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Unformatted text preview: Econ302 Homework Assignment 2 Summer 2009 Solutions 1. Suppose that the price of gasoline has risen by 50%. What happens to a consumer's level of well- being given he spends some of his income on gasoline? Diagram the impact of the increase in gas prices in a commodity space diagram, and show the relevant indifference curves. Now, if the individual's income rises just enough so that his original consumption bundle exactly exhausts his income, will the individual purchase more or less gasoline (this level of income implies the consumer can afford his original consumption bundle)? Is the individual better-off at the higher price level of gasoline with the higher income level or the original price of gas and income? Solution: Initially, the consumer is on budget constraint BC 1 , consuming g 1 units of gasoline on indifference curve I 1 , where M is the individual's income level and P 1 is the price of gasoline. If only the price of gasoline changes to P 2 , the horizontal axis intercept of the budget constraint moves towards the origin. This is illustrated above by a movement to the budget constraint BC 2 . On indifference I 2 , his level of satisfaction is lower than before. Now, if the individual's income increases just enough so that his original consumption bundle exactly exhausts his new budget. However, the slope of the budget constraint (BC 3 ) that runs through his original consumption bundle is steeper due to the higher price of gas. This also implies that his MRS is less than the ratio of prices. Thus, the individual can attain a higher level of utility by purchasing less gasoline than g 1 . The individual is better-off at higher prices and income than at original levels. 1 2. Consider a consumer with the utility function ( , ) 10 ( , ) U X Y Min X Y = , where Min is the minimum of the two values of X and Y. a. Draw the indifference curves corresponding to the utility levels of 30 and 60, respectively. To draw the indifference curve corresponding to the utility level of 30, we set 30 = 10Min (X ,Y). Divide both sides by 10 to get 3 = Min (X,Y). This means all baskets where the minimum of the two goods is 3 will yield a utility level of 30. For example, some of these baskets are (3, 3), (3,4), (3, 10), (5,3), (8,3), (10,3). Show these baskets on a graph and you will get an L-shaped indifference curve. Similarly, to draw the indifference curve corresponding to the utility level of 60, we set 60 = 10Min (X ,Y). Divide both sides by 10 to get 6 = Min (X,Y). This means all baskets where the minimum of the two goods is 3 will yield a utility level of 60. b. If the prices of the two goods are $4 X P = and $8 Y P = , and the consumer income is $60, find the optimum consumption basket. What is the level of utility at the optimum basket?...
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- Spring '08