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)1 Best response curve (with higher unemployment Status quo best 0.85 response curve 0.75 Best response curve (with higher unemployment benefit) 0.6 Effort per hour, e 0 Reservation Status quo Reservation 18 ware with reservation wage with higher wage higher unemployment unemployment benefit Hourly wage, w ($) Suppose that, with the status quo best response curve in Figure 6.7, the firm chooses the wage to minimize the cost of effort, and the worker's best response is an effort level of 0.6. If unemployment rose: 1. Would effort be higher or lower than 0.6 if the firm did not change the wage? 2. How would the firm change the wage if it wanted to keep the effort level at 0.6? 3. How would the wage change if the firm minimized the cost of effort at the new unemployment level?(a) First consider an economy where the government budget is required to be balanced in recession. The economy is given by: Czcu+c1(YT) T=t+t1Y I=I_ G=T With{61{1,{t1{1 i. Derive an expression for Equilibrium output. ii. Suppose for that for some reason demand were to fall, so that en were to decrease. We are interested in by how much output would fall due to this decline in ca. Derive an expression for the decrease in y do to a decrease in Ca. (b) Now ippose that the economy is the same as above except that G = G, La. that G is constant, and the government budget is not required to be balanced in recession. i. Derive an expression for equilibrium output. ii. Derive an expression for the decrease in 3,; due to a decrease in [30. (c) Interpretation: i. Based on the expressions you derived in aii and bii, would the same decline in g cause a larger decline in the economy with a balanced budget requirement, or the economy in which the government was not required to run a balanced budget? ii. In economy a, the govermnent's budget remains balanced after the decline in output, i.e. that (T G) = 0. Suppose that in economy I: the government's budget was balanced before the decline in output. What happens to the government's budget after the decline in gutput; is it still balanced, in surplus, or decrt? 1.e (T G) 2: [1? iii. How do you think the condition of the government's budget af fects how the economy responds to a decline in demand in the two eoonomies above? How does the answer to part cii concern- ing the state of the government's budget relate to your answer in part ci concerning which economy would experience a. larger decline in output given the same fall in ca