ECO333H1 Study Guide - Midterm Guide: Hectare, Economic Equilibrium, European Route E20

Suppose that Sally's preferences over baskets containing coffee (good x), and milk (good y), are described by the utility function U(x,y) = 40x+y. Sally's corresponding marginal utilities are MUx=40 and MUy=1. The price of coffee is Px = $4 per cup, and the price of milk is Py = $1 per litre. Sally's income is I = $200.

Question 1: Without deriving the optimal consumption basket, show that the basket with x = 25 cups of coffee, and y = 50 liters of milk, is NOT optimal. (3 Marks)

Question 2: Derive the expression for Sally's marginal rate of substitution. (1 Mark)

Question 3: Find Sally's optimal consumption basket. (3 Marks)

Question 4: Find Sally's new optimal consumption basket if the price of coffee increases to Px = $5 per cup. (3 Marks)

Question 5: Is coffee a Giffen good for Sally? Briefly explain. Your answer must reference the consumption baskets you found in questions 3 and 4. (3 Marks)

Question 6: Find the income and substitution effects associated with an increase in the price of coffee from $4 to $5 a cup. (4 Marks)

Question 7: Describe the relationship between Sally's demand for coffee and her income. Your answers must reference your previous answers AND use the correct term to describe the relationship. (3 Marks)

Suppose that there are two firms competing in the market for taxi services. Big Ben Taxis has the marginal cost MCB = $9 per trip, and the fixed cost FCB = $3,000,000. While Whitehall Taxis has the marginal cost MCW = $15 per trip, and the fixed cost FCW = $1,000,000. Inverse demand for taxi trips in the market is given by the function, P = 75 - Q/10,000. In this equation, P is the price of a taxi trip, and Q is the total quantity of taxi trips supplied by the two taxi companies.

Question 1: Find the equilibrium price and quantities for the case in which the two taxi companies engage in Cournot (quantity) competition. What profits will Big Ben Taxis and Whitehall Taxis earn? (11 Marks)

Question 2: Using your answers to question 1, determine which firm has the greater market power. (4 Marks)

Question 3: Now suppose that a firm can only supply taxi services if it purchases a license from the government. What is the highest fee that the government can charge for a license if the government wants both Big Ben Taxis and Whitehall Taxis to purchase a license? (Note: A license does not place a limit on the number of taxi trips a company can supply. You should assume that both firms are charged the same fee.) (2 Marks)

Question 4: If, instead, the government wants to maximize the revenue it receives from taxi license fees, how many licenses should it sell, and what fee should it charge? (8 Marks)

Q1 and Q2 answered, can anyone help with Q3 and Q4?

Questions 1 and 2 do not need to be answered, they are just there for questions 3 and 4. Only bolded need answered.

1.Graph the following market demand function Q = 300-25P, plotting P (prices) on the vertical axis, and Q (quantity), on the horizontal axis. Next, show how much quantity demanded changes when the price of the good given by this demand function increases from $5 to $7?

2.Consider that the demand curve in part (a) above represents the market demand for a steak burger meal in a local area. This local area has three fast-food restaurants that exclusively produce these meals, and they are owned by Sam, Sony, and Sheila. Their supply curves for a steak burger meal are given as follows:

3.Consider the exercise in Question 2. The government now declares that steak burger meals in that locality should sell for $5.00. Given the correct answers in Question 1(b), would this represent a price ceiling or a price floor? Explain. Further, determine what would be the quantity of shortage or surplus that would exist in this market, and be explicit whether it is a surplus or a shortage and explain why.

4.Given the readings you looked at on price controls, what other problems typically arise, besides shortages or surpluses, when price controls are put in place within well-functioning markets?