ECON 4020 B Mid-Term Examination Tuesday, February 9, 2021
Prof. K. G. Armstrong Name:
Instructions: Answer all questions in the space provided. Show your work for each one.
1. Consider the production possibilities set
=(12): 2 + ,
where and are positive constants. (a) Draw the graph of .
(b) Show whether or not is closed, convex, and satisfies free disposal.
(c) Characterize the set of efficient points of .
(d) What returns to scale property does exhibit, if any?
(e) If ( 1 2) = ( ), which production plan will a profit-maximizing firm select from and how much profit will it make?
2. Consider the cost function
( 1 2 ) = ( ) 1 1 + 2 2 + 2 ( 1 2 ) 12 ,
where 1 0, 2 (a) Show that ( 1
(b) Show that ( 1
(c) Show that ( 1
0, 0and : + + isafunction.
2 ) has the correct homogeneity property.
2 ) has the correct monotonicity property.
2 ) has the correct curvature property.
(d) Find the associated conditional factor demands.
(e) ?What aspect of ( 1 2 ) determines its returns-to-scale property and how?
(f) ?The right-hand side of the given expression is known as the “generalized Leontief” functional form. Why? [Hint: Think about how it relates to the standard Leontief functional form.]
3. T. Edison, “On Average and Marginal Cost,” The Wall Street Journal, 20 December 1911:
“I was the first manufacturer in the United States to adopt the idea of dumping surplus goods upon the foreign market. Thirty years ago my balance sheet showed me that
I was not making much money. My manufacturing plant was not running to its full capacity. I couldn’t find a market for my products. Then I suggested that we undertake to run our plant on full capacity and sell the surplus products in foreign markets at less than the cost of production.
“Every one of my associates opposed me. I had my experts figure out how much it would add to the cost of operating the plant if we increased this production 25%. The figures showed that we could increase the production 25% at an increased cost of only about 2%. On this basis I sent a man to Europe who sold lamps there at a price less than the cost of production in Europe.”
Suppose Edison’s plant had constant marginal cost and fixed costs were $2 875 per month. Suppose his original production level was 10 000 lamps per month and that a 25% increase corresponded to full capacity.
(a) What is the (implicitly) assumed functional form of the (monthly) cost function
( )? Use that functional form to derive the functional forms for the average cost
function 1( ) and marginal cost function 0( ).
(b) ?Use the foregoing to show that = 0 025 .
(c) ?Assume now that the marginal cost was indeed 2.5 cents and the domestic price was 30 cents. If only the domestic market was served (with 10 000 lamps), what was the original profit and average cost?
(d) ?Suppose an additional 2 500 lamps were then sold in the foreign market at 20 cents each. What was the total profit and average cost?
(e) ?Assuming that Edison faced downward-sloping demands for his lamps in domestic and foreign markets, if 10 000 lamps at 30 cents each in the U.S. together with 2 500 lamps at 20 cents each in Europe was profit-maximizing, how should the relevant first-order necessary condition be characterized?
(f) ?Under the conditions of part (e), what must have been the numerical values of the elasticities of demand in the two markets？