Question

Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 5 units of good Y. Consumer B is given an initial endowment of 5 units of good X and 3 units of good Y. Consumer A’s utility function is given by:

U_A(X,Y) = X + 4Y,

and consumer B’s utility function is given by

U_B(X,Y) = MIN (X, 2Y).

If the prices are P_X = 1 and P_Y = 3, if each consumer sells her initial endowment and buys back her optimal bundle, which of the following statements is true?

Group of answer choices

Both Markets are in Equilibrium

There is Excess Demand in the Market for Good X = 2.4

There is Excess Demand in the Market for Good Y = 0.8

There is Excess Supply in the Market for Good Y = 1.6

There is Excess Supply in the Market for Good X = 1.6

Answer 1

Let every one sells whatsover he had,

Total available quantity for X=3+5=8

Total available quantity for Y=5+3=8

Now consider the case of A

Amount received after selling whatsoever he had=3*1+5*3=$18

MU for good X for A=MUX=dU/dX=1

MU for good Y for A=MUY=dU/dY=4

MUX/PX=1/1=1

MUY/PY=4/3=4/3

We see that (MUY/PY)>(MUX/PX).

A will consume Y only to maximize utility.

Quantity demanded of X for A=0

Quantity demanded of Y for A=Total amount/PY=18/3=6

Now we consider the case of B

Amount received after selling whatsoever he had=5*1+3*3=$14

Utility function indicates that B will buy 2 units of X for every 1 unit of Y to maximize utility.

We can say that B will buy in bundle, One bundle will include 2 units of X and 1 unit of Y.

Price of bundle=2*1+3=$5

Number of bundles that can be bought=14/5=2.80

He can afford 2.80 bundles in what amunt he has

Quantity demanded of X for B=2*2.8=5.6

Quantity demanded of Y for B=2.8

Total demand for X=0+5.6=5.6

Total demand for Y=6+2.8=8.8

Excess supply for X=8-5.6=2.4

Excess demand for Y=8.8-8=0.80

Correct option is

There is excess demand in the market for good Y=0.80