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Econ 302

Homework #2

1.  (12 Total Points)

Suppose a Consumer’s utility function is given by U(X,Y) = X^1/2Y^1/2.

· The Consumer has $108 to spend (M = $108).

· The price of Good Y is P_Y = $1.  

· The price of Good X is initially P_X = $1, and then the price of Good X increases to P_X = $9.

a) (4 points) Calculate the Compensating Variation (Note that since P_X increases, this will be a positive number.)

Compensating Variation =  ________________________

b) (4 points) Calculate the Equivalent Variation (Note that since P_X increases, this will be a positive number.)

Equivalent Variation =  ________________________

C (4 points) Of the total change in the quantity demanded of Good X, how much is due to the substitution effect and how much is due to the income effect?

SE = __________________

IE = __________________

2. (22 Total Points) Suppose a Consumer’s utility function is given by U(X,Y) = MIN(3X,Y).

· The Consumer has $36 to spend (M = $36).

· The price of Good Y is P_Y = $1.  

· The price of Good X is P_X = $1.

a) (2 points) How much X and Y should the consumer purchase in order to maximize her utility?

X* = ________________

Y* = ________________

b) (2 points) How much total utility does the consumer receive?

U(X*, Y*) = _________________

c) (2 points) Now suppose P_X increases to $3.  What is the new bundle of X and Y that the consumer will demand?

X** = ________________

Y** = ________________

d) (2 points) Calculate the Compensating Variation (Note that since P_X increases, this will be a positive number.)

Compensating Variation =  ________________________

e) (2 points) Calculate the Equivalent Variation (Note that since P_X increases, this will be a positive number.)

Equivalent Variation =  ________________________

f) (2 points) Of the total change in the quantity demanded of Good X, how much is due to the substitution effect and how much is due to the income effect?

SE = __________________

IE = __________________

f) (10 points) In the space below, draw on a graph the

· original budget constraint (draw this in black)

· new budget constraint (draw this in green)

· compensated budget constraint (draw this in red)

Also, on your graph, indicate the optimal bundle on each budget constraint.  

· Label the optimal bundle on the original budget constraint X* and Y*

· Label the optimal bundle on the new budget constraint X** and Y**

· Label the optimal bundle on the compensated budget constraint X^C and Y^C

In order to receive full credit, your graph must be neat, accurate, and fully labeled.  Make sure to label each budget constraint with the correct values of M, P_X, and P_Y.  Also make sure to identify the correct values of X and Y in each bundle.  

3.  (16 Total Points) Suppose a consumer’s utility function is given by U(X,Y) = 5X + 2Y.  Also, the consumer has $30 to spend, and the price of Good X, P_X = $1.  Let Good Y be a composite good (Good Y is the “numeraire”) whose price is P_Y = $1.  So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X.

Suppose the Price of Good X increases to P_X = $3.

a) (4 points) Calculate the Compensating Variation: (Note that since P_X increases, this will be a positive number.)

CV = _____________________

b) (4 points) Calculate the Equivalent Variation: (Note that since P_X increases, this will be a positive number.)

EV = _____________________

C) (8 points) In the table below, fill in the Quantity Demanded of Good X (Q_D) at each price: