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EC2104 Problem Set 2

EC 2104 Quantitative Methods for Economic Analysis
Problem Set 2
Students will solve the problems from the following questions during tutorial sessions for the week
of February 1, 2021.
1. Given that the Total Revenue function =P (Q) · Q, where P (Q) refers to the inverse demand
function, find the relationship between Marginal Revenue and the Price Elasticity of Demand,
εD . Hence, or otherwise, show that the firm will never produce in the inelastic part of its
demand curve.
at the point (x, y) = (1, 2)
2. Assume that F is a differentiable function with F 0 (2) = 5. Find
if y is defined implicitly by the equation
= y2
Note that x, y and F are not related except through this equation. In particular, y 6= F (x).
3. Sample Mid-Term Question: Let U(x) be the utility of Gary and V(x) be the utility of Ji
Hyo, when they consume good x. We note that Gary’s utility is affected by Ji Hyo’s utility
in the following manner: U (x) = x.V (x). Now, we know that for Ji Hyo, V (4) = 8 and
V 0 (4) = 7. Find U’(4), ie. Gary’s marginal utility of consuming 4 units of the good.
(A) 8
(B) 10
(C) 16
(D) 4
(E) None of the above
4. The inverse demand function for a good that a firm produces is given by p(q) = 1440000 −
300q 2 . This gives the price that each good will sell for on the market, given that the firm
produced q of the good. The firm’s total cost is given by c(q) = 337500q + 1000000.
(a) Find the production level q that minimizes total cost.
(b) Find the production level q that maximizes total revenue.
(c) Find the profit-maximizing level of q. What is the firm’s profit at this level of output?
(d) Find the price elasticity of demand at the profit-maximizing q.