Reference no: EM132414978
Suppose a firm has the following production function
f (x1, x2) = x11/2 x21/3
In addition, suppose the firm is making short run decisions by choosing x1, while keeping x2 = x2 at a fixed level. Let the input prices be denoted bby w1, w2 and the output price be denoted by p
(1) Derive the short run demand for input 1 and the short run supply.
(2) Graph the demand for input 1 and the supply making sure you label the graphs accordingly [you only need to show how the general shape of the lines are].
(3) Suppose there is a technology improvement that leads to a reduction in the price of input 1. Analyze the effect of the price change on the demand for input 1 as well as the supply of the output. Use the following two graphs to show the effect of the change. Be sure to indicate the original points as well as the ones after the change.
(4) Suppose the income of consumers in the market for the product increase, analyze the effect on the demand for input 1 and the supply of the product. Be sure to indicate the original points as well as the ones after the change.
(5) Suppose the manager of the firm is now deciding on the long run input. Derive the long run demand for both inputs and the supply of the product
(6) Analyze below how the manager's long run choice affects her choices in the short run. Be sure to indicate the original points as well as the ones after the change.