1. Derive the Slutsky equation in a three commodity world.
2. Let , , be positive constants and let function f be defined as f(x, y, z) = ln x + ln y + ln z for all positive values of x, y and z. Show that f is a quasi-concave function. Give the definitions of quasi-concavity in this context.
3. Using the Roy's identity derive the demand functions for the utility function given by U (x1, x2) = b1 ln (x1 - c1) + b2 ln (x2 - c2).
4. Show that for homothetic production functions, the output at which average cost is a minimum is independent of factor prices.