Economic Homework:
Q1. What is the difference between economies of scale and economies of scope?
Q2. What three conditions must be satisfied for a firm to engage in price discrimination?
Q3. Briefly explain why a monopoly does not have a supply curve.
Q4. Briefly explain how supply is related to marginal and average variable costs.
Q5. Why must an inferior good also be normal at a lower income level?
Q6. How is a production possibility frontier derived from an Edgeworth box diagram for production?
Q7. State and briefly explain the three primary assumptions about preferences in consumer choice. Apply these properties to prove by contradiction that indifference do not cross each other.
Q8. Suppose that on the first day of your new job as a consultant, you are asked whether a firm should lower or raise price of its products to increase revenue. Answer the following, draw graphs as necessary.
Use this given information to answer questions 9, 10 and 11 -
Applied - Suppose that a firm's output follows the Cobb-Douglas production function
Q = LaKb,
where Q is the amount production given a certain amount of labor, L, and capital K. Suing calculus, we can show that
MPL = tQ/L,
MPK = tQ/K
where MLP and MPK are the marginal products of labor and capital respectively. The firm rents inputs on a competitive market, so its total costs are
TC = wL + rK,
where w is the wage rate and r is the rental rate of capital.
Suppose further that a = ¼, b = ¾, w = $10 per hour, r =$15 per hour.
Q9. Does the firm's production function exhibits constant, increasing or decreasing returns to scale? Show your work.
Q10. Find the optimal ratio of capital and labor along the firm's expansion path. Show your work.
Q11. Presently, the firm employs L = 5 units of labor and K = 2 units of capital to produce Q = 2.5 units of outputs at a total cost TC = 80. Graph the firm's isocost and isoquant lines, showing your work. Specifically, do the following.
i. Label the y-axis capital, K, and the x-axis labor, L.
ii. Graph the firm's current level of production, drawing dashed lines from the axes to the point (L = 5, K = 2).
iii. Graph the isocost line, labeling the numeric values for the intercept and slope.
iv. Graph a representative iso-quant, showing the present point or points of intersection with the isocost line. (Hint: The firm is not presently cost minimizing. You must determine if it is using too much capital or too much labor to correctly graph the isoquant.)
Use this given information to answer questions 12, 13, 14, and 15 -
Firm A operates a monopoly facing a linear market demand curve of Q = 12 - 1 · P and a constant marginal cost of MCA = 4.
Q12. Graph the firm's costs and production decisions, showing your work. Specifically, do the following.
i. Label the y-axis price, P, and x-axis quantity, QA.
ii. Graph the inverse demand curve, labeling the numeric values for the intercept and slope.
iii. Graph the marginal revenue curve, labeling the numeric values for the intercept and slope.
iv. Graph the horizontal marginal cost curve at MCA = 4.
v. Calculate the optimal quantity and price, label them on the y-and x-axis respectively, and draw dashed lines to the point representing the optimal quantity and price.
Q13. What two part tariff would the monopolist use to maximise profit.
Q14. Suppose that a second firm, Firm B, enters the market. Firm B has a marginal cost of MCB = 4 with best response (reaction) function Qa = 4 - ½QA. If the firm A moved first in Stackelberg competition, and Firm B was the second mover, find the resulting equilibrium quantities Q*A and Q*B. (Hint: The quantity supplied in the market is the sum of quantity supplied by each firm, so that Q = QA + QB.)
Q15. Suppose again a second firm, Firm B, enters the market. Firm B has marginal cost of MCB = 4. However, suppose now that the market the firms engage in Bertnand competition. What would the resulting equilibrium price be?