Question

Suppose there are two goods, good X and good Y . Both goods are available in arbitrary non-negative quantities; that is, the consumption set is R2++. A typical consumption bundle is denoted (x,y), where x is the quantity of good X and y is the quantity of good Y .

A consumer, Alia, faces two constraints. First, she has a limited amount of wealth, w > 0, to spend on the goods X and Y , and both of these goods have strictly positive prices, pX > 0 (for good X) and pY >0(forgoodY).Second,she has a limited amount of time,T>0, to purchase the goods, and it takes a strictly positive amount of time to purchase each of the goods. In particular, suppose that it takes tX > 0 units of time to purchase one unit of good X, and tY units of time to purchase one unit of good Y .

(a)Suppose that w=T =10,pX =tY =2,and pY =tX =1. In an appropriate diagram, illustrate (i) Alia’s monetary budget constraint, (ii) Alia’s time budget constraint, and (iii) Alia’s overall budget constraint.

(b)With w=T=10,pX =tY =2,andpY =tX =1asabove, can Alia consume the bundle (6, 2)? Can she consume the bundle (2, 6)? Explain your answers. In particular, what constraint (the money constraint or the time constraint) is relevant for each of these consumption bundles?

Answer 1

SOL;

Given

W = T = 10 , p^x = t^y = 2 , p^y = t^x = 1

a

i

equation of monetary budget constraint

p^x x + p^y y = w , putting values given

2x + y = 10

ii

equation of time constraint

t^x x + t^y y = T , putting values given

x + 2y = 10

iii

over all budget constraint is area common to monetary and time constraint.

AB is monetary constraint

CD is time constraint

CHB is over all constraint

b

For bundle [6,2] required money is 2*6 + 1*2 = 14 which violates monetary constraint. So this bundle can not be bought.Although time constraint is satisfied 6+4 = 10

For bundle [2,6] , required money is 2*2 +1*6 = 10 .,money constraint is satisfied.

required time is 1*2 + 2*6 = 14 ,time constraint is violated.