Question

Suppose there are only two goods (X and Y) and only two individuals (numbered 1 and 2) in an economy. Let PX be the price of good X and PY be the price of good Y. And finally, let I1 represent the income of individual 1 and I2 the income of individual 2.

Suppose the quantity of good X demanded by individual 1 is given by

X1 = 10 - 2 Px + 0.01 I1 + 0.4 Py ,

and the quantity of X demanded by individual 2 is

X2 = 5 - Px + 0.02 I2 + 0.2 Py .

a) What is the market demand function for total X (= X1 + X2) as a function of PX, I1, I2, and PY?

b) Graph the two individual demand curves (with X on the horizontal axis, PX on the vertical axis) for the case

I1 = 1000, I2 = 1000; and Py = 10.

c) Using these individual demand curves, construct the market demand curve
for total X. What is the algebraic equation for this curve?

d) Now suppose I1 increases to 1100 and I2 decreases to 900. How would the
market demand curve shift? How would the individual demand curves shift?
Graph these new curves.

e) Suppose PY rises to 15. Graph the new individual and market demand
curves that would result.