Quantitative Economics Mock Exam
by Daniel Schoch
Answer all questions.
1. A firm offers his products in two markets. The demand functions are
P1 = 150 − 3Q1
P2 = 75 − 5Q2
The total cost function is
TC = 120 + 5 · Q,
where the total quantity produced is Q = Q1 + Q2.
a) Find the maximum profit and the equilibrium quantities and prices with price dis-
crimination.
b) Find the maximum profit and the equilibrium total quantity and price without
price discrimination.
Hint: You must find the price as a function of Q.
c) Show for both cases that at equilibrium, marginal revenue equals marginal cost.
2. Finance
a) A bank offers a 6% continuously compounded interest rate for an investment over
one year. How much would the interest rate be if it had to be calculated annually
compounded?
b) Consider the following investment opportunities
Year A B
1 3% 4%
2 6% 5%
2 7% 5%
Calculate the net present value of both investments. Which one is better?
c) An individual is saving 100 Dollar at the beginning of each year. The bank offers a
return of 5% interest rate annually compounded.
i. Determine the amount saved after 10 years.
ii. After how many years does the amount first exceed 2000 Dollar?
3. A production function is given by
Q(L, K) = 10L1/3K 2/3.
Here, K denotes factor capital and L denotes factor labor. Unit cost of labour is 4 and
unit cost of capital is 7, and the budget of the firm is 100.
a) Find and interpret the marginal product and output elasticities of both factors.
b) Find the maximal output.
c) Show that the marginal rate of technical substitution equals the price ratio.
d) Show that the production function has constant return to scale.
