I think this is the question itself. What knowledge do you need me to provide? Please let me know

3. You are hired to evaluate the production behavior of a cost-minimizing firm that produces a single output and purchases its inputs in a perfectly competitive market. Let x = (x1, x2) represent the firm's inputs, w = (W1, W2) represent input prices, y = g(x1, x2) be the production function, and t > 0 be an exogenous technology index parameter. You discover that the firm's indirect cost function is given by, c(y,w, t) = 3y4w wit- (a) Calculate the Allen elasticity of substitution between the two inputs. (b) Let the firm produce a single unit of output and face prices w1 = 3 and W2 = 6. Use the concepts of average and marginal costs to evaluate the scale elasticity (SE) of the firm. How does the SE change when the price of wi increases? Why? (c) The firm benefits from technological progress, represented by an increase in t. Evaluate aC/t and Ox/t. Briefly interpret the economic implications of this progress for the firm (1-2 sentences). (d) Using information from the results above, can you recover an explicit functional form for the firm's production technology g(x1, x2)? If so, do it and determine whether the production technology is homothetic. If not, then explain why not. 3. You are hired to evaluate the production behavior of a cost-minimizing firm that produces a single output and purchases its inputs in a perfectly competitive market. Let x = (x1, x2) represent the firm's inputs, w = (W1, W2) represent input prices, y = g(x1, x2) be the production function, and t > 0 be an exogenous technology index parameter. You discover that the firm's indirect cost function is given by, c(y,w, t) = 3y4w wit- (a) Calculate the Allen elasticity of substitution between the two inputs. (b) Let the firm produce a single unit of output and face prices w1 = 3 and W2 = 6. Use the concepts of average and marginal costs to evaluate the scale elasticity (SE) of the firm. How does the SE change when the price of wi increases? Why? (c) The firm benefits from technological progress, represented by an increase in t. Evaluate aC/t and Ox/t. Briefly interpret the economic implications of this progress for the firm (1-2 sentences). (d) Using information from the results above, can you recover an explicit functional form for the firm's production technology g(x1, x2)? If so, do it and determine whether the production technology is homothetic. If not, then explain why not