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380 problem set 4- budget constraint

380 problem set 4- budget constraint - x y I p x p y ≥...

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The Budget Constraint Problem Set #4 Econ 380 R. Pope Winter 2011 1. a) Graph the budget constraint 200= $2x + $4y where income is 200, and the price of x is $2 while the price of y is $4. b) What is the maximum amount of x and y that can be purchased? c) What is the meaning of the relative price of x, p x /p y =$2/$4? In what units is this relative price measured? d) What is the slope of the budget constraint? 2. Suppose that the budget constraint in 1. is amended to read: For the first 50, the price of x will be three, p x = 3 for x 50 p x = 1 for additional x, x > 50. a) Graph the budget constraint. b) If a person purchases 75 units of x, what is the average price and the marginal price? 3. John has the budget constraint in 1., except that he must spend 10 units of y to go across town to have the opportunity to buy x a) Graph the budget constraint. b) Distinguish numerically the average from the marginal price of x, x > 0. 4. Using symbols only, the budget set looks like {x,y:
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Unformatted text preview: x y I p x p y ≥ + } with budget constraint {x,y: I=p x x + p y y} where I is income, and x and y are two goods with respective prices p x and p y . a) Write the equation in intercept-slope form with y as the dependent variable? b) What is the y intercept of the equation? x intercept? c) What is the slope of the equation? How is it interpreted? d) If now p x and p y are factory prices and transport costs are t per unit for both x and y to ship from the factory to the consumer, what is the new relative price of x ( x y p p ) for a consumer? If t were $1 using the prices in problem 1, would the relative price of x be higher or lower for the consumer compared to at the factory? 5. Interpret t in problem 4. as an ad valorem tax rate (the tax rate is applied times price, e.g., 50%) and apply it only to x, how does this change the budget constraint in 4a)? Include how the tax changes the relative price of x to the consumer?...
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