Business Economics and Game Theory for Decision Making

Assignment Task

Each question is worth 18 marks with the exception of question 2, which is worth, for an assignment total of 100 marks. To ensure that you receive the most marks possible, make sure to show all your calculations.

1. Leann, with a $300,000 bequest from her father and a business degree from Athabasca University, is considering opening a gift shop in North Edmonton. If her shop is highly successful, she expects an annual net profit of $220,000. If the business is moderately successful, she expects $130,000. If not successful, she expects to have zero net profit. Under any circumstances, she is not contemplating any loss. Her anticipated probabilities of these three options are: 0.5, 0.3 and 0.2, respectively.

• Calculate her expected net profit. Also calculate the standard deviation of her profit
• The business requires a $300,000 investment. If she has a 20% opportunity cost on invested funds of similar riskiness, should the project be undertaken
• Suppose Leann considers two alternative investment options instead of opening a gift shop. She has the option to buy a risk free asset that will pay 10%, or she can invest in a stock that has a 0.3 chance of paying 10%, a 0.2 chance of paying 22%, and a 0.5 chance of providing a 20% return. If she invests $160,000 in the stock and $140,000 in the risk free asset, determine the expected percentage return on the stock and the standard deviation.

2. Consider the following payoff matrix for Firm A and Firm B. Firm A sells ski equipment and Firm B sells ski clothing (complementary goods). These two firms are choosing the location of their stores in a mall and will increase profits if they choose to locate in the same corner. There are two available spots in both the NW corner and the SW corner of the shopping mall. Determine whether Firm A and Firm B have a dominant strategy. Work through the equilibrium mixed strategy and find the expected payoffs.

3. Given the following information, P = 15 – Q (where Q = Q₁ + Q₂) and MC = ATC = 3, find the Cournot equilibrium quantity, price, and profits for each of the duopolists.

4. Andy has a monopoly in the sale of engineering services in the local market and employs only highly skilled labour. Suppose the supply of labour to Andy’s firm is given by L=100w, demand for labor is given by L = 1000–100MRP_L and MC of labour is given by MC_L =L/50, where L is the labour demanded and supplied and w is the wage rate per hour.

•  If Andy has monopoly power in the market, how many workers will he hire in order to maximize profit? What will the wage be?
• Suppose Andy hires workers from a competitive market, but still acts as a monopolist when selling services. How many workers will the firm hire, and what will the wage be?
• Suppose the above firm has the following information: MPL = 12.4 – 0.08L and output price = $400. Based on the new information, determine the equation that represents the MRP_L  How many employees will be hired if the daily wage rate is $320?

5. A dry-cleaning business operates in a monopolistically competitive market with the following demand and marginal revenue curves:
P = 100–5Q

        TR = 100Q–5Q²
        MR = 100–10Q

The business’s total and marginal cost curves are:
          TC = 4Q + Q²  + 5
          MC = 4+2Q
where P is in dollars per unit, output rate Q is in units per time period, and total cost C is in dollars.

i. Determine the price and output rate that will allow the firm to maximize profit or minimize losses. Is this a long-run equilibrium? Why or not?

ii. Suppose the short-run marginal product of labour curve for the dry cleaner is MP_L = 6.20 – 0.04L. The business is running a special promotion and will charge $30 per family.

• Determine how many employees will be hired by the dry cleaner if the daily wage rate is $168.
• Determine how many employees will be hired by dry cleaner if the daily wage rate declines to $150.
• Suppose the dry cleaner hires labour from competitive factor markets. Graphically illustrate and discuss the effect of an increase in the wage rate in a competitive labour market.

6. Cindy has the option to invest her savings in one of two investment opportunities. The payoffs and the probability associated with payoff for each option is listed below:

1. Find the expected return and standard deviation of each investment.

2. If Cindy has the utility function U = 1.5I, where I denotes the payoff, which investment will she choose?

3. Suppose Cindy’s utility function has changed to U = 2√I. Which investment will she choose?

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