Kindly help clearly showing each step
A Firm uses capital and labor to produce steel. The production function is CobbDouglas, Y = AK ^(1/3) L ^(2/3) , where K is capital stock and L is number of workers employed. A is a measure of technology level (total factor productivity), and we currently assume A =1. Capital is a fixed input and cannot be adjusted in the short run. Labor is a variable input and can be adjusted. Suppose the input prices for capital and labor are WK = 1, WL = 2. The firm needs to produce 100 units of steel, Y = 100, which is determined by the market demand. a. Suppose in the short run, the number of capital is fixed at K = 196. Solve for the short-run total cost function. What is the total cost to produce 100 units of steel? b. In the long run, both capital and labor can be adjusted. Solve for the long-term optimal usage of capital and labor to produce 100 units of steel.Assume the market demand and market supply functions for pears in the United States are given by QU = 36 - 3p and Q = =6 + 4p, respectively. p represents the price of pears. a) Find producer and consumer surplus when the market is in equilibrium. bl Suppose the federal government introduces a price ceiling of $5.50. a. Compute and graphically show the impact of the program on producer surplus. b. Calculate and graphically show the impact of the program on consumer surplus. C. How does the government implement the program? d. What is the deadweight loss of this policy? (calculate and show graphically)The demand and supply functions for basic cable TV in the local market are given as: Q(D) = 200,000 - 4,000P and Q(S) = 20,000 + 2,000P a. Calculate the consumer and producer surplus in the market. b. If the government implements a price ceiling of $15 on the price of basic cable service, calculate the new levels of consumer and producer surplus.One of the common examples of a price ceiling policy is the setting of maximum rent in big cities such as New York and San Francisco. Now consider the market for rental apartments in Madison and assume that all the apartments are the identical. Use graphs to help visualize the following changes. Demand and Supply equations for the market are as follows: Demand for apartments in Madison: Qd = 450 - (1/2)P Supply of apartments in Madison: P= Qs +210 a) What is the equilibrium price and quantity in the market for apartment rentals? b) What is the value of consumer surplus and producer surplus in the market for apartment rentals in Madison? Draw a graph illustrating your answer and then provide a numerical calculation for these two values. c) Suppose the government decides to enact a price ceiling in the market for apartments in Madison. The price ceiling is set at $500. Given this price ceiling what is the quantity of apartments demanded in this market and what is the quantity of apartments supplied in this market? Is there a shortage or a surplus in the market once the price ceiling is implemented? Calculate the deadweight loss, consumer, producer and total surplus given this policy relative to no government intervention in this market. d) Suppose the government implements a price ceiling of $400 in the market for apartments in Madison. Given this price ceiling what is the quantity of apartments demanded in this market and what is the quantity of apartments supplied in this market? Is there a shortage or a surplus in the market once the price ceiling is implemented? Calculate the consumer surplus and producer and total surplus given this policy relative to no government intervention in this market
