ENGM9011 Assignment 2: Economics Solutions and Analysis

This document presents a complete solution to an economics assignment, addressing four key problems. The first problem focuses on calculating cross-price and own-price elasticities of demand based on changes in prices and quantities of goods. The second problem delves into a competitive firm's production function, calculating the firm's labor demand, total revenue, and profit. The third problem tackles a long-run minimization problem, deriving cost functions and analyzing average costs. Finally, the fourth problem examines a cost function in a perfectly competitive market, determining the firm's output, price, and the number of firms in the market. The solutions include detailed calculations and explanations to facilitate understanding of economic principles.

Running head: ECONOMICS
Economics
Name of the student
Name of the university
Author note

ECONOMICS
Answer 1
Initial price of three goods were Px = 1 PY =2 PZ = 3 the initial demand on he other hand was
500, 450 and 200.
When the price of good X increases to 25 percent, the new price becomes 1.25
The new demand changes to xn , 465 and 190
a.
therefore, the cross price elasticity Exy will be change
the cross price elasticity will be % change in the demand of Y / % change in the price of X
which will be 0.133
cross price elastocty of Exz will be -0.2
b
The own price elasticity of demand is calculated by % change in the demand of X / %
change the price of X
Here, change in price of X is xn - 500 and change in price of X is 1.25 -1
Therefore, own price elasticity will be calculated as Xn−500
1.25−1 × 1
500 = Xn−500
125
Answer 2
a.
q = -0.01 L3 + L2 + 36L
Where P = 0.10 and W = 4.80
MPL = dq/dl = - 0.03L2 + 2L + 36

ECONOMICS
Now, MPL × P = W
(- 0.03L2 + 2L + 36 ) 0.10 = 4.80
(- 0.03L2 + 2L + 36 ) = 48
L = 60
The firms demand for labour is 60
b.
Total revenue will be price multiplied by the quantity which will be -0.01(60)3 +602 +36.60
= -2160 + 3600 + 2160
= 3600
Total cost will be 4.8*60= 288
Therefore profit will be TR – TC = 3600 -288 = 3312
Answer 3
a.
solving the long run minimization problem
𝑦 = l
1
3 k2/ 3 subject to TC = wl + rk
ƛ
wl + rk+ ƛ [Y - l
1
3 k2/ 3 ¿
d ƛ / d k = r + ƛ 2 / 3 k (2/3 -1)

ECONOMICS
r + ƛ 2/3 k (2/3 -1) = 0
r = - ƛ 2/3 k (2/3 -1)
ƛ = - 3 r k1/ 3
2 l1 /3
d ƛ / d l = w + ƛ 1/3 l
1
3 −1
w + ƛ 1/3 l
1
3 −1 = 0
w = - ƛ 1/3 l
1
3 −1
ƛ = 3 w l2/ 3
k2/ 3
w l2 /3∗w l
2
3 =k 2/ 3* r k1 /3
2wl = rk
L= rk/ 2w
Now, Y = l
1
3 k2/ 3
Y = ¿) 1/3 k 2/3
Now, K = Y
r /2 w1 /3
Therefore,
Total cost will be wl + r. Y
r /2 w1 /3
b.

ECONOMICS
c.
total cost at k= 8 will be w × 8r
2 w +8 r
= 4r+ 8r = 12r
d. average cost will be
TC/ Y=
wl+ r . Y
r /2 w1 /3
l
1
3 k 2/ 3
Average fixed cost
Here fixed cost is rk or r Y/〖r/2w〗^(1/3)
AFC =
r Y
r / 2 w1/ 3
l
1
3 k2 /3
AVC = WL/ l
1
3 k2/ 3
e.

ECONOMICS
the competitive firm will be producing as much quanity it wishes as long it accepts the
prevailing market price.
Since p is the price total revenue will be PY which is p. l
1
3 k2/ 3
Answer 4
The cost function is C= 0.01𝑞3 − 1.2𝑞2 + 111q
In perfect competition price is equal to the average cost
Therefore the average cost will be AC= 0.01q2 – 1.2q +11
Min AC
dq/dc =0.02q-1.2
0.02q =1.2
q = 60
The firm’s output q is 60.
b.
Since Price is equal to Marginal cost and average cost in the long run, therefore for quantity
60
P = 0.01(60)2 – 1.2(60) +111
Price is 75
Answer c
𝑄 = 6000 − 20𝑝
Putting the value of P in the above equation, we get

ECONOMICS
Q = 6000-20(75)
Q = 6000 – 1500
= 4500
Since each firm is making 60 units, there must be 4500/60 which is 75 firms which are
identically sized.