**Answer questions 1, 2 and 3 (all parts) clearly and concisely. **You** must show** all your calculations and work.

1. a) John Wilson, the owner of a fast food restaurant, estimated that he can sell 1,000 additional hamburgers per day renting more automated equipment at a cost of $100 per day. Alternatively, he estimated that he could sell an extra 1200 hamburgers by keeping the restaurant open for two more hours a day at a cost of $50 per hour. Which one should he choose?

b) What type of returns to scale the following two production functions exhibit?

i) Q = 5L + 2L^{2}K^{3 }

ii) Q = 100 + L ^{0.5}K^{0.3}

^{ }

c. What is economies of scope? Consider the following cost function for a firm that produces two goods, Q_{1} and Q_{2} are the units of good 1 and good 2 produced:

C = 230 – Q_{1}Q_{2} + 2Q_{1}^{2} + Q_{2}^{2}

^{ }

To meet the market demand, the firm needs to produce 20 units of good 1 and 15 units of good 2. Does the firm have economies of scope in the production process? Show all your work and explain the answer.

2.a) You are the manager of a monopoly that faces a demand curve described by P = 85-5Q. The corresponding marginal revenue is given by MR = 85 – 10Q. Your costs are C = 20 + 15Q and the marginal cost of production is $15 per unit.

i) What are the profit maximizing price and output?

ii) What is the monopoly profit?

b) Compare your answers found in part a) with profit maximizing quantity, price and output if the underlying market structure were perfect competition.

3. a) The manager of an Electronic Corporation has estimated the total fixed and the total variable cost function for producing a particular type of camera to be:

TVC = 60Q + 12Q^{2}

TFC = $1200

If the Corporation sells the cameras at a price of $60 each, how many cameras at the minimum it must produce in order to avoid loss?

b) Suppose you are a manager of a watch making firm operating in a competitive market. Your cost of production is given by: C = 100 + Q^{2}, where Q is the level of output and C is the total cost. The marginal cost is 2Q. The marginal cost of production is 2Q.

i) If the price of watch is $60, how many watches should you produce to maximize profit?

ii) What will your profit level be? Will there be entry or exit?

iii)At what minimum price will you produce a positive output?

Subject | Mathematics |

Due By (Pacific Time) | 07/03/2015 02:00 pm |

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