intercept and the C-axis intercept. 2. Write the expression for Holga's budget constraint. Holga's utility from leisure/home production and consumption is U(C,L)=C1/3L2/3. 3. Holga's utility function belongs to the class of functions called Cobb-Douglas. Write one salient feature of these utility functions that you remember. 4. Write the expression of Holga's marginal rate of substitution as a function of L and C. (Keep in mind that leisure time is measured along the horizontal axis). 5. By solving Holga's tangency condition and budget constraint or by invoking the properties of Cobb-Douglas utility functions find Holga's optimal number of hours of leisure time, her optimal number of hours worked, and her optimal consumption. 6. Add an indifference curve to you graph and illustrate Holga's optimal choice. In your graph, do not forget to also mark Holga's number of hours worked. uppose Holga decides to become an Airbnb host and starts letting one of the rooms in her home. On average, she earns $300 per week rent 7. Explain why hosting for Airbnb does not changes Holga's opportunity cost of leisure time. Then, in your graph, illustrate how hosting for Airbnb affects Holga's budget constraint. 8. Now that she hosts for Airbnb will Holga work longer hours, shorter hours, or the same number of hours? ast consider Dana. Dana is a single parent and her utility for consumption and leisure time/home production is UD=4C+L. Just like Holga, Dana can work at a rate of w=$20 an hour. 9. Suppose that just like Holga, Dana decides to become a Airbnb host. Will she work shorter hours, the same number of hours or longer hours than before
