Assessment 2: Exercises on Production Function and Market Equilibrium

You should attempt to answer ALL parts of all questions in the exercises below.

You may write rather than type your answers and scan it. However, it is important that your answers are neat and legible. You may lose marks if your answers are difficult to read.

When you draw a graph, make sure that the graph is neat, clear, and clearly labelled. If you type your assessment, you can insert graphs as pictures in your document.

This assessment is an individual assignment. You may not discuss the exercises or your answers with anyone else including other students.

You should submit electronic copy of your answers using the submission link provided on MyAberdeen, Assignment 2 link under Assignment on the MyAberdeen course page. The Assignment 2 link is currently not active but should be available in the next few days. Check your emails and course announcements on MyAberdeen for updates on electronic submission.

E-Systems, a high-tech IT company, has the following production function:

, where L is the weekly labour hour, K is machinery used, and Q is the quantity of manufactured computer chip. The marginal product of labour and marginal product of capital are:

(a) What kind of returns to scale does E-System’s production function exhibit? Explain your answer.

(b) Calculate the rate of technical substitution of L for K, MRTS_LK.

(c) In the short-run, E-Systems can rent only 4 pieces of machinery. How many labour hours is needed to produce 36 computer chips?

(d) What is the cost of producing 36 chips?

(e) What is the long-run optimal choices of labour and machinery to minimize the cost of producing 100 computer chips?

Suppose the market for computer chips is perfectly competitive. Firms active in this market are identical with the cost function: TC = 200 + 2Q²

(f) If the market is at the equilibrium price=£80, how many chips each firm would produce?

(g) What is the profit each firm makes?

(h) Will any of the firms shut down and exit from the market? Explain.

(i) What is likely to happen to this market in the long run? Show your answer in words and on graph.

Demand for rental one-bedroom apartments in Aberdeen is given by Q= 500 − P where P is the price of monthly rent in £, and Q is the number of apartments. They supply function is Q= 3P − 300. Assume this market is perfectly competitive.

(a) Show the demand and supply curves on a graph.

(b) Calculate the price and quantity at the equilibrium.

(c) What are the consumer and producers’ surplus at the equilibrium?

(d) Government introduces a quantity tax that suppliers should pay £20 for every apartment they rent out. What would be the new equilibrium price for the consumers? And how much would the suppliers receive? What is the new equilibrium number of apartments rented?

(e) Show the imposition of tax on a graph.

(f) Calculate the consumer’s surplus and government tax revenue after tax.

(g) Which side of the market would bear more tax burden? Explain that using the relationship between the tax burden and elasticity.

(h) What is the value of the deadweight loss due to imposition of tax?