**Task**

Respond (discuss/analyse/evaluate/interpret/conclude where relevant or as directed) to the following Short Answer/Problem/Case Studies questions.

**Question 1**

(i). Based on your understanding of Quantitative Demand Analysis, write-down a hypothetical demand function and:

(a). Explain why you picked the particular explanatory variables that appear in the function. Also explain why you have given the particular sign (+ or -) in front of each coefficient in the function, (that is the rationale for + or sign)

(b). What are the demand elasticities that you can discuss using your hypothetical model, and how do you identify a normal/inferior good; and a substitute/complement using the signs of the particular elasticity coefficient?

(ii). The largest electricity provider in the state has two main electricity generating facilities to provide demand for electricity in the state. The demand for electricity in the state is given by the following inverse demand function:

P = 1,200 4Q

The provider produces Q_{1} kilowatts from facility 1, and Q_{2} kilowatts from facility 2,

so the total production is Q = Q_{1} + Q_{2}

The cost functions for the two facilities are given by:

C_{1}(Q_{1}) = 8,000 + 6Q_{1}^{2} and

C_{2}(Q_{2}) = 6,000 + 3Q_{2}^{2}

Determine:

(a). The profit maximising amounts of electricity to produce at the two facilities.

(b). Optimal price; and

(c). Optimal quantity

**Question 2 **

Arid Water is a privately owned company that is the sole supplier of water to a rural town in Remote Country. The owner of the firm has provided the manager of the company an incentive to maximize the firms profits, and the manager is currently selling 100,000 litres of water per week at a price of $0.05 per litre. The marginal cost of water is zero, but the firms average cost of this level of output is $0.01 per litre

(a). Determine Arid Waters profits. [2 marks]

(b). Now suppose that the local government imposes a price ceiling on water at a price of $0.01 per litre.Will the firm earn economic profits of zero as a result of this price ceiling? Explain. [2 marks]

(c). Does the price ceiling of $0.01 per litre result in a shortage of water in Arids service area

**Question 3 **

You are an industry analyst who specialises in an industry where the market inverse demand function is: P = 200 4Q.

The external marginal cost of producing the product is: MC_{External} = 6Q, and the internal cost is: MC_{Internal} = 12Q.

(a). What is the socially efficient level of output?

(b). Given these costs and market demand, how much output would a competitive industry produce?

(c). Given these costs and market demand, how much output would a monopolist produce?

(d). Discuss actions the government might take to induce firms in the industry to produce the socially efficient level of output?

**Question 4 **

(i). Explain the concepts of Economies of Scale, and Diminishing Marginal Rate of Technical Substitution.

(ii). You are the manager of a firm that sells output at a price of $40 per unit. You are interested in hiring a new worker who will increase your firms output by 2,000 units per year. Several other firms also are interested in hiring this worker.

a. What is the highest annual salary you should be willing to pay this worker to come to your firm?

- What will determine whether or not you actually have to offer this much to the worker to induce him to join your firm?

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