Econ 393 — Winter 2020 — Assignment 1 The assignment is due in class on Monday, January 27‘“. Answer each of the following
questions. You must provide justification to receive marks. Students may collaborate in solving
the problems but must individually write up their answers. Question 1. A consumer has preferences over expenditure on food (X1) and money spent on
other goods be) represented by ii) vi) U(x1,x2) = xi/ngls (CD with a = 1/5) Derive the ordinary demand functions X1(p1 , I) and X2(p1 , I) if the price of food is p1
and the consumer has disposable income I per period. Note that X2 is a composite
good so we take p2 =1. Derive the compensated demand functions for food and all other goods, h1(p1 , u)
and h2(p1 , u) given some constant value for the utility level u, by solving the
expenditure minimization problem. Assume the consumer’s disposable income is I = $1000/period. What is the
consumer’s utility maximizing choice (X1, X2) if p1 = $20/unit? What about if p1 =
SS/unit? In a graph, represent the price effect (AX1) of the change in price p1A= SZO/unit to
p1B = SS/unit. Calculate and show the substitution effect in the same graph using the
compensated demand functions to make the calculations, and a sketch of the
relevant indifference curves. In a second graph, sketch the (inverse) ordinary demand curve (price on vertical axis,
quantity demanded on the horizontal) using quantity- price pairs arising from p1A = $20/unit and p1B = SS/unit assuming that the consumer’s income remains at I =
$1000/period. Add the compensated demand curve to your sketch in v) and illustrate the
substitution and income effects. Use only the qualitative properties (as given by the
Slutsky Equation) that relate the compensated and ordinary demand curves as they
pass through the point (x1(20,1000), 20).