Introductory Mathematics for Economists Mock Final Exam

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Introductory Mathematics for Economists

Mock Final Exam

Question 1. (5%) Find the derivative of the following function:

y = ln (2×3 + 3xe3x)

Question 2. A perfectly competitive firm sells two goods. The price for the first good is ￡58. The price for the second good is ￡21. The total cost for a firm is given by the expression:

TC (Q1, Q2) = (5/2) Q12 + 2Q1Q2 + (1/2) Q22 + 7Q1

(A) (35%) Find the maximum profit and the optimal values of Q1 and Q2 .

(Β) (35%) If the firm cannot produce in total more than 10 units, then what would be the maximum profit and the optimal values of Q1 and Q2 Find your answer using the Lagrange multiplier. Find the value ofthe Lagrange multiplier. What economic interpretation has the Lagrange multiplier in this context

Question 3. (15%) Find the producer’s surplus at P = 9 for the following supply function:

P = 3 Q1/2 + 3

Question 4. (10%) An automobile dealer calculates the proportion ofnew cars sold that have been returned a various number of times for the correction of defects during the warranty period. The results are shown in the following table.

Number ofreturns 0 1 2 3

Proportion 0.05 0.21 0.43 0.31

Find the mean and the vatriance ofthe number ofreturns of a car for correction for defects during the warranty period.