UNIVERSITY OF TORONTO SCARBOROUGH
DEPARTMENT OF MANAGEMENT
MGEB02: Price Theory: A Mathematical Approach
Instructor: A. Mazaheri
Sample Test-1.1 (Solutions)
Instructions: This is a closed book test.
You have 2 Hours.
FOR MARKERS ONLY:
Q1 Q2 Q3 Q4 Q5 Total
Marks 40 15 15 18 12 100
Page 1 of 15 Answer all following 5 questions:
Question-1 [40 Points] Answer the following Short Questions:
a) [4 points] You are analyzing the market for Crude oil in the last decade or so, you know that
the price has risen from $20 or so to $100+ during this period. Show what must have happened to
the demand and supply to lead to such an equilibrium.
Demand shifts right, P & Q increase
b) [6 Points] In the following, the initial equilibrium is given. Suppose price of X declines.
Assuming X is Giffen, draw the new equilibrium. On the same graph show the income and the
Page 2 of 15 c) [6 Points] Draw representative indifference curves for the followings:
i) Sandra has a strange habit and she insists on it; she likes to eat an apple and two bananas
ii) Adam does not care about orange juice or apple juice as long as he has juice.
Page 3 of 15 d) [6 Points] Assume you have a fixed budget of $10. Further assume that you spend your entire
budget. Both good X and good Y cost $1 each. You are spending all your money on X. At this
bundle, your marginal utility of X is 10 while your marginal utility of Y is 5.
Are you optimizing your utility? Why or why not? Using a graph explain your answer.
(1) spend your entire income because you are on the budget line
(2) The MRS = 10/5=2 > 1, or (MU x/ Px) > (MU y Py).
That is, the marginal utility of X per dollar spent is higher than that of Y. However, you
already gave away all Y and cannot get more X. Therefore your optimal consumption
bundle is a corner solution where you consume no Y.
Page 4 of 15 e) [8 Points] Assume a utility function that is given by U(X,Y) = X Y . Further assume a
budget of $50. When the prices wherX P and PY=1, you consumed X= 25 and Y = 25, while
when the prices changed tX P =2 anY P =1, you consumed X= 12.5 and Y = 25. With the help of
the following graph decompose the total effect of the price change into the substitution and
We know TE = 25-12.5. We need to find the SE. Having SE we can solve for IE as
TE=SE+IE. SE is the change in the quantity of x demanded, if (1) the individual remains at
the same indifference curve and (2) if MRS is equal to the new price ration.
0.5 0.5 0.50.5
1:U = 25 ×25 = 50 = X Y
2 :MRS = = => Y = 2X
(1),(2) => 25 =X 0.(2X) 0.=> X =17.68
SE =17.68 − 25 = −7.32
IE =12.5−17.68 = −5.18
17.68 25 50
Page 5 of 15 f) [5 Points] You have 5 spent on two products, a composite product (Y) with a price of p = 1 y
and coffee (X) with a price of px = 1. If you purchase three cups of coffee, you will be offered one
coffee for free and a 50% discount on each additional cup of coffee purchased. Show graphically
how this affects your budget line.
3 4 8
Page 6 of 15 g) [5 Points] Ahmed only consumes hamburger (Y) and coffee (X). He wants two cups of coffee.
If he gets less than two cup of coffee he will not care about anything else and if he is given more
than two cups of coffee he will discard it. Graph his representative indifference map.
Page 7 of 15 Question-2 [15 Points] As a manufacturer you are interested in obtaining quick estimates of the
supply and demand curves for your product. You have done some research and you know that for
your product the elasticity of supply is 2, the elasticity of demand is -1.5. You also know that the
current price and quantity are $50 and 1,000, respectively. Assume that both demand and supply
a) [6 Points] What is the supply and demand curves at the current price and quantity.
b) [4 Points] What impact would a 10% decline in demand have on the equilibrium price and
d) [5 Points] Ignore part (b). Suppose the government subsidizes your product by 5 dollars per
unit. What would be the new