Question

Suppose that you currently hold 4 shares of Google stock and 2 shares of Microsoft stock. Initially, both prices are $1 per share, but then the price of Google stock suddenly doubles to $2 per share. Suppose that your preferences are Cobb-Douglas, u(x, y) = xy. Find the optimal portfolio choices under the original prices and the new prices. Show how much of the change in your portfolio (i.e. the change in demand for both goods) is due to pure substitution, pure income, and endowment income effects.

Answer 1

u(x,y) = xy such that 6 = x + y as p-p,-1 google stocks and y microsoft stock optimizing the utility we can find the value γ = xy + X(6-x-y) portfolio value is 9 if the google price increases to $2 the demand for 2-as 10- 2r + y since pr - 2 portfolio value changes to 11.1 total change in the port folio value is 2.1