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Practice Problem for Midterm Examination

Econ 2210, Fall Semester 2020

no need to submit your work

1. True or False. Explain why.

(a) We have observed that a consumer chose to consume x = 20 and y = 10 when P = 2 and Py =

6 and chose to consume x = 18 and y = 4 when P = 3 and Py = 5 . This consumerss choice does not violate the Revealed Preference theorem.

(b) The price elasticity of demand for each product in an economy cannot all be greater than zero.

(d) Consider a firm that uses only one variable factor of production labor. Suppose the marginal product of labor is constant and the short-run average total cost is higher than the marginal cost when the total output level is low. Then the short-run average total cost curve is always downward sloping.

2. A consumer goes to the gym and also consumes other goods. The price of other goods is $1 per unit and his income is $10. Now suppose the gym has two promotions. The first promotion gives the consumer first 2.5 hours for free and then charges $1 per hour for the following hours. The second promotion charges $0.5 per hour for the first 5 hours and then charges $1 per hour for the following hours.

(a) Draw the budget line for both promotions. Place gym hours on the x-axis and other goods on the

y-axis.

(b) Is it true that the consumer never strictly prefers the second promotion to the first one? Why?

(c) The consumerss preference can be represented by U(x, y) = x a y1−a in which x is the hours of gym and y is the amount of other goods. Calculate the MRS when x = 5 and y = 7.5, and when x = 2.5 and y = 10.

(d) What is the range of α so that the consumer strictly prefers the first promotion to the second one?

3. A consumerss preference can be represented by U(x, y) = x + √y . The price of good x is p , the price of good y is py and the consumerss income is I.

(a) Find the consumerss demand function of x and y when I = 20.

(b) Suppose I = 20, p = 1 and py can vary. What is the price-consumption curve of y? Are the

two products complements or substitutes?

(d) Suppose I = 20, py = 1/2 and p decreases from 2 to 1. What is the total effect of the price change on the demand of x? Decompose the total effect into the income and substitution effect.

4. A firmss production function is given by q = min{K, √L}. What is the long-run expansion path?

5. A firm has production function q = F0 + F1 √KL + F2K + F3L, where F1, F2 and F3 are between 0 and 1.

(a) Under what condition (with regard to F0, F1, F2 and F3 ) does the firm has constant returns to scale?

(b) Verify that the production function has diminishing marginal returns to labor and diminishing marginal returns to capital at any K and L.

6. Assume the industry is perfectly competitive and has constant cost. Each individual firm has long-run total cost function LTC = 0. 1q3 − 1.2q2 + 111q . The market demand curve is Q = 6000 − 20p, where Q is the total output of the industry.

(a) What is the long-run equilibrium output of one firm?

(b) How many firms are there in the long-run equilibrium?

7. An industry used to be perfectly competitive before time t. Starting from time t, an entrant is required to pay entry cost E > 0. Suppose there is also a demand shock at time t such that the demand curve has a parallel upward shift.

(a) Suppose industry A is a constant cost industry. Illustrate the following statement graphically: if the demand shock at time t is small enough, then even if the current incumbents enjoy positive economic profit, there is no entry.

(b) Suppose industry B is an increasing cost industry. Other things are the same as in industry A. Does the maximum demand shock which does not attract entry in industry A induces entry in industry B?