Problem Set 2 – due 1/26/2017

ECN 312 – Intermediate Microeconomic Theory Spring 2017

Please make sure that your problem set is legible and stapled. Please write your name and section number on your problem set. On your graphs, please label axes, curves, intercepts, and all points relevant to the question. Explain your work thoroughly in order to receive full credit. In particular, “True or False? Explain” questions must be accompanied by an explanation to receive any credit. Possible points are given in parentheses.

1. (20) Consider the following three schedules, which specify Leslie’s preferences over two goods, earrings (E) and necklaces (N).

Utility = 100

E

N

10

6

11

5

12

4

Utility = 101

E

N

10

7

11

6

12

5

Utility = 103

E

N

10

8

11

7

12

6

True or False? Explain.

(a) (7) The marginal utility of necklaces diminishes as N increases, holding E constant. (b) (7) The marginal utility of earrings increases as E increases, holding N constant.

(c) (6) These preferences give rise to indifference curves that satisfy the convexity property.

2. (20) Consider the following utility function, which specifies Giulia’s preferences over two goods, x-ray goggles (x) and yellow sweaters (y). (Please note that this is an example of a quasi-linear utility function.)

U(x,y)=14 x+7y(a) (5) Plot an indifference curve map for this utility function (please put x on the horizontal

axis and y on the vertical one). In order to do so, follow the following instructions: i. Consider some fixed level of utility, U0. Write and expression for y as a function x and

U0.

ii. Consider a particular value for U0 (in this case, choose U0 = 35) and calculate the value of y for x = 0, 1, 2, 3, 4, and 5.

iii. Plotting these values will yield the U0 = 35 indifference curve for this utility function. iv. Repeat this process for U1 = 42.

1. (b)  (5) What is the marginal utility of x? What is the marginal utility of y?

2. (c)  (5) What is the slope of the U0 indifference curve at x = 4 ? Interpret this number in terms

of Giulia’s willingness to trade y for x.

3. (d)  (5) What happens to the slope of the indifference curve as we move from U0 to U1 at x = 4?

3. (10) Consider Cruz who has preferences over hours playing video games (V) and hours playing board games (B). Putting V on the horizontal axis and B on the vertical axis, draw at least three indifference curves describing Cruz’s preferences in the following scenarios.

1. (a)  (5) Cruz’s level of utility today is given by the activity he spends highest number of hours on today.

2. (b)  (5) Cruz’s level of utility today is given by the activity he spend the lowest number of hours on today.

Problem Set 2 – due 1/26/2017

ECN 312 – Intermediate Microeconomic Theory Spring 2017

Please make sure that your problem set is legible and stapled. Please write your name and section number on your problem set. On your graphs, please label axes, curves, intercepts, and all points relevant to the question. Explain your work thoroughly in order to receive full credit. In particular, “True or False? Explain” questions must be accompanied by an explanation to receive any credit. Possible points are given in parentheses.

1. (20) Consider the following three schedules, which specify Leslie’s preferences over two goods, earrings (E) and necklaces (N).

Utility = 100

E

N

10

6

11

5

12

4

Utility = 101

E

N

10

7

11

6

12

5

Utility = 103

E

N

10

8

11

7

12

6

True or False? Explain.

(a) (7) The marginal utility of necklaces diminishes as N increases, holding E constant. (b) (7) The marginal utility of earrings increases as E increases, holding N constant.

(c) (6) These preferences give rise to indifference curves that satisfy the convexity property.

2. (20) Consider the following utility function, which specifies Giulia’s preferences over two goods, x-ray goggles (x) and yellow sweaters (y). (Please note that this is an example of a quasi-linear utility function.)

U(x,y)=14 x+7y(a) (5) Plot an indifference curve map for this utility function (please put x on the horizontal

axis and y on the vertical one). In order to do so, follow the following instructions: i. Consider some fixed level of utility, U0. Write and expression for y as a function x and

U0.

ii. Consider a particular value for U0 (in this case, choose U0 = 35) and calculate the value of y for x = 0, 1, 2, 3, 4, and 5.

iii. Plotting these values will yield the U0 = 35 indifference curve for this utility function. iv. Repeat this process for U1 = 42.

1. (b)  (5) What is the marginal utility of x? What is the marginal utility of y?

2. (c)  (5) What is the slope of the U0 indifference curve at x = 4 ? Interpret this number in terms

of Giulia’s willingness to trade y for x.

3. (d)  (5) What happens to the slope of the indifference curve as we move from U0 to U1 at x = 4?

3. (10) Consider Cruz who has preferences over hours playing video games (V) and hours playing board games (B). Putting V on the horizontal axis and B on the vertical axis, draw at least three indifference curves describing Cruz’s preferences in the following scenarios.

1. (a)  (5) Cruz’s level of utility today is given by the activity he spends highest number of hours on today.

2. (b)  (5) Cruz’s level of utility today is given by the activity he spend the lowest number of hours on today.