INTERMEDIATE MICROECONOMICS, Spring 2017
Assignment 2
Hand in solutions to question 3 before Thursday, February 9th at 13.00 by mail to your
seminar teacher or in the black letter box by the entrance to the Department of Economics at
floor 4. Solutions should be handed in by groups of two or three persons. Answers have to be
in English. Do not forget to state the course (intermediate micro), the exercise group number,
the names of all group members and the name of the teacher on the papers that you hand in.
Mail addresses are as follows: Zana Hussan, [email protected], (groups 1 and 2), Johanna
Nolgren, [email protected], (groups 3 and 4), Jon Olofsson, [email protected],
(groups 5 and 6). Make sure that files you send are readable.
1. The firm “Construct” digs ditches. To dig the firm uses shovels (S) and workers (L). Let D
denote the number of kilometers dug.
a) Explain what the marginal product is.
b) What is the interpretation of a decreasing marginal product? Explain why it is plausible that
a production technology as the one mentioned here has a decreasing marginal productivity in
S as well as in L.
c) Derive the marginal product of labor for the following production functions:
(i) D = S0,5 L0,5
(ii) D = min {S, L}
(iii) D = S + L
In each case decide whether there is decreasing marginal product of workers. Which
production function describes the technology of “Construct” best?
d) Explain what the Marginal Rate of Technical Substitution (MRTS) is.
e) Derive the MRTS for the production functions (i) - (iii) above. Is the MRTS decreasing?
f) Explain the relation between convex isoquants and decreasing MRTS.
2.
a) Explain what decreasing, constant and increasing returns to scale are.
b) Determine the returns to scale for the following production functions: f(L,K) = L2·K,
f(L,K) = 2L + K, f(L,K) = min {2L, K}.
c) Let q be output and w, r prices for the L- and K-factors. Determine the cost function, C(q,
w, r), for each of the production functions: q = 2L + K, q = min {2L, K}.
3*. Iris considers starting to produce tulip bulbs. Her production inputs are labor N (expressed
in hours) and greenhouse area A (expressed in square meters). The price of one hour of labor
is 400 SEK, while a square meter of greenhouse area costs 100 SEK. The production function
for tulip bulbs is given by q = 2 N½A½.
a) State Iris’s cost minimization problem and use it to derive the optimal quantities of N and A
given the number of tulips produced.
b) Derive Iris’s total cost function.
c) Derive the marginal cost function of producing tulip bulbs.
d) Should Iris start production of tulip bulbs if the price is 100 SEK per bulb?
4) Consider a simple economy with two “commodities” only, leisure and a consumption
commodity, one worker/consumer and one producer.
The worker has a utility function U = C ´ 1 - L where C represents the consumption
commodity and 1-L represents the consumption of leisure. The worker’s budget constraint is:
pC = wL + p , where p is the price of the consumption good, w the wage rate and p the profit
the consumer gets from owning the producer.
The producer transforms L (labor) into the consumption commodity according to a
technology: C = L .
a) Derive the demand functions for the consumption good and the supply of labor.
b) Derive the supply function for the consumption good and the demand for labor.
c) Derive the profit and insert it into the demand functions.
d) Normalize w to 1 (that is set w=1) and write the excess demand function for the
consumption good and illustrate it in a diagram. Which price of the consumption good
clears the market? (Hint: calculate the market clearing price from the excess demand
function or by assuming that the equilibrium is efficient)
e) Does the general equilibrium satisfy the marginal conditions for Pareto-efficiency?