Question

1. If a consumer's budget constraint has a slope that is less than -1:

   	A.	the consumer gets less utility from good X than from good Y.
   	B.	the price of good X is less than the price of good Y.
   	C.	the consumer gets more utility from good X than from good Y.
   	D.	the price of good X is greater than the price of good Y.

1. A consumer has U = X^0.5Y^0.5 for a utility function, with MU_x = 0.5 X^–0.5Y^0.5 and MU_y = 0.5 X^0.5Y^–0.5. If she has income of $100, the price of X is $5, and the price of Y is $10, this consumer will use _____units of X and _____units of Y in equilibrium.

1. The consumer's utility function for goods X and Y is U = 3X + 15Y. Good X is placed on the x-axis and good Y is placed on the y-axis. Which of the following statements is TRUE?
   
   I. The marginal utility of good Y is 15.
   II. The MRS_XY = 5.
   III. The consumer is always willing to trade away 5 units of good X for 1 unit of good Y.

   	A.	I, II, and III
   	B.	I and III
   	C.	I and II
   	D.	II only

Answer 1

1. If the consumer's budget constraint has a slope that is less than -1 implies that the price of good X is less than the price of good Y. Because the slope of budget constraint is (-Px/Py) and if it is less than -1, this means that Px<Py. Hence, option(B) is correct.

2. MUx= 0,5 X^-0.5 Y^0.5

MUy = 0.5X^0.5 Y^-0.5

MRS = MUx/ MUy = (0,5 X^-0.5 Y^0.5) / (0.5X^0.5 Y^-0.5)

MRS = Y/X

Px= $5 and Py = $10

At optimal : MRS= Px/Py

Y/X = 5/10

X= 2Y

Budget constraint : Px X + Py Y = M

5X + 10Y =100

Now ,put X=2Y in this ,we get:

5(2Y) + 10Y = 100

20Y =100

Y = 5

X= 2(5)= 10

Hence, this consumer will consume 10 units of X and 5 units of Y in equilibrium.

3. MUx = 3

MUy = 15

MRS = MUx / MUy = 3/15 =1/5

This means that consumer is always willing to trade away 5 units of good X for 1 unit of good Y.

Hence,option(B) i.e I and III is correct.