Provide solutions to the attached questions.

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.Economics 302: Intermediate Microeconomics II Assignment 3 (Due in my office 3:00, Thursday March 10) 1. Consider two firms, 1 and 2, each producing an identical good simultaneously. This good has market demand given by the (inverse) demand function p = 10 - Y, where p is price, and Y = yi + 2 is market quantity. y, represents the amount produced by firm i. These firms have cost functions as follows: C, = cy, where c = c2 = 1. (60 pts) a) Solve algebraically for these firm's reaction functions, expressing each firm's optimal output level given some level of its competitor's output. b) Graph these reaction functions and show the equilibrium point. Include isoprofit contours through the equilibrium point for both firms. c) Solve algebraically for the equilibrium: Determine the equilibrium market price, as well as each firm's equilibrium quantity and profit. d) Is your answer to part c) the only equilibrium possible? Explain. 2. Take the same industry outlined in question 1 and imagine that firms choose prices rather than quantities. Consumers split themselves evenly across the firms if the firms set the same prices, otherwise all consumers shop at the lower-priced firm. Define a Nash equilibrium in prices pi and p2. Solve for the equilibrium and explain your work. (20 pts)3. Consider the following delegation versus centralisation model of decision making, loosely based on some of the discussion in class. A principal wishes to implement a decision that has to be a number between 0 and 1; that is, a decision d needs to be implemented where 0 S d S 1. The difculty for the principal is that she does not know what decision is appropriate given the current state of the economy, but she would like to implement a decision that exactly equals what is required given the state of the economy. In other words, if the economy is in state s (where 0 S s s 1) the principal would like to implement a decision d = s as the principal's utility Up (or loss 'om the maximum possible prot) is given by UP = is d | . With such a utility mction, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels of s are 0.4 and 0.7, and each occurs with probability 0.5. There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.4 to be implemented, and incurs a disutility UA that is increasing the further from 0.4 the decision d that is actually implement, specically, U A = 'OA d|. Similarly, Manager B always wants a decision of 0.7 to be implement, and incurs a disutility UB that is (linearly) increasing in the distance between 0.7 and the actually decision that is implemented - that is U B = |0.7 d l . Each manager is completely informed, so that each of them knows exactly what the state of the economy 5 is