Question 3 and 4
TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON 3250H ASSIGNMENT #1 Dr. M. Arvin 2021-2022 DATE GIVEN: Wednesday, September 22, 2021. DUE DATE: Beginning of class on Wednesday, October 13, 2021. As your course outline states: “late penalty is 20% for each day or part thereof for which the assignment is late.” You have three weeks to complete this assignment. Please complete your assignment in ink or type it. Your assignment will not be marked unless you are officially registered in this course. (20) 1. Suppose the demand for housing D is given by the function 21100 −−= rpD where p is the price of housing and r is the mortgage interest rate. Treat r as exogenous. The supply of housing is given by __ SS = , where __ S is exogenous. i) Solve for the equilibrium housing price and then by partially differentiating your reduced form, carry out a comparative static analysis with respect to the mortgage interest rate and the housing supply. Explain (in plain English) why your answers make sense and be sure to depict each change that takes place in a simple (two-dimensional) diagram. ii) Suppose the demand for housing is changed from above to a general function ),( rpDD = 0,0 rP DD The supply of housing is still the same. Again, conduct a comparative static analysis with respect to the mortgage interest rate and the housing supply. (20) 2. A consumer spends time t searching for a good, the price of which is p(t). Assume the longer the search goes, the lower price the consumer would pay for the good. Furthermore, assume there are diminishing returns to the search since it is harder to find even lower prices as the search continues; that is: p″(t) > 0. Without search the consumer would pay the current going price of the good p0 . While searching, the consumer loses income at a constant rate w . i) Find the condition for an optimal search time t, if q number of units of the good are bought. Explain what your condition is saying in plain English. ii) Check to make sure your second-order condition is satisfied. iii) What is the impact of a change in the consumer’s wage rate w on the optimal search time if nothing else changes? Explain why your answer makes sense. iv) What is the impact of a change in the number of units q on the optimal search time if nothing else changes? Again, provide the necessary intuition. (30) 3. A closed economy is described by the following equations representing the goods and money markets: )(rII = 0rI ),( rySS = 0,0 ry SS GG = TT = 0,0),( = r d y ddd MMryMM p M M s = I is real investment, S is real savings, G is real government expenditure, T is real taxation, dM is real demand for money, sM is real supply of money, y is real income, r is real rate of interest, M is nominal money supply, and P is the price level. A bar over a variable indicates exogeneity. i) What is the effect of an increase in the nominal money supply on the equilibrium p and r ? Explain. ii) Find the partial elasticities of equilibrium p and equilibrium r with respect to M . iii) Explain your results in part ii) in plain English (here I am looking for some sort of intuition on why you think your results make sense; simply writing a mathematical result in English – i.e., stating that your result carries a certain sign – will receive little credit because that is not intuition). (30) 4. Suppose a profit maximizing automobile manufacturer produces its output in two plants, one in the U.S. and the other in Canada. The total costs of producing in the two plants are identical, except that the output produced in the U.S. is subject to a per unit tax, t. Suppose the two total cost functions are USUSUSUS tQQQTC +++= 12/ 2 12/2 ++= CANCANCAN QQTC . The firm’s demand function is P=26-QT , where QT is total output in U.S. and Canada. i) Find the first-order conditions for this problem. ii) Find the reduced form solutions for optimum values of QUS and QCAN . iii) Show that the second-order condition for this problem is satisfied. iv) By partially differentiating your reduced form solutions, describe (both mathematically and in words) the effect of a change in per unit tax on optimum output in both countries. v) Now find the same comparative static results by totally differentiating your first-order conditions, rearranging them, writing them in a matrix form, etc.