In: Economics
Suppose an individual’s utility function is u = x11/2x21/2. Let p1=4, p2=5, and income equal $200.
a. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility.
b. What is the optimal amount of x1 consumed?
c. What is the optimal amount of x2 consumed?
d. What is the marginal rate of substitution at the optimal amounts of x1 and x2?
e. As functions of p1, p2, and m, derive x1’s demand curve?
f. As functions of p1, p2, and m, derive x2’s demand curve?