Exercise 1 A consumer preferences over x and y are described by the utility function u(x,y)=xy. a)Draw two indifference curves. One representing all bundles providing utility 9 and one representing all bundles providing utility 16.
Exercise 1 The government has decided that the free market price of tobacco is too low. b)Let the price of good x be 10 and that of good y 10. Let the consumer’s income be 60. Calculate the consumer’s optimal consumption bundle and represent your solution graphically. Determine the consumer’s utility. At optimum, the slope of the indifference curve = slope of the budget constraint MRS = Px/Py MRS = Mux/Muy = du/dx / du/dy = y/x So we have y/x = 10/10 => x = y Budget constraint is 10x + 10y = 60 Since x = y, we can rewrite this as 10x + 10x = 60 So x = 3, y = 3
Exercise 1 c)Redraw the graph of part b). Let income increase to 80. Depict the effect of this change in wealth on the graph. Calculate the new consumer’s optimal consumption bundle. Determine the consumer’s utility and compare with the one of part b. Now the bc is 10x + 10y = 80 So x = y = 4
Exercise 1 d)Redraw the graph of part b. Keep income at its initial level 60 and let the price of good x fall to 5. Depict on the graph this change in prices. Calculate the new consumer’s optimal consumption bundle. Determine the consumer’s utility. Finally, represent the income and substitution effects graphically. From the drawn income and substitution effects is good x normal or inferior? Now y/x = 5/10 = ½ The budget constraint is 5x + 10y = 60 Solving we get x = 6, y = 3.
Chapter 5: Exercise 6 A person who consumes wine and cheese gets a rise, so his income increases from 3000 to Use diagrams to show what happens if both wine and cheese are normal goods. Now show what happens if cheese is an inferior good. 1 st figure shows the effect of an increase in income. The rise in income shifts the budget constraint out from BC1 to BC2. If both wine and cheese are normal goods, consumption of both increases. If cheese is an inferior good, the increase in income causes the consumption of cheese to decline, as shown in 2 nd figure.
Chapter 6: Exercise 5 A consumer has income of a year and divides this income between buying food and spending on leisure. The price of food is 15 and of leisure is 10. Draw the consumer’s BC and an IC to show an optimum. Assume that the price of food rises in three stages over the year in 10 increments while the price of leisure stays at 10. Draw new BCs and identify new optimums. Derive the demand curve for food.
Chapter 6: Exercise 5
Discussion In small groups, consider: Economic models optimize some function with some constraint. Design a study with a utility function and constraint where the study is not of consumption goods with prices. Is utility real? Can it be seen in brain scans?