Potato is produced according to the function: q = 1040/1-a where q is the quantity produced, & represents land and I represents the number of workers. The farmer is a price taker with respect to all prices. Assume a = 0.5. (a) Write the general form for the farmer's cost minimization problem. (b) Derive the conditional input demand functions for k" and (" given this particular production function. (c) Derive the Total Cost Function. (d) Suppose wage of workers=9 and rent for land=4 and the farmer wants to produce q = 100 units of output.Find the optimal land and labor demand. (e) Derive the Short-Run Total Cost Function. (f) Suppose the firm wants to increase the output level to 120. What is the labor and land demand in the short run? Show that short-run total cost is higher than long run total cost in that case.Problem 15 Labour Demand with Perfect Competition in the Labour Market and Perfect Competition in the Output Market in Short Run. You are the manager of a business that operates in perfectly competitive markets (both the Labour Market and Output Market). The production function of the business is given by: Q -40LU . The price of the product is 100. The wage rate is 20. a. Calculate the level of output and amount of labour hired by the firm. b. Derive the demand for labour (Hint: solve for L in terms of w). c. Calculate the elasticity of Labour Demand and interpret the result in WORDS. d. Make diagrams for your solutions.A firm's existing assets either have a high value of $345 million (the undervalued firm) or a low value of $135 million (the overvalued firm). The firm's manager knows the value of her firm's assets, but the market does not. The market assesses that there is a 50% chance the firm has high value assets and a 50% chance the firm has low value assets. Regardless of the value of the firm's current assets, the manager and the market are both aware that the firm has the opportunity to invest $30 million in a new project that will generate a cash flow with a present value of $60 million. The firm currently has 900,000 shares outstanding. The firm does not have the internal cash to fund the project, and thus if they want to fund the project they must conduct an equity issue immediately. In the long-run (i.e., next year) the markets will learn whether the firm was the undervalued or overvalued. Assume that managers act to maximize the long-run value of existing shareholder's claims when making the equity issue/investment decision. (a)Show that there is an equilibrium where both undervalued firms and overvalued firms issue equity to invest in the project. In this equilibrium how many shares will be sold? At what price will they be sold? What are the predicted long run stock prices for the undervalued firm and for the overvalued firm in this equilibrium? [Note: By long run I mean after any share sale and after the market learns/realizes the true value of the firm's assets.]
