ECONOMICS

Economics



Economics

Q9)

 

$

Total Interest+princial in 2 years

6760

Loan Amount

5000

2 years Interest (Difference)

1760

1 year Interest

880

Per week Interest in $

16.92308

Interest Rate per week in %

0.003385

0.338462

Annual Percentage Rate

40.13%

Question 10)

Total Cost function TC = 20 + 4q + 0.4q 2 where p is price (in £) and q is quantity demanded:

a.

TR = p x Q

TR = (460 - 2q) x q

TR = 460q - 2q2

MR = 460 - (2x2q)

MR = 460 - 4q

b. Maximum Total Revenue Output

460 - 4q = 0

Q = 460/4

Q = 115

Revenue will maximize at output of 115 units.

P = 460 - 2(115)

P = 230

In order to maximize revenue, price should be set as 230/unit.

C. Average Total Cost function (AC).

TC = 20 + 4q + 0.4q 2

AC = TC/q = (20 + 4q + 0.4q 2) / q

AC = 4 + 0.4q

d. AC minimum value output

4+ 0.4q = 0

0.4 q = -4

Q = -4/0.4

Q = 10units (ignoring negative sign)

e. Marginal Cost function (MC). Comment on its nature.

TC = 20 + 4q + 0.4q 2

dTC/dq = MC = 4+ 0.8q

d2TC/dq2 = 0.8

Since the slope of MC is positive, therefore, MC has minimum value.

f. Profit (() Function

TR = 460q - 2q2

TC = 20 + 4q + 0.4q 2

Profit = TR- TC = 460q - 2q2 - (20 + 4q + 0.4q 2)

Profit = 460q - 2q2 - 20 - 4q - 0.4q 2)

Profit = 456q - 20 - 2.4q2

g. Profit maximising output

dProfit / dq = 456- 4.8q

456- 4.8q = 0

q = -456/-4.8

q = 95

Profit will be maximized at output level of 95 units.

h. Tax impositition and its imapct on Profit Level

Profit = 456q - 20 - 2.4q2 - T (456q - 20 - 2.4q2)

Max. Profit without Tax

Profit = 456(95) - 20 - 2.4(95)2

Profit = 21640

Profit = 456q - 20 -250 - 2.4q2

i. Price and output change due to lump sum tax of £250 imposition and Economic rationale of results. Sketch a graph to illustrate this answer.

By imposing fixed tax, output level will not change. However, profit will reduce by additional 250 pounds.

Profit = 21640-250

Profit = 21390

Profits have decline constantly at all output level because direct taxes do not change with the output level. Therefore, constant decline occurred in profits (John, 2006, 222).

Partial differentiation to derive MPL

Q = 40K0.4L0.6

Q = 0.8K + 2.5L

Q = 40K0.4L0.6

MPL = 0.6 x 40K0.4

MPL = 24K0.4

Since the equation shows that Marginal product of labor is an exponential function of product K, ...