Microeconomics Homework

Questions and Answers

1) (20 points) Phil’s utility function is U (x,y)=max{x,y}.

a) Draw at least three indifference curves for Phil for different bundles.

b) Plot the bundle (1,3) on the graph. Give an example bundle, which Phil is indifferent. Show it on the graph and explain.

On the graph, Phil is indifferent to point B because it falls below the indifference curve and he has the opportunity to maximize his utility.

c) Plot the bundle (2,2) on the graph. Give an example bundle, which Phil prefers to (better off). Show it on the graph and explain.

2) (20 points) Suppose demand for good A is given by Q d= 400 −5 P+ P + 0.5Iwhere P is the price of good A, PB is the price of some other good B, and I is income. Assume that PA is currently $10, PB is currently $5, and I is currently $75.

a) What is the elasticity of demand for good A with respect to the price of good A at the current situation?

D=.000248292986Q, which I determined by plugging the provided values into the following equation: Q/D=10(400)-10+.5(75). To arrive at the answer, I solved the equation for D.

b) What is the cross-price elasticity of the demand for good A with respect to the price of good B at the current situation?

D= .000247678019Q, which I determined by plugging the provided values into the following equation: Q/D=10(400)-5+5+.5(75). To arrive at the answer, I solved the equation for D.

c) What is the income elasticity of demand for good A at the current situation?

A=2D-7980, which I determined by plugging the provided values into the following equation: Q/D=10(400)-10+.5(I). To arrive at the answer, I solved the equation for I.

3) Consider the utility functions: U(x, y) = 8x2 + 2 x y3+7 and U(x, y) =4x2y3. Answer the following questions for each utility function.

a) Is the assumption that “more is better” satisfied for both goods?

Yes, the “more is better” assumption is satisfied for both goods because both marginal utilities are always positive. When you add more of either x or y in both cases, the total utility will increase.

b) What is the MRSx,y for this utility function?

MRSx,y = 2 because MUx/MU y =2/1=2

c) Is the MRSx,y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve?

The MRSx,y is diminishing because the ratios decrease as they move along the curve.

4) (20 points) From the table below:

(Table omitted for preview. Available via download)

a) Calculate the price elasticity of demand when the price is $60 and when the price is $120.

The price elasticity of demand when the price is $60 and when the price is $120 is .2. I obtained this answer through the following equation: ((20-16)/(20))/((60-120)/(60)))

b) Calculate the price elasticity of supply when the price is $60 and when the price is $120.

The supply elasticity of supply when the price is $60 and when the price is $120 is 3/7. I determined this by utilizing the following equation: ((14-20)/(14))/((60-120)/(60)))

c) What are the equilibrium price and quantity?

From the above solutions, the equilibrium price is $80 and the equilibrium quantity is 16 million units.

5) (20 points) Jill likes both apples and peaches. The consumption bundle where Jill consumes X bushels of apples per year and Y bushels of peaches per year is (X, Y). Last year, Jill consumed 20 bushels of apples and 5 bushels of peaches

a) On a graph, plot several points that lie on the indifference curve that passes through the point (20,5), and sketch this curve. Do the same for the indifference curve passing through the point (1

b) For each of the following statements about Jill’s preferences, write “true” or “false.” (30,5) indifferent to (10,15)

False.

(10,15) preferred to (20,5)

True.