ECON 20002 Intermediate Microeconomics - Assignment 1

ECON 20002 Intermediate Microeconomics
Assignment 1
Knowledge is not power. It is the implementation of knowledge that is power.
Problem 1. (12 points). Consumer Theory: Consumer’s choice and
compensation.
Happy Goluki likes tea (good 1) and cookies (good 2).
Her preferences are represented by the utility function U(q?,q?) = (q?)0.5+(q?)0.5, where q? is
the number of cups of tea and q? is the number of cookies.
Goluki is given I = $120 that she is allowed to spend as she wishes on tea and cookies.
a) Calculate Goluki's optimal bundle if the price of tea is p?=$1 and the price of cookies is
p?=$2. Call this bundle A and show it on a diagram (put tea on the horizontal axis).
b) Suppose that the price of tea increases to $8 (I know, I can’t believe it either, but Melbourne
does have some very fancy tea places) and the price of cookies stays the same. Calculate
Goluki's new optimal bundle of tea and cookies (call it bundle B). Show it on a diagram
from part a).
c) Calculate the income required so that Goluki can obtain the same utility as from the original
bundle (from part a) but at the new prices.
d) Calculate this new bundle at this new income and new prices. Call it bundle D and show it
on the diagram from part a).
e) What is the total effect, income effect and substitution effect (on tea) of an increase in price
of tea from $1 to $8? Show them on a diagram from part a).
f) Goluki's parents are willing to compensate her for an increase in prices. How much extra
money would they have to give her to make her as well-off as she was at the old prices?
This amount is called the compensating variation.
g) Suppose that Goluki's parents gave her enough money, so that she can afford the same
combination of tea and cookies, as in part a) at the new prices. Find her new optimal bundle
(call it G) in that case and show it on the same diagram as in part e). Is Goluki better off
with bundle G or with the bundle chosen in part f)? Please use one diagram for all parts.
If any optimal bundle you calculate contains a number of cups of tea or cookies which is not an
integer (a whole number), please round up to the closest integer (for example, write 10 cookies
instead of 9.6 cookies). Econ 20002 – 2017 summer Assignment 1. A1. Page 1 of 2 Problem 2 (8 points). Producer Theory: Cost Minimisation.
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function
is:
q = min {L0.5, K/3},
where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example,
if he uses 3 kg of kiwi fruits and one hour of labour, he can produce 1 bottle of juice.
a) Draw isoquants for q = 1, q = 2 and q = 3 on a diagram with labour on horizontal axis
and kiwi fruits on vertical.
b) Let the price of labour-hour be given by w = $17 and the price for each kg of fruit be
given by p = $4. What is the optimal amount of labour and fruit to use to produce q
bottles of juice, if Cheburashka strives to minimise costs? Illustrate on the diagram from
a) by drawing corresponding isocost lines.
c) Draw the Cheburaska’s expansion path on a diagram from a). Derive an expression for
the expansion path, i.e. K as a function of L. How does it depend on the wage and the
price of kiwi?
d) What is Cheburashka’s long-run total cost function, C(q)? Sketch it on a diagram.
e) One of Cheburashka’s advisers, Madam Shapoklyak, suggests that if wage keeps
increasing as predicted, he should start hiring less labour and use more kiwi fruits
instead, in order to minimise his costs. Briefly evaluate the quality of her advice. (If
you agree with her advice, explain why; if you disagree with it, please explain why and
suggest an alternative.) Econ 20002 – 2017 summer Assignment 1. A1. Page 2 of 2