Econ 100A Spring Practice Midterm I

Transcription

1 Econ 100A Spring 2013 Practice Midterm I 10 T/F Questions 1. Finishing position in the Tour de France is an ordinal measure. TRUE 2. More is better means that marginal utility is never negative. TRUE 3. An individual's Engel curve can be derived from the price-consumption curve. FALSE, it can be derived from the income-consumption curve. 4. If cross-price elasticity of two goods is +1%, then the goods are neither complements nor substitutes. FALSE, they are substitutes. 5. When the price of oranges decreases, the quantity demanded of apples increases. Therefore, the price elasticity of demand for apples is positive. False, price elasticity of demand for apples has nothing to do with the price of oranges. 6. If price elasticity of demand is negative then the good must be normal. False, it can be inferior. 7. The substitution effect measures the effect of a price change on consumption, keeping utility constant. TRUE. 8. Along a single *linear* demand curve, elasticity is increasing as quantity is decreasing. TRUE 9. U.S.A. should reform its health care system is a good example of a positive statement. FALSE 10. The compensated demand curve is more elastic than the uncompensated demand curve when a good is normal. FALSE, the uncompensated demand is more elastic when the good is normal.

2 Short-Answer Questions 1. What does MU x /p x = MU y /p y means in words? The last $ spent on good X yields as much utility as the last $ spent on good Y. This equality holds at an interior solution. 2. Assume people consume one of two goods to operate their vehicle: electricity or gasoline. Draw the following indifference curves for the consumption of electricity and gasoline: a. A person with an electric car b. A person with a hybrid car (either imperfect substitutes or perfect substitutes is OK here) 3. Jason consumes 10 slices of pizza a month when his income was $1000 a month. Now he gets a raise of $100, meaning he makes $1100 a month. He now consumes 12 slices of pizza. What is his income elasticity? Explain in words what your answer means. Income elasticity of demand: Q/ I*I/Q Where I is income and Q is quantity demanded. = 2/100*1000/10 = 2% When Jason s income increases by 1% his consumption of pizza increases by 2%.

3 4. Harold regards pizza (x-axis) and burgers (y-axis) as imperfect substitutes. The price of burgers decreases and Harold consumes the same amount of pizza. a. Graph this scenario and mark the price-consumption curve on your graph. b. Can U = X 2 Y be a utility function representative of these preferences? Show with math why or why not. Burgers Price consumption curve Pizza For part b, you had to find the demand for good y and see whether px was in that expression. If so, then clearly it cannot be represented by these preferences. MUx/MUy = 2XY/X 2 = P x /P y 2P y Y = P x X 2P y Y = I P y Y -> Y = I/3P y X = 2I/3P x Since the demand for X does not include the price of good Y, then this potentially could be a representation of the preferences above.

4 Long-Answer Question 1. Elizabeth is indifferent between consuming 1 chocolate bar and 1 energy bar. She has $8. The price of energy bars is $2 and of chocolate bars is $1. Let energy bars be on the x-axis and chocolate bars on the y-axis. a. Draw a couple of Elizabeth s indifference curves, budget constraint and her Chocolate bars optimal bundle. Indifference Curves in black, budget constraint in orange Energy bars b. How many energy bars and chocolate bars will Elizabeth consume? 0 energy bars and 8 chocolate bars c. The price of cacao increases significantly due to weather shock in the tropics. Now a chocolate bar costs $4. Draw the new budget constraint and optimal bundle. How many energy bars and chocolate bars will Elizabeth consume?

5 New budget constraint in blue. She consumes 4 energy bars and no chocolate bars. 2. Consider the CES utility function U(X,Y) = (X Y 0.5 ) 2 a. Find the expression for the indifference curve and plot an indifference curve for U = 64. U 0.5 = X Y 0.5 Y 0.5 = U X 0.5 Y = (U X 0.5 ) 2 = (8 - X 0.5 ) 2 b. Based on the shape of the indifference curve, can you say which good is more preferred? Explain your answer. The indifference curve is relatively flat which means that the good on the y-axis is more preferred to the good on the x-axis. c. Using the Lagrangian method, find the optimal quantities of X and Y consumed, given Px, Py and I (income).

6 d. Find whether good X and good Y are inferior or normal. They are both normal as the sign of dx/di and dy/di is positive e. Can you say whether X & Y are substitutes or complements? Explain Well, this is a constant elasticity of substitution utility, which should have given you a big hint that these indeed are substitutes. If you derive the solution for Y using the quotient rule, you get a positive sign, therefore these are substitutes.