Question

In class, we solved the firm's cost-minimization problem when its production functiorn is given by f(x1, T2) ??? X2-a, where ? E (0, 1). Now suppose that with ?, ? 0. f you were to solve the cost-minimization problem (given some a 1, ?2, and y) and derive the results in the lecture slides again, what would change and what would not change? Explain. (You don't have to solve the problem again although you can if you choose to.) b) What conditions must be placed on ? and ? to ensure that the new production function exhibits increasing return to scale (IRS)? DRS? CRS:? c) For a generic input bundle, (x1, C2), how do the marginal products and the marginal rate of technical substitution depend on ? and ? (consider increasing just ?. Just ß, and multiplying both ? and ? with some factor k 1)? d) How does the elasticity of substitution at (T1,T2) depend on ? and ??