Suppose we have preferences U(X,Y)=10X2/3Y1/3. Create a table and graph/sketch the indifference curve through the bundle X=30 and Y=30. The Marginal Rate of Substitution is MRSXY=2Y/X. For the bundle (X=30,Y=30), calculate and then interpret what the value of the MRS means. Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain. From (d) we can show that optimal demands are: X=2/3M/Px and Y=1/3M/Py. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands ( X, Y) and utility if Px=10,Py=5 and income M=1200. Suppose Px falls to Px=8 but Py and M are unchanged (Py=5 and M=1200 ). Calculate the new optimal demands and utility. Compare to the original optimal choices in (e) and discuss. Show that, if M falls to $1034, with Px=8 and Py=5, then this has the same utility as the equilibrium in (e) above. Eg confirm that utility is unchanged but with this new income and prices. What do we mean by Compensating Variation (CV) ? What is the value of the CV in this example? Explain. Suppose we have preferences U(X,Y)=10X2/3Y1/3. Create a table and graph/sketch the indifference curve through the bundle X=30 and Y=30. The Marginal Rate of Substitution is MRSXY=2Y/X. For the bundle (X=30,Y=30), calculate and then interpret what the value of the MRS means. Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain. From (d) we can show that optimal demands are: X=2/3M/Px and Y=1/3M/Py. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands ( X, Y) and utility if Px=10,Py=5 and income M=1200. Suppose Px falls to Px=8 but Py and M are unchanged (Py=5 and M=1200 ). Calculate the new optimal demands and utility. Compare to the original optimal choices in (e) and discuss. Show that, if M falls to $1034, with Px=8 and Py=5, then this has the same utility as the equilibrium in (e) above. Eg confirm that utility is unchanged but with this new income and prices. What do we mean by Compensating Variation (CV) ? What is the value of the CV in this example? Explain
