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hw4solution08(2) - Fall 2007 73-150 Microeconomics Problem...

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Fall 2007 73-150 Microeconomics Problem Set #4 Solution Key 1) BC original : p x x + p y y= Income BC subsidy : (p x -s)x+ p y y= Income BC income grant : p x x + p y y = Income+sx subsidy From figure 1, above, we see that the optimal bundle C under the income grant program is at a higher indifference curve than the optimal bundle B under the subsidy program, so it shows that income grant to a person provides more utility than does a subsidy on good x that costs the same amount to the government.. Graphing BC original and BC subsidy The government wants to spend the same amount of money on income grant or subsidy. Before any changes, we will see the BC original is our normal budget constraint given by Indiff. income grant Indiff. subsidy B BC income grant BC subsidy x y C A Indiff. original BC original x subsidy
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p x x+p y y= Income. The goal of subsidy is to reduce price of x for a consumer, and the government is paying s dollar per unit of x for the consumer. Looking at the equation for BC subsidy : (p x -s)x + p y y= Income, s is the amount of subsidy paid by the government for each good x, and because s>0, the new price, p x -s, of x is lower than the old price (p x ). The slope of budget constraint is y x p p , so if p x , y x p p would also , which tells us that BC subsidy is less steep than BC original . After you graph the two budget constraints, you will find A to be the optimal bundle given BC original , and B to be the optimal bundle given BC subsidy . If bundle B is (x subsidy , y subsidy ), because the government will pay s dollar for any amount that is being consumed (the bundle chosen tells us that the costumer chooses to consume x subsidy) , the total expenditure of the government on the subsidy program would be s* x subsidy . Graphing BC income grant From the previous section we know the total expenditure on the subsidy program is s* x subsidy , and because the government wants to spend the same amount of money on income grant or subsidy, we know: the cost of subsidy program= the cost of income grant program the cost of income grant program = s* x subsidy
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