QUESTION 1Assume the market demand curve faced by a monopolist isQ D =500 - 10 P,and itsshort-run total cost function is...

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Assume the market demand curve faced by a monopolist

April 14, 2018

QUESTION 1
Assume the market demand curve faced by a monopolist is

Q D =500 - 10 P,

and its

short-run total cost function is SRTC (Q) =25 +2Q.
(a)
(b)
(c)
(d)
(e)

Derive the inverse demand curve for the monopolist.
Using the result obtained in part (a), derive the monopolist’s total revenue
curve as a function of Q. Compute the corresponding marginal revenue
function.
Compute the firm’s short run marginal cost curve.
Using the results obtained in part (b) and part (c), derive the monopolist’s
short-run profit-maximizing level of output.
Determine the price charged by the profit-maximizing monopolist and the
amount of profit earned.

QUESTION 2
Consider a broking firm that supplies consulting services. The corresponding demand
3Q 2 Q 3
relation and cost functions are 4 P +Q - 16 =0 and TC (Q) =4 +2Q + ,
10 20
respectively.
(a)
(b)
(c)

Derive the first-order condition for the firms profit maximization. Determine the
profit maximizing level of Q.
Verify that, at the point of maximum profit that the second-order sufficient
condition holds.
Check that marginal revenue is equal to marginal cost at the profit-maximizing
level of output determined in (b).

QUESTION 3
A firm’s production function is given by
Q =L2 e - 0.01L .
Find the value of L which maximizes the average product of labour. Ensure you have
found the value of L that maximizes the average product.
QUESTION 4
A firm produces three products—leather, cardboard and string—denoted y1 , y2 and
y3 , respectively. The corresponding total revenue function has the form
2
TR =5 +75 y1 - 2 y12 +8 y2 - ½ y1 y2 +4 y3 .

At what combination of outputs will the marginal revenues of all three products be
simultaneously equal zero?










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